Vijaya Sree

Browse & Download Go Math Grade 4 Answer Key Homework Practice FL Chapter 10 Two-Dimensional Figures pdf from here & start your preparation. Students of 4th grade can easily grasp the Two-dimensional figures notations by using the CCSSMathAnswers provided HMH Go Math Answer Key Grade 4 Homework Practice FL 10 Two-Dimensional Figures pdf. Also, this guide is used as homework help and let the students complete the homework or any assessments in no time.

Go Math Grade 4 Answer Key Homework Practice FL Chapter 10 Two-Dimensional Figures

Download Chapter 10 Go Math HMH Grade 4 Solution Key and practice all Two-Dimensional Figures covered concepts like Lines, Rays and Angles, Classify Triangles, Parallel Lines and Perpendicular Lines, Classify Quadrilaterals, Line Symmetry, etc in an easy manner. Simply click on the provided pdf links and ace up your preparation. Also, find some more questions from Go Math Grade 4 Answer Key Chapter 10 Two-Dimensional Figures to score maximum marks in the exams.

Lesson: 1 – Lines, Rays, and Angles

• Common Core – Two-Dimensional Figures – Page No. 189
• Common Core – Two-Dimensional Figures – Page No. 190

Lesson: 2 – Classify Triangles

• Common Core – Two-Dimensional Figures – Page No. 191
• Common Core – Two-Dimensional Figures – Page No. 192

Lesson: 3 – Parallel Lines and Perpendicular Lines

• Common Core – Two-Dimensional Figures – Page No. 193
• Common Core – Two-Dimensional Figures – Page No. 194

Lesson: 4 – Classify Quadrilaterals

• Common Core – Two-Dimensional Figures – Page No. 195
• Common Core – Two-Dimensional Figures – Page No. 196

Lesson: 5 – Line Symmetry

• Common Core – Two-Dimensional Figures – Page No. 197
• Common Core – Two-Dimensional Figures – Page No. 198

Lesson: 6 – Find and Draw Lines of Symmetry

• Common Core – Two-Dimensional Figures – Page No. 199
• Common Core – Two-Dimensional Figures – Page No. 200

Lesson: 7 – Problem Solving Shape Patterns

• Common Core – Two-Dimensional Figures – Page No. 201
• Common Core – Two-Dimensional Figures – Page No. 202

Chapter 10 – Extra Practice

• Common Core – Two-Dimensional Figures – Page No. 203
• Common Core – Two-Dimensional Figures – Page No. 204

Common Core – Two-Dimensional Figures – Page No. 189

Lines, Rays, and Angles

Draw and label an example of the figure.

Question 1.
obtuse ∠ABC

Think: An obtuse angle is greater than a right angle. The middle letter, B, names the vertex of the angle.
________

Answer:

Explanation:
An obtuse angle is greater than a right angle. The middle letter, B, names the vertex of the angle.

Question 2.
\(\overrightarrow{G H}\)

Answer:

Explanation:
GH is a ray that has one endpoint and continues without an end in one direction.

Question 3.
acute ∠JKL
________

Answer:

Explanation:
Angle JKL is an acute angle that is less than a right angle.

Question 4.
\(\overline{B C}\)

Answer:

Explanation:
BC is a line that continues without an end in both directions.

Use the figure for 5–8.

Question 5.
Name a line segment.

Answer:
line segment EF

Explanation:
EF line is a straight path of points that continues without an end in both directions.

Question 6.
Name a right angle.
∠ _____

Answer:
∠EJF

Explanation:
EJF is a right angle that forms a square corner.

Question 7.
Name an obtuse angle.
obtuse ∠ _____

Answer:
∠CEJ

Explanation:
CEJ is an obtuse angle that is greater than a right angle.

Problem Solving

Use the figure at the right for 9–11.

Question 9.
Classify ∠AFD
________

Answer:
Obtuse Angle

Explanation:
AFD is an obtuse angle that is greater than a right angle.

Question 10.
Classify ∠CFE.
________

Answer:
Right Angle

Explanation:
∠CFE is a right angle that forms a square corner.

Question 11.
Name two acute angles.
acute ∠ _____ acute ∠ _____

Answer:
∠AFB and ∠DFE

Explanation:
∠AFB and ∠DFE are two acute angles with less than a right angle.

Common Core – Two-Dimensional Figures – Page No. 190

Lesson Check

Question 1.
The hands of a clock show the time 12:25.

Which best describes the angle between the hands of the clock?
Options:
a. acute
b. right
c. obtuse
d. straight

Answer:
c. obtuse

Explanation:
The hands of the time 12:25 are forming greater than a right angle. So, the answer is the Obtuse angle.
Thus the correct answer is option c.

Question 2.
Which of the following name two different figures?
Options:
a. \(\overline{A B} \text { and } \overline{B A}\)
b. \(\overleftrightarrow { AB } \) and \(\overleftrightarrow { BA } \)
c. \(\overrightarrow { AB } \) and \(\overrightarrow { BA } \)
d. ∠ABC and ∠CBA

Answer: \(\overrightarrow { AB } \) and \(\overrightarrow { BA } \)

Explanation:
In \(\overrightarrow { AB } \) A is an end point and B continues without end in one direction.
In \(\overrightarrow { BA } \) B is an end point and A continues without an end in one direction.
Thus the correct answer is option c.

Spiral Review

Question 3.
Jan’s pencil is 8.5 cm long. Ted’s pencil is longer. Which could be the length of Ted’s pencil?
Options:
a. 0.09 cm
b. 0.8 cm
c. 8.4 cm
d. 9.0 cm

Answer:
d. 9.0 cm

Explanation:
9 ones is greater than 8 ones. So, 9.0 cm > 8.5 cm
Thus the correct answer is option d.

Question 4.
Kayla buys a shirt for $8.19. She pays with a $10 bill. How much change should she receive?
Options:
a. $1.81
b. $1.89
c. $2.19
d. $2.81

Answer:
a. $1.81

Explanation:
Kayla buys a shirt for $8.19. She pays with a $10 bill. To find the change she received, $10 – $8.19 = 1.81
Thus the correct answer is option a.

Question 5.
Sasha donated \(\frac{9}{100}\) of her class’s entire can collection for the food drive. Which decimal is equivalent to \(\frac{9}{100}\) ?
Options:
a. 9
b. 0.99
c. 0.9
d. 0.09

Answer:
d. 0.09

Explanation:
\(\frac{9}{100}\) is 9 hundredths. So, the decimal is 0.09.
Thus the correct answer is option d.

Question 6.
Jose jumped 8 \(\frac{1}{3}\) feet. This was 2 \(\frac{2}{3}\) feet farther than Lila jumped. How far did Lila jump?
Options:
a. 5 \(\frac{1}{3}\)
b. 5 \(\frac{2}{3}\)
c. 6 \(\frac{1}{3}\)
d. 11

Answer: 5 \(\frac{2}{3}\)

Explanation:
Jose jumped 8 \(\frac{1}{3}\) feet. This was 2 \(\frac{2}{3}\) feet farther than Lila jumped.
8 \(\frac{1}{3}\) feet – 2 \(\frac{2}{3}\)
= 25/3 – 8/3
= 7/3
= 5 \(\frac{2}{3}\)
Thus the correct answer is option b.

Common Core – Two-Dimensional Figures – Page No. 191

Classify Triangles

Classify each triangle. Write acute, right, or obtuse.

Question 1.

Think: Angles A and C are both acute.
Angle B is obtuse.

Answer:
Obtuse triangle;
Angle A and Angle C are both acute.
Angle B is obtuse.

Explanation:
From triangle, ABC, Angle A, and Angle C are both acute with less than a right angle. Angle B is an obtuse angle that is greater than a right angle.

Question 2.

________

Answer:
Right Triangle; Triangle DEF;
∠D and ∠F are acute angles.
∠E is Right angle

Explanation:
∠D and ∠F are acute angles with less than a right angle. ∠E is the Right angle that forms a square corner. A triangle that has one right angle is called a right triangle.

Question 3.

________

Answer:
Acute triangle;
Angle G, Angle J, and Angle H are acute angles.

Explanation:
From triangle GJH, Angle G, Angle J, and Angle H are acute angles with less than a right angle. A triangle with three acute angles called an acute triangle. So, the given triangle is an acute triangle.

Question 4.

________

Answer:
Obtuse triangle;
Angle L and Angle N are both acute.
Angle M is obtuse.

Explanation:
From triangle LMN, Angle L and Angle N are both acute with less than a right angle. Angle M is an obtuse angle that is greater than a right angle. A triangle with an obtuse angle is called an obtuse triangle.

Problem Solving

Question 5.
Use figure ABCD below. Draw a line segment from point B to point D. Name and classify the triangles formed.

Two _______ triangles
△ _______
△ _______

Answer:

Two Acute triangles.
△ ABD
△ BCD

Explanation:
If we draw a line segment from point B to point D, then there are two traingles formed with less than right angles. They are △ ABD and △ BCD.

Question 6.
Use figure ABCD below. Draw a line segment from point A to point C. Name and classify the triangles formed.

Two _______ triangles
△ _______
△ _______

Answer:

Two Acute triangles.
△ ABC
△ ADC

Explanation:
If we draw a line segment from point A to point C, then there are two triangles formed with less than right angles. They are △ ABC and △ ADC.

Common Core – Two-Dimensional Figures – Page No. 192

Lesson Check

Question 1.
Stephen drew this triangle. How many obtuse angles does the triangle have?

Options:
a. 0
b. 1
c. 2
d. 3

Answer: a. 0

Explanation:
The given image has three acute angles. So, there are 0 obtuse angles.
Thus the correct answer is option a.

Question 2.
Joan was asked to draw a right triangle. How many right angles are in a right triangle?
Options:
a. 0
b. 1
c. 2
d. 3

Answer:
b. 1

Explanation:
A right triangle has only one right angle.
Thus the correct answer is option b.

Spiral Review

Question 3.
Oliver drew the figure below to show light traveling from the sun to Earth. Name the figure he drew.

Options:
a. segment SE
b. ray SE
c. line SE
d. ray ES

Answer:
b. ray SE

Explanation:
SE is a ray that has one endpoint and continues without an end in one direction.
Thus the correct answer is option b.

Question 4.
Armon added \(\frac{1}{10}\) and \(\frac{8}{100}\). Which is the correct sum?
Options:
a. \(\frac{18}{10}\)
b. \(\frac{9}{10}\)
c. \(\frac{9}{100}\)
d. \(\frac{18}{100}\)

Answer: d. \(\frac{18}{100}\)

Explanation:
\(\frac{10}{100}\) + \(\frac{8}{100}\) = \(\frac{18}{100}\)
Thus the correct answer is option d.

Question 5.
Sam counted out loud by 6s. Jorge counted out loud by 8s. What are the first three numbers both students said?
Options:
a. 8, 16, 24
b. 14, 28, 42
c. 24, 48, 72
d. 48, 96, 144

Answer:
c. 24, 48, 72

Explanation:
Sam counted out loud by 6s = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72.
Jorge counted out loud by 8s = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80.
Both students said the first three numbers are 24, 48, 72.
Thus the correct answer is option c.

Question 6.
A basketball team averaged 105 points per game. How many points did the team score in 6 games?
Options:
a. 605 points
b. 630 points
c. 900 points
d. 6,030 points

Answer:
b. 630 points

Explanation:
A basketball team averaged 105 points per game.
They score in 6 games = 6 x 105 = 630 points.
Thus the correct answer is option b.

Common Core – Two-Dimensional Figures – Page No. 193

Parallel Lines and Perpendicular Lines

Use the figure for 1–3.

Question 1.
Name a pair of lines that appear to be perpendicular.
Think: Perpendicular lines form right angles.
\(\overleftrightarrow { AB } \) and \(\overleftrightarrow { EF } \) appear to form right angles.
\(\overleftrightarrow { AB } \) and \(\overleftrightarrow { EF } \)

Answer:
\(\overleftrightarrow { AB } \) and \(\overleftrightarrow { EF } \)

Explanation:
Perpendicular lines form right angles.
\(\overleftrightarrow { AB } \) and \(\overleftrightarrow { EF } \) appear to form right angles.
\(\overleftrightarrow { AB } \) and \(\overleftrightarrow { EF } \)

Question 2.
Name a pair of lines that appear to be parallel.
____ and ____

Answer:
\(\overleftrightarrow { AB } \) and \(\overleftrightarrow { CD } \)

Explanation:
Parallel lines never interest each other. \(\overleftrightarrow { AB } \) and \(\overleftrightarrow { CD } \) are parallel lines.

Question 3.
Name another pair of lines that appear to be perpendicular.
____ and ____

Answer:
\(\overleftrightarrow { CD } \) and \(\overleftrightarrow { EF } \)

Explanation:
Perpendicular lines form right angles.
\(\overleftrightarrow { CD } \) and \(\overleftrightarrow { EF } \) appear to form right angles.
\(\overleftrightarrow { CD } \) and \(\overleftrightarrow { EF } \)

Draw and label the figure described.

Question 4.
\(\overleftrightarrow { MN } \) and \(\overleftrightarrow { PQ } \) intersecting at point R

Answer:

Explanation:
MN and PQ are two lines and interesting at point R.

Question 5.
\(\overleftrightarrow { WX } \) || \(\overleftrightarrow { YZ } \)

Answer:

Explanation:
WX and YZ are parallel lines and they never intersect with each other.

Question 6.
\(\overleftrightarrow { FH } \) ⊥ \(\overleftrightarrow { JK } \)

Answer:

Explanation:
FH and JK are two lines and intersecting each other to form four right angles.

Problem Solving

Use the street map for 7–8.

Question 7.
Name two streets that intersect but do not appear to be perpendicular.
Type below:
_______

Answer:
Maple and Oak or Oak and Birch

Explanation:
Maple and Oak or Oak and Birch; They are intersecting with each other and not perpendicular.

Question 8.
Name two streets that appear to be parallel to each other.
Type below:
_______

Answer:
Maple and Birch

Explanation:
Maple and Birch are streets and not intersect with each other. They appear to be parallel to each other.

Common Core – Two-Dimensional Figures – Page No. 194

Lesson Check

Question 1.
Which capital letter appears to have perpendicular line segments?
Options:
a. N
b. O
c. T
d. V

Answer:
c. T

Explanation:
T has two lines and interesting to form four right angles.

Question 2.
In the figure, which pair of line segments appear to be parallel?

Options:
a. \(\overline{F G} \text { and } \overline{G H}\)
b. \(\overline{F J} \text { and } \overline{G H}\)
c. \(\overline{F G} \text { and } \overline{J H}\)
d. \(\overline{J H} \text { and } \overline{F J}\)

Answer:
c. \(\overline{F G} \text { and } \overline{J H}\)

Explanation:
\(\overline{F G} \text { and } \overline{J H}\) are parallel lines that never intersect

Spiral Review

Question 3.
Nolan drew a right triangle. How many acute angles did he draw?
Options:
a. 0
b. 1
c. 2
d. 3

Answer:
c. 2

Explanation:
A triangle with one right angle will have two acute angles.

Question 4.
Mike drank more than half the juice in his glass. What fraction of the juice could Mike have drunk?
Options:
a. \(\frac{1}{3}\)
b. \(\frac{2}{5}\)
c. \(\frac{3}{6}\)
d. \(\frac{5}{8}\)

Answer:
d. \(\frac{5}{8}\)

Explanation:
Mike drank more than half the juice in his glass. He drunk \(\frac{5}{8}\) of the juice.

Question 5.
A school principal ordered 1,000 pencils. He gave an equal number to each of 7 teachers until he had given out as many as possible. How many pencils were left?
Options:
a. 2
b. 4
c. 6
d. 142

Answer:
c. 6

Explanation:
A school principal ordered 1,000 pencils. He gave an equal number to each of the 7 teachers until he had given out as many as possible. He shared 142 pencils for each of the 7 teachers. So, 142 × 7 = 994. The remaining pencils are 6.

Question 6.
A carton of juice contains 64 ounces. Ms. Wilson bought 6 cartons of juice. How many ounces of juice did she buy?
Options:
a. 364 ounces
b. 370 ounces
c. 384 ounces
d. 402 ounces

Answer:
c. 384 ounces

Explanation:
A carton of juice contains 64 ounces. Ms. Wilson bought 6 cartons of juice. 64 X 6 = 384 ounces juice she can buy.

Common Core – Two-Dimensional Figures – Page No. 195

Classify Quadrilaterals

Classify each figure as many ways as possible. Write quadrilateral, trapezoid, parallelogram, rhombus, rectangle, or square.

Question 1.

Type below:
________
Answer:
Quadrilateral, Parallelogram, and rhombus.

Explanation:
2 pairs of parallel sides
4 sides of equal length
0 right angles
Quadrilateral, Parallelogram, and rhombus.

Question 2.

Type below:
________

Answer:
Quadrilateral, Parallelogram, Rectangle

Explanation:
2 pairs of parallel sides
2 pairs of sides of equal length
4 right angles
Quadrilateral, Parallelogram, Rectangle

Question 3.

Type below:
________

Answer:

Explanation:
1 pair of parallel sides
2 sides of equal length
0 right angles
Quadrilateral, Trapezoid

Question 4.

Type below:
________

Answer:
Quadrilateral

Explanation:
0 pair of parallel sides
0 sides of equal length
0 right angles
Quadrilateral

Question 5.

Type below:
________

Answer:
Quadrilateral, Parallelogram, and rhombus

Explanation:
2 pairs of parallel sides
4 sides of equal length
0 right angles
Quadrilateral, Parallelogram, and rhombus

Question 6.

Type below:
________

Answer:

Explanation:
1 pair of parallel sides
0 sides of equal length
2 right angles
Quadrilateral, Trapezoid

Question 7.

Type below:
________

Answer:

Explanation:
2 pairs of parallel sides
2 pairs of sides of equal length
0 right angles
Quadrilateral, Parallelogram

Problem Solving

Question 8.
Alan drew a polygon with four sides and four angles. All four sides are equal. None of the angles are right angles. What figure did Alan draw?
________

Answer:
Quadrilateral or rhombus

Explanation:
Alan drew a polygon with four sides and four angles. All four sides are equal. None of the angles are right angles. Alan drew Quadrilateral or rhombus

Question 9.
Teresa drew a quadrilateral with 2 pairs of parallel sides and 4 right angles. What quadrilateral could she have drawn?
________

Answer:
square or rectangle

Explanation:
2 pairs of parallel sides and 4 right angles. she could draw a square or rectangle.

Common Core – Two-Dimensional Figures – Page No. 196

Lesson Check

Question 1.
Joey is asked to name a quadrilateral that is also a rhombus. What should be his answer?
Options:
a. square
b. rectangle
c. parallelogram
d. trapezoid

Answer:
a. square

Explanation:
The quadrilateral square is also called a rhombus. Both square and rhombus have 2 pairs of parallel sides and 4 sides of equal length.
Thus the correct answer is option a.

Question 2.
Which quadrilateral has exactly one pair of parallel sides?
Options:
a. square
b. rhombus
c. parallelogram
d. trapezoid

Answer:
d. trapezoid

Explanation:
A trapezoid has exactly one pair of parallel sides.
Thus the correct answer is option d.

Spiral Review

Question 3.
Terrence has 24 eggs to divide into equal groups. What are all the possible numbers of eggs that Terence could put in each group?
Options:
a. 1, 2, 3, 4
b. 2, 4, 6, 8, 12
c. 1, 2, 3, 4, 6, 8, 12, 24
d. 24, 48, 72, 96

Answer:
c. 1, 2, 3, 4, 6, 8, 12, 24

Explanation:
Terrence has 24 eggs to divide into equal groups. Terence could put in each group in 1, 2, 3, 4, 6, 8, 12, 24 ways.
Thus the correct answer is option c.

Question 4.
In a line of students, Jenna is number 8. The teacher says that a rule for a number pattern is add 4. The first student in line says the first term, 7. What number
should Jenna say?
Options:
a. 31
b. 35
c. 39
d. 43

Answer:
b. 35

Explanation:
In a line of students, Jenna is number 8. The teacher says that a rule for a number pattern is to add 4. The first student in line says the first term, 7.
7 + 4 = 11
11 + 4 = 15
15 + 4 = 19
19 + 4 = 23
23 + 4 = 27
27 + 4 = 31
31 + 4 = 35.
Jenna says 35.
Thus the correct answer is option b.

Question 5.
Lou eats \(\frac{6}{8}\) of a pizza. What fraction of the pizza is left over?
Options:
a. \(\frac{1}{8}\)
b. \(\frac{1}{4}\)
c. \(\frac{1}{2}\)
d. \(\frac{3}{4}\)

Answer:
b. 1/4
Explanation:
Lou eats 6/8 of a pizza. So, 6 parts of the pizza are finished and the remaining 2 parts of the pizza have remained. So, the left over pizza is 2/8 = 1/4.
Thus the correct answer is option b.

Question 6.
Which capital letter appears to have parallel lines?
Options:
a. D
b. L
c. N
d. T

Answer:
c. N

Explanation:
N has two parallel lines and never intersect each other.
Thus the correct answer is option c.

Common Core – Two-Dimensional Figures – Page No. 197

Line Symmetry

Tell if the dashed line appears to be a line of symmetry. Write yes or no.

Question 1.

yes

Answer:
Yes

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Question 2.

____

Answer:
No

Explanation:
The line of symmetry divides a shape into two parts that are not of the same size and shape.

Question 3.

____

Answer:
Yes

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Question 4.

____

Answer:
No

Explanation:
The line of symmetry divides a shape into two parts that are not of the same size and shape.

Question 5.

____

Answer:
No

Explanation:
The line of symmetry divides a shape into two parts that are not of the same size and shape.

Question 6.

____

Answer:
Yes

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Question 7.

____

Answer:
No

Explanation:
The line of symmetry divides a shape into two parts that are not of the same size and shape.

Question 8.

____

Answer:
Yes

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Complete the design by reflecting over the line of symmetry.

Question 9.

Answer:

Question 10.

Answer:

Problem Solving

Question 11.
Kara uses the pattern below to make paper dolls. The dashed line represents a line of symmetry. A complete doll includes the reflection of the pattern over the line of symmetry. Complete the design to show what one of Kara’s paper dolls looks like.

Answer:

Common Core – Two-Dimensional Figures – Page No. 198

Lesson Check

Question 1.
Which best describes the line of symmetry in the letter D?

Options:
a. horizontal
b. vertical
c. diagonal
d. half turn

Answer:
a. horizontal

Explanation:
The horizontal line of symmetry in the letter D can exactly separate two parts equally.

Question 2.
Which shape has a correctly drawn line of symmetry?
Options:
a.
b.
c.
d.

Answer:
b.

Spiral Review

Question 3.
The class has 360 unit cubes in a bag. Johnnie divides the unit cubes equally among 8 groups. How many unit cubes will each group get?
Options:
a. 40
b. 44
c. 45
d. 48

Answer:
c. 45

Explanation:
The class has 360 unit cubes in a bag. Johnnie divides the unit cubes equally among 8 groups. 360/8= 45.

Question 4.
There are 5,280 feet in one mile. How many feet are there in 6 miles?
Options:
a. 30,680
b. 31,260
c. 31,608
d. 31,680

Answer:
d. 31,680

Explanation:
There are 5,280 feet in one mile. So, for 6 miles = 6 x 5, 280 = 31,680.

Question 5.
Sue has 4 pieces of wood. The lengths of her pieces of wood are \(\frac{1}{3}\) foot, \(\frac{2}{5}\) foot, \(\frac{3}{10}\) foot, and \(\frac{1}{4}\) foot. Which piece of wood is the shortest?
Options:
a. the \(\frac{1}{3}\) foot piece
b. the \(\frac{2}{5}\) foot piece
c. the \(\frac{3}{10}\) foot piece
d. the \(\frac{1}{4}\) foot piece

Answer:
d. the 1/4 foot piece

Explanation:
The lengths of 1/4 foot piece is less compared to other lengths.

Question 6.
Alice has \(\frac{1}{5}\) as many miniature cars as Sylvester has. Sylvester has 35 miniature cars. How many miniature cars does Alice have?
Options:
a. 7
b. 9
c. 40
d. 175

Answer:
a. 7

Explanation:
Alice has 1/5 as many miniature cars as Sylvester has. Sylvester has 35 miniature cars. Alice has 1/5 × 35 = 7 miniature cars.

Common Core – Two-Dimensional Figures – Page No. 199

Find and Draw Lines of Symmetry

Tell whether the shape appears to have zero lines, 1 line, or more than 1 line of symmetry. Write zero, 1, or more than 1.

Question 1.

1

Answer:
more than 1

Explanation:
There is more than 1 line of symmetry that separates two parts equally.

Question 2.

________

Answer:
more than 1

Explanation:
There is more than 1 line of symmetry that separates two parts equally.

Question 3.

________

Answer:
Zero

Explanation:
There are 0 lines of symmetries.

Question 4.

________

Answer:
more than 1

Explanation:

There is more than 1 line of symmetry that separates two parts equally.

Does the design have line symmetry? Write yes or no.
If your answer is yes, draw all lines of symmetry.

Question 5.

____

Answer:
Yes

Question 6.

____

Answer:
Yes

Question 7.

____

Answer:
No

Question 8.

____

Answer:
Yes

Draw a shape for the statement. Draw the line or lines of symmetry.

Question 9.
zero lines of symmetry

Answer:

Question 10.
1 line of symmetry

Answer:

Question 11.
2 lines of symmetry

Answer:

Problem Solving

Use the chart for 12–13.

Question 12.
Which number or numbers appear to have only 1 line of symmetry?
____

Answer:
3

Explanation:
The number 3 has only 1 line of symmetry.

Question 13.
Which number or numbers appear to have 2 lines of symmetry?
____

Answer:
0 and 8

Explanation:
The numbers 0 and 8 appear to have 2 lines of symmetry.

Common Core – Two-Dimensional Figures – Page No. 200

Lesson Check

Question 1.
How many lines of symmetry does this shape appear to have?

Options:
a. 0
b. 2
c. 6
d. 12

Answer:
c. 6

Explanation:

The given shape has 6 lines of symmetry.
Thus the correct answer is option c.

Question 2.
Which of the following shapes appears to have exactly 1 line of symmetry?
Options:
a.
b.
c.
d.

Explanation:

The trapezoid has exactly 1 line of symmetry.
Thus the correct answer is option d.

Spiral Review

Question 3.
Richard practiced each of 3 piano solos for \(\frac{5}{12}\) hour. How long did he practice in all?
Options:
a. \(\frac{2}{3}\) hours
b. 1 \(\frac{1}{4}\) hours
c. 1 \(\frac{1}{3}\) hours
d. 1 \(\frac{5}{12}\) hours

Answer:
b. 1 1/4 hours

Explanation:
Richard practiced each of 3 piano solos for 5/12 hour. 5/12 hour = 1 1/4 hours hours.
Thus the correct answer is option b.

Question 4.
Which of the following decimals is equivalent to three and ten hundredths?
Options:
a. 0.30
b. 0.31
c. 3.01
d. 3.1

Answer:
d. 3.1

Explanation:
three and ten hundredths = 310 hundredths = 3.1
Thus the correct answer is option d.

Question 5.
Lynne used \(\frac{3}{8}\) cup of flour and \(\frac{1}{3}\) cup of sugar in a recipe. Which number below is a common denominator for \(\frac{3}{8}\) and \(\frac{1}{3}\)?
Options:
a. 8
b. 12
c. 16
d. 24

Answer:
d. 24

Explanation:
Lynne used 3/8 cup of flour and 1/3 cup of sugar in a recipe. To find the common denominator for 3/8 and 1/3, multiply 8 X3 and 3 X 8 = 24.
Thus the correct answer is option d.

Question 6.
Kevin draws a figure that has four sides. All sides have the same length. His figure has no right angles. What figure does Kevin draw?
Options:
a. square
b. trapezoid
c. rhombus
d. rectangle

Answer:
c. rhombus

Common Core – Two-Dimensional Figures – Page No. 201

Problem Solving Shape Patterns

Solve each Problem.

Question 1.
Marta is using this pattern to decorate a picture frame. Describe the pattern. Draw what might be the next three figures in the pattern.

Possible answer: the pattern repeats: one trangle followed by two squares.

Answer:

The pattern repeats one triangle followed by two squares.

Question 2.
Describe the pattern. Draw what might be the next three figures in the pattern. How many circles are in the sixth figure in the pattern?

____ circles

Answer:

Add one more column with 1 more circle than in the previous column; 21.

Question 3.
Larry stencils this pattern to make a border at the top of his bedroom walls. Describe the pattern. Draw what might be the missing figure in the pattern.

Answer:

2 triangles placed side to side followed by 2 sets of 2 triangles placed vertex to vertex

Common Core – Two-Dimensional Figures – Page No. 202

Lesson Check

Question 1.
What might be the next three figures in this pattern?

Options:
a.
b.
c.
d.

Answer:
a.

Explanation:
the pattern has odd numbers of up arrows then even number of down arrows. So, the next three figures are

Question 2.
Which might be the missing figure in the following pattern?

Options:
a.
b.
c.
d.

Answer:
a.

Explanation:
From the pattern, the missing image will have a vertical rectangle with the circle and X mark in it.

Spiral Review

Question 3.
Chad has two pieces of wood. One piece is \(\frac{7}{12}\) foot long. The second piece is \(\frac{5}{12}\) foot longer than the first piece. How long is the second piece?
Options:
a. \(\frac{2}{12}\) foot
b. \(\frac{1}{2}\) foot
c. \(\frac{12}{18}\) foot
d. 1 foot

Answer:
d. 1 foot

Explanation:
7/12 + 5/12 = 12/12 = 1 foot.

Question 4.
Olivia finished a race in 40.64 seconds. Patty finished the race in 40.39 seconds. Miguel finished the race in 41.44 seconds. Chad finished the race in 40.46 seconds. Who finished the race in the least time?
Options:
a. Olivia
b. Patty
c. Miguel
d. Chad

Answer:
b. Patty

Explanation:
Patty finished the race in 40.39 seconds that is the least time compared to others.

Question 5.
Justin bought 6 ribbons for an art project. Each ribbon is \(\frac{1}{4}\) yard long. How many yards of ribbon did Justin buy?
Options:
a. \(\frac{2}{3}\) yard
b. 1 \(\frac{1}{4}\) yards
c. 1 \(\frac{1}{2}\) yards
d. 1 \(\frac{3}{4}\) yards

Answer:
c. 1 1/2 yards

Explanation:
Justin bought 6 ribbons for an art project. Each ribbon is 1/4 yard long. So, 6 X 1/4 = 3/2 = 1 1/2 yards.

Question 6.
Kyle and Andrea were asked to make a list of prime numbers.
Kyle: 1, 3, 7, 19, 23
Andrea: 2, 3, 5, 7, 11
Whose list is correct?
Options:
a. Only Kyle’s list
b. Only Andrea’s list
c. Both lists are correct.
d. Neither list is correct.

Answer:
b. Only Andrea’s list

Explanation:
1 is not a prime number. So, the answer is Only Andrea’s list is correct.

Common Core – Two-Dimensional Figures – Page No. 203

Lesson 10.1

Draw and label an example of the figure.

Question 1.
acute ∠MNP
Type below:
_________

Answer:

Question 2.
\(\overline{Q R}\)
Type below:
_________

Question 3.
\(\overrightarrow { TS } \)
Type below:
_________

Lesson 10.2

Classify each triangle. Write acute, right, or obtuse.

Question 4.

_____

Answer: Acute

Explanation:
The above triangle is less than 90º, thus the above figure is an acute angle triangle.

Question 5.

_____

Answer: Obtuse

Explanation:
The above triangle is greater than 90º, thus the above figure is an obtuse angle triangle.

Question 6.

_____

Answer: Right

Explanation:
The above figure has 90º, thus the above figure is an right angle triangle.

Lesson 10.3

Use the street map for 1–2.

Question 7.
Name two streets that appear to be parallel.
_________

Answer: Oak and elm

Explanation:
By seeing the above figure we say that Oak and Elm are two non-intersecting lines. Thus the two streets that appear to be parallel are Oak and Elm.

Question 8.
Name two streets that appear to be perpendicular.
Type below:
_________

Answer: Park and Oak or Park and Elm

Explanation:
Park and Oak, Park and Elm are intersecting lines, thus the two streets that appear to be perpendicular are Park and Oak or Park and Elm.

Lesson 10.4

Classify each figure as many ways as possible. Write quadrilateral, trapezoid, parallelogram, rhombus, rectangle, or square.

Question 9.

Type below:
_________

Answer:
Quadrilateral, Parallelogram, Rectangle

Explanation:
2 pairs of parallel sides
2 pairs of sides of equal length
4 right angles
Quadrilateral, Parallelogram, Rectangle

Question 10.

Type below:
_________

Answer: Quadrilateral, Trapezoid

Explanation:
1 pair of parallel sides
2 sides of equal length
0 right angles
Quadrilateral, Trapezoid

Common Core – Two-Dimensional Figures – Page No. 204

Lesson 10.5

Tell if the dashed line appears to be a line of symmetry.
Write yes or no.

Question 1.

_____

Answer: Yes

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Question 2.

_____

Answer: Yes

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Question 3.

_____

Answer: Yes

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Lesson 10.6

Does the design have line symmetry? Write yes or no.

If your answer is yes, draw all lines of symmetry.

Question 4.

_____

Answer: Yes

Explanation:
The line of symmetry divides a shape into two parts that are not with the same size and shape. The above figure is not symmetrical.

Question 5.

_____

Answer: Yes

The above figure is symmetrical.

Question 6.

_____

Answer: Yes

Explanation: The above figure is symmetrical.

Lesson 10.7

Question 7.
Sonia made a pattern. The first nine shapes are shown below. Describe the pattern. Draw what might be the next three shapes in Sonia’s pattern.

Type below:
_________

Answer: The pattern repeats circle, square, circle.

Question 8.
Leo makes a pattern with triangles. Draw what might be the next figure in the pattern. How can you describe the pattern?

Type below:
_________

Answer: The pattern grows by one triangle each time.

Conclusion:

Access the links and avail the grade 4 Ch 10 Go Math Answer Key a quick learning guide with clear-cut explanations to understand the concepts. Also, you can refer to the Go Math Grade 4 Answer Key Chapter 10 Two-Dimensional Figures for better idea of the questions.

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Go Math Grade 4 Answer Key Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers

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Lesson: 1 – Multiples of Unit Fractions

• Common Core – Multiply Fractions by Whole Numbers – Page No. 157
• Common Core – Multiply Fractions by Whole Numbers – Page No. 158

Lesson: 2 – Multiples of Fractions

• Common Core – Multiply Fractions by Whole Numbers – Page No. 159
• Common Core – Multiply Fractions by Whole Numbers – Page No. 160

Lesson: 3 – Multiply a Fraction by a Whole Number Using Models

• Common Core – Multiply Fractions by Whole Numbers – Page No. 161
• Common Core – Multiply Fractions by Whole Numbers – Page No. 162

Lesson: 4 – Multiply a Fraction or Mixed Number by a Whole Number.

• Common Core – Multiply Fractions by Whole Numbers – Page No. 163
• Common Core – Multiply Fractions by Whole Numbers – Page No. 164

Lesson: 5 – Problem Solving Comparison

• Common Core – Multiply Fractions by Whole Numbers – Page No. 165
• Common Core – Multiply Fractions by Whole Numbers – Page No. 166

Lesson: 6

• Common Core – Multiply Fractions by Whole Numbers – Page No. 167
• Common Core – Multiply Fractions by Whole Numbers – Page No. 168

Common Core – Multiply Fractions by Whole Numbers – Page No. 157

Multiples of Unit Fractions

Write the fraction as a product of a whole number and a unit fraction.

Question 1.

Explanation:
Given that 5/6 or 5 sixth-size parts.
Each sixth-size part of the given fraction can be shown by the unit fraction 1/6.
You can use unit fractions to show 5/6
5/6 = 5 x 1/6.

Question 2.
\(\frac{7}{8}\)
Type below:
_________

Answer:
7 x 1/8

Explanation:
Given that 7/8 or 7 eighth-size parts.
Each eighth-size part of the given fraction can be shown by the unit fraction 1/8.
You can use unit fractions to show 7/8
7/8 = 7 x 1/8.

Question 3.
\(\frac{5}{3}\)
Type below:
_________

Answer:
5 x 1/3

Explanation:
Given that 5/3 or 5 third-size parts.
Each third-size part of the given fraction can be shown by the unit fraction 1/3.
You can use unit fractions to show 5/6
5/3 = 5 x 1/3.

Question 4.
\(\frac{9}{10}\)
Type below:
_________

Answer:
9 x 1/10

Explanation:
Given that 9/10 or 9 tenth-size parts.
Each tenth-size part of the given fraction can be shown by the unit fraction 1/10.
You can use unit fractions to show 9/10
9/10 = 9 x 1/10.

Question 5.
\(\frac{3}{4}\)
Type below:
_________

Answer:
3 x 1/4

Explanation:
Given that 3/4 or 3 fourth-size parts.
Each fourth-size part of the given fraction can be shown by the unit fraction 1/4.
You can use unit fractions to show 5/6
3/4 = 3 x 1/4.

Question 6.
\(\frac{11}{12}\)
Type below:
_________

Answer:
11 x 1/12

Explanation:
Given that 11/12 or 11 twelve-size parts.
Each twelve-size part of the given fraction can be shown by the unit fraction 1/12.
You can use unit fractions to show 5/6
11/12 = 11 x 1/12.

Question 7.
\(\frac{4}{6}\)
Type below:
_________

Answer:
4 x 1/6

Explanation:
Given that 4/6 or 4 sixth-size parts.
Each sixth-size part of the given fraction can be shown by the unit fraction 1/6.
You can use unit fractions to show 4/6
4/6 = 4 x 1/6.

Question 8.
\(\frac{8}{20}\)
Type below:
_________

Answer:
8 x 1/20

Explanation:
Given that 8/20 or 8 twenty-size parts.
Each twenty-size part of the given fraction can be shown by the unit fraction 1/20.
You can use unit fractions to show 8/20
8/20 = 8 x 1/20.

Question 9.
\(\frac{13}{100}\)
Type below:
_________

Answer:
13 x 1/100

Explanation:
Given that 13/100 or 13 hundred-size parts.
Each hundred-size part of the given fraction can be shown by the unit fraction 1/100.
You can use unit fractions to show 13/100
13/100 = 13 x 1/100.

List the next four multiples of the unit fraction.

Question 10.
\(\frac{1}{5}\),
Type below:
_________

Answer:
2/5, 3/5, 4/5, 5/5

Explanation:

2/5, 3/5, 4/5, 5/5

Question 11.
\(\frac{1}{8}\),
Type below:
_________

Answer:
2/8, 3/8, 4/8, 5/8

Explanation:

2/8, 3/8, 4/8, 5/8

Problem Solving

Question 12.
So far, Monica has read \(\frac{5}{6}\) of a book. She has read the same number of pages each day for 5 days. What fraction of the book does Monica read each day?
\(\frac{□}{□}\) of the book

Answer: 1/6 of the book

Explanation:
Monica has read 5/6 of a book. She has read the same number of pages each day for 5 days.
For 1 day, she read one page. In total, she read 5 pages in 5 days. So, Monica read 1/6 of a book each day.

Question 13.
So far, Monica has read \(\frac{3}{8}\) of a book. She has read the same number of pages each day for 5 days. What fraction of the book does Monica read each day?
\(\frac{□}{□}\) pound of cheese

Answer: 1/8 pound of cheese

Explanation:
Nicholas buys 3/8 pound of cheese. He bought 3 sandwiches. Then, he applied 3/8 pound of cheese on 3 sandwiches. So, 3 x 1/8 cheese he put on 3 sandwiches. So, for one sandwich he put 1/8 pound of cheese.

Common Core – Multiply Fractions by Whole Numbers – Page No. 158

Lesson Check

Question 1.
Selena walks from home to school each morning and back home each afternoon. Altogether, she walks \(\frac{2}{3}\) mile each day. How far does Selena live from school?
Options:
a. \(\frac{1}{3}\) mile
b. \(\frac{2}{3}\) mile
c. 1 \(\frac{1}{3}\) miles
d. 2 miles

Answer: a. 1/3 mile

Explanation:
Selena walks from home to school each morning and back home each afternoon.
Altogether, she walks 2/3 miles each day.
The distance between home and school will remain the same.
So, 2/3 x 1/2 = 1/3 mile far Selena live from the school.
Thus the correct answer is option a.

Question 2.
Will uses \(\frac{3}{4}\) cup of olive oil to make 3 batches of salad dressing. How much oil does Will use for one batch of salad dressing?
Options:
a. \(\frac{1}{4}\) cup
b. \(\frac{1}{3}\) cup
c. 2 \(\frac{1}{3}\) cups
d. 3 cups

Answer: \(\frac{1}{4}\) cup

Explanation:
Will uses 3/4 cups of olive oil to make 3 batches of salad dressing.
To know the one batch of salad dressing, we need to take one part of salad dressing = 1/3.
So, 3/4 x 1/3 = 1/4 cup of olive oil will use for one batch of salad dressing.
Thus the correct answer is option a.

Spiral Review

Question 3.
Liza bought \(\frac{5}{8}\) pound of trail mix. She gives \(\frac{2}{8}\) pound of trail mix to Michael. How much trail mix does Liza have left?
Options:
a. \(\frac{1}{8}\) pound
b. \(\frac{2}{8}\) pound
c. \(\frac{3}{8}\) pound
d. \(\frac{4}{8}\) pound

Answer: c. 3/8 pound

Explanation:
Liza bought 58 pound of trail mix. She gives 28 pounds of trail mix to Michael.
So, Liza has left 5/8 – 2/8 = 3/8 trail mix.
Thus the correct answer is option c.

Question 4.
Leigh has a piece of rope that is 6 \(\frac{2}{3}\) feet long. How do you write 6 \(\frac{2}{3}\) as a fraction greater than 1?
Options:
a. \(\frac{11}{3}\) pound
b. \(\frac{15}{3}\) pound
c. \(\frac{20}{3}\) pound
d. \(\frac{62}{3}\) pound

Answer: c. 20/3

Explanation:
Multiply the denominator with the whole number. i.e Multiply 3 with 6 in the given example, 6 (2/3).
3 x 6 =18.
Add 18 + 2 =20.
Keep the Denominator the same i.e. 3.
The obtained fraction is 20/3.
Thus the correct answer is option c.

Question 5.
Randy’s house number is a composite number. Which of the following could be Randy’s house number?
Options:
a. 29
b. 39
c. 59
d. 79

Answer: b. 39

Explanation:
The composite numbers can be defined as the whole numbers that have more than two factors. Whole numbers that are not prime are composite numbers because they are divisible by more than two numbers. 39 is the composite number. 39 is divide by 13 and 3.
Thus the correct answer is option b.

Question 6.
Mindy buys 12 cupcakes. Nine of the cupcakes have chocolate frosting and the rest have vanilla frosting. What fraction of the cupcakes have vanilla frosting?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{1}{3}\)
c. \(\frac{2}{3}\)
d. \(\frac{3}{4}\)

Answer: a. 1/4

Explanation:
Mindy buys 12 cupcakes.
Nine of the cupcakes have chocolate frosting = 9/12.
The rest have vanilla frosting. So, there are 3 cups remained = 3/12 = 1/4.
1/4 cupcakes have vanilla frosting.
Thus the correct answer is option a.

Common Core – Multiply Fractions by Whole Numbers – Page No. 159

Multiples of Fractions

List the next four multiples of the fraction.

Question 1.
\(\frac{3}{5}\),
Type below:
_________

Answer:
6/5, 9/5, 12/5, 20/5

Explanation:
1 x 3/5 = 3/5.
2 x 3/5 = 6/5.
3 x 3/5 = 9/5.
4 x 3/5 = 12/5.
5 x 4/5 = 20/5.
The next four multiples of 3/5 are 6/5, 9/5, 12/5, 20/5.

Question 2.
\(\frac{2}{6}\),
Type below:
_________

Answer:
4/6, 6/6, 8/6, 10/6

Explanation:
1 x 2/6 = 2/6.
2 x 2/6 = 4/6.
3 x 2/6 = 6/6.
4 x 2/6 = 8/6.
5 x 2/6 = 10/6.
The next four multiples of 2/6 are 4/6, 6/6, 8/6, 10/6.

Question 3.
\(\frac{4}{8}\),
Type below:
_________

Answer:
8/8, 12/8, 16/8, 20/8

Explanation:
1 x 4/8 = 4/8.
2 x 4/8 = 8/8.
3 x 4/8 = 12/8.
4 x 4/8 = 16/8.
5 x 4/8 = 20/8.
The next four multiples of 4/8 are 8/8, 12/8, 16/8, 20/8.

Question 4.
\(\frac{5}{10}\),
Type below:
_________

Answer:
10/10, 15/10, 20/10, 25/10

Explanation:
1 x 5/10 = 5/10.
2 x 5/10 = 10/10.
3 x 5/10 = 15/10.
4 x 5/10 = 20/10.
5 x 5/10 = 25/10.
The next four multiples of 5/10 are 10/10, 15/10, 20/10, 25/10.

Write the product as the product of a whole number and a unit fraction.

Question 5.

2 × \(\frac{4}{5}\) =
Type Below:
_________

Answer: 8/5 = 8 x 1/5

Explanation:
1 group of 4/5 = 4/5
2 groups of 4/5 = 8/5
2 x 4/5 = 8/5 = 8 x 1/5.

Question 6.

5 × \(\frac{2}{3}\) =
Type below:
_________

Answer:
10/3 = 10 x 1/3

Explanation:
1 group of 2/3 = 2/3
2 group of 2/3 = 4/3
3 group of 2/3 = 6/3
4 group of 2/3 = 8/3
5 group of 2/3 = 10/3
5 x 2/3 = 10/3 = 10 x 1/3.

Problem Solving

Question 7.
Jessica is making 2 loaves of banana bread. She needs \(\frac{3}{4}\) cup of sugar for each loaf. Her measuring cup can only hold \(\frac{1}{4}\) cup of sugar. How many times will Jessica need to fill the measuring cup in order to get enough sugar for both loaves of bread?
_____ times

Answer: 6 times

Explanation:
Jessica is making 2 loaves of banana bread. She needs a 3/4 cup of sugar for each loaf.
For 2 loaves, she needs 2 x 3/4 = 6/4 cups of sugar.
Her measuring cup can only hold 1/4 cup of sugar. So, to get the 3/4 cup of sugar, she needs to fill the cup 3 times. 1/4 + 1/4 + 1/4 = 3/4.
So, to fill 2 loaves, she needs to fill cup 3 x 2 = 6 times.

Question 8.
A group of four students is performing an experiment with salt. Each student must add \(\frac{3}{8}\) teaspoon of salt to a solution. The group only has a \(\frac{1}{8}\) teaspoon measuring spoon. How many times will the group need to fill the measuring spoon in order to perform the experiment?
_____ times

Answer: 12 times

Explanation:
A group of four students is performing an experiment with salt. Each student must add a 3/8 teaspoon of salt to a solution. 4 x 3/8 = 12/8 teaspoon of salt required to finish the experiment.
If they have 1/8 teaspoon measuring spoon, 12 x 1/8.
So, the group needs to fill the measuring spoon 12 times in order to perform the experiment.

Common Core – Multiply Fractions by Whole Numbers – Page No. 160

Lesson Check

Question 1.
Eloise made a list of some multiples of \(\frac{5}{8}\). Which of the following lists could be Eloise’s list?
Options:
a. \(\frac{5}{8}, \frac{10}{16}, \frac{15}{24}, \frac{20}{32}, \frac{25}{40}\)
b. \(\frac{5}{8}, \frac{10}{8}, \frac{15}{8}, \frac{20}{8}, \frac{25}{8}\)
c. \(\frac{5}{8}, \frac{6}{8}, \frac{7}{8}, \frac{8}{8}, \frac{9}{8}\)
d. \(\frac{1}{8}, \frac{2}{8}, \frac{3}{8}, \frac{4}{8}, \frac{5}{8}\)

Answer: b. 5/8, 10/8, 15/8, 20/8, 25/8
Explanation:
1 x 5/8 = 5/8.
2 x 5/8 = 10/8.
3 x 5/8 = 15/8.
4 x 5/8 = 20/8.
5 x 5/8 = 25/8.
The next four multiples of 5/8 are \(\frac{5}{8}, \frac{10}{8}, \frac{15}{8}, \frac{20}{8}, \frac{25}{8}\)
Thus the correct answer is option b.

Question 2.
David is filling five \(\frac{3}{4}\) quart bottles with a sports drink. His measuring cup only holds \(\frac{1}{4}\) quart. How many times will David need to fill the measuring cup in order to fill the 5 bottles?
Options:
a. 5
b. 10
c. 15
d. 20

Answer: c. 15

Explanation:
David is filling five 3/4 quart bottles with a sports drink = 5 x 3/4 = 15/4.
His measuring cup only holds 1/4 quart.
So, 15 x 1/4. David needs to fill the measuring cup 15 times in order to fill the 5 bottles.
Thus the correct answer is option c.

Spiral Review

Question 3.
Ira has 128 stamps in his stamp album. He has the same number of stamps on each of the 8 pages. How many stamps are on each page?
Options:
a. 12
b. 14
c. 16
d. 18

Answer: c. 16

Explanation:
Ira has 128 stamps in his stamp album. He has the same number of stamps on each of the 8 pages.
128/8 = 16 stamps on each page.
So, there are 16 stamps on each page.
Thus the correct answer is option b.

Question 4.
Ryan is saving up for a bike that costs $198. So far, he has saved $15 per week for the last 12 weeks. How much more money does Ryan need in order to be able to buy the bike?
Options:
a. $ 8
b. $ 18
c. $ 48
d. $ 180

Answer: b. $ 18

Explanation:
Ryan is saving up for a bike that costs $198.
So far, he has saved $15 per week for the last 12 weeks = $15 x 12 = $180.
$198 – $180 = $18 need in order to buy the bike.
Thus the correct answer is option b.

Question 5.
Tina buys 3 \(\frac{7}{8}\) yards of material at the fabric store. She uses it to make a skirt. Afterward, she has 1 \(\frac{3}{8}\) yards of the fabric leftover. How many yards of material did Tina use?
Options:
a. 1 \(\frac{4}{8}\)
b. 2 \(\frac{1}{8}\)
c. 2 \(\frac{4}{8}\)
d. 5 \(\frac{2}{8}\)

Answer: c. 2  4/8

Explanation:
Tina buys 3 7/8 yards of material at the fabric store. She uses it to make a skirt. Afterward, she has 1 3/8 yards of the fabric leftover.
3 -1 = 2; 7/8 – 3/8 = 4/8.
So, the answer is 2 \(\frac{4}{8}\).
Thus the correct answer is option c.

Question 6.
Which list shows the fractions in order from least to greatest?
Options:
a. \(\frac{2}{3}, \frac{3}{4}, \frac{7}{12}\)
b. \(\frac{7}{12}, \frac{3}{4}, \frac{2}{3}\)
c. \(\frac{3}{4}, \frac{2}{3}, \frac{7}{12}\)
d. \(\frac{7}{12}, \frac{2}{3}, \frac{3}{4}\)

Answer: d. \(\frac{7}{12}, \frac{2}{3}, \frac{3}{4}\)

Explanation:
2/3 = 0.666
3/4 = 0.75
7/12 = 0.5833
\(\frac{7}{12}, \frac{2}{3}, \frac{3}{4}\)
Thus the correct answer is option d.

Common Core – Multiply Fractions by Whole Numbers – Page No. 161

Multiply a Fraction by a Whole Number Using Models

Multiply.

Question 1.

Question 2.
3 × \(\frac{2}{5}\) = \(\frac{□}{□}\)

Answer:

3 x 2/5 = 6/5

Question 3.
7 × \(\frac{3}{10}\) = \(\frac{□}{□}\)

Answer:

7 x 3/10 = 21/10

Question 4.
3 × \(\frac{5}{12}\) = \(\frac{□}{□}\)

Answer:

3 x 5/12 = 15/12

Question 5.
6 × \(\frac{3}{4}\) = \(\frac{□}{□}\)

Answer:

6 x 3/4 = 18/4

Question 6.
4 × \(\frac{2}{8}\) = \(\frac{□}{□}\)

Answer:

4 x 2/8 = 8/8

Question 7.
5 × \(\frac{2}{3}\) = \(\frac{□}{□}\)

Answer:

5 x 2/3 = 10/3

Question 8.
2 × \(\frac{7}{8}\) = \(\frac{□}{□}\)

Answer:

2 x 7/8 = 14/8

Question 9.
6 × \(\frac{4}{5}\) = \(\frac{□}{□}\)

Answer:

6 x 4/5 = 28/5

Problem Solving

Question 10.
Matthew walks \(\frac{5}{8}\) mile to the bus stop each morning. How far will he walk in 5 days?
\(\frac{□}{□}\)

Answer: 25/8 miles

Explanation:
Matthew walks 5/8 mile to the bus stop each morning.
In 5 days, 5 x 5/8 = 25/8 miles.

Question 11.
Emily uses \(\frac{2}{3}\) cup of milk to make one batch of muffins. How many cups of milk will Emily use if she makes 3 batches of muffins?
\(\frac{□}{□}\)

Answer: 6/3 cups of milk

Explanation:
Emily uses a 2/3 cup of milk to make one batch of muffins.
Emily use 3 x 2/3 = 6/3 cups of milk to make 3 batches of muffins

Common Core – Multiply Fractions by Whole Numbers – Page No. 162

Lesson Check

Question 1.
Aleta’s puppy gained \(\frac{3}{8}\) pound each week for 4 weeks. Altogether, how much weight did the puppy gain during the 4 weeks?
Options:
a. \(\frac{8}{12}\) pound
b. 1 \(\frac{2}{8}\) pounds
c. \(\frac{12}{8}\) pounds
d. 4 \(\frac{3}{8}\) pounds

Answer: \(\frac{12}{8}\) pounds

Explanation:
Aleta’s puppy gained 3/8 pound each week.
It gained 4 x 3/8 = 12/8 pounds in 4 weeks.
Thus the correct answer is option c.

Question 2.
Pedro mixes \(\frac{3}{4}\) teaspoon of plant food into each gallon of water. How many teaspoons of plant food should Pedro mix into 5 gallons of water?
Options:
a. \(\frac{3}{20}\) teaspoon
b. \(\frac{4}{15}\) teaspoon
c. \(\frac{8}{4}\) teaspoons
d. \(\frac{15}{4}\) teaspoons

Answer: d. \(\frac{15}{4}\) teaspoons

Explanation:
If Pedro mixes 3/4 teaspoon of plant food into each gallon of water, then 5 x 3/4 = 15/4 teaspoon of plant food mix into 5 gallons of water.
Thus the correct answer is option d.

Spiral Review

Question 3.
Ivana has \(\frac{3}{4}\)pound of hamburger meat. She makes 3 hamburger patties. Each patty weighs the same amount. How much does each hamburger patty weigh?
Options:
a. \(\frac{1}{4}\) pound
b. \(\frac{1}{3}\) pound
c. 2 \(\frac{1}{4}\) pounds
d. 3 pounds

Answer: a. \(\frac{1}{4}\) pound

Explanation:
Ivana has 3/4 pound of hamburger meat. She makes 3 hamburger patties.
Each patty weighs the same amount. So, each hamburger patty weighs 1/4 pound.
Thus the correct answer is option a.

Question 4.
Which of the following expressions is NOT equal to \(\frac{7}{10}\)?
Options:
a. \(\frac{5}{10}+\frac{1}{10}+\frac{1}{10}\)
b. \(\frac{2}{10}+\frac{2}{10}+\frac{3}{10}\)
c. \(\frac{3}{10}+\frac{3}{10}+\frac{2}{10}\)
d. \(\frac{4}{10}+\frac{2}{10}+\frac{1}{10}\)

Answer: c. 3/10+3/10+2/10

Explanation:
a. 5/10+1/10+1/10 = 7/10
b. 2/10+2/10+3/10 = 7/10
c. 3/10+3/10+2/10 = 8/10
d. 4/10+2/10+1/10 = 7/10
The expression not equal to \(\frac{7}{10}\) is \(\frac{8}{10}\)
Thus the correct answer is option c.

Question 5.
Lance wants to find the total length of 3 boards. He uses the expression \(3 \frac{1}{2}+\left(2+4 \frac{1}{2}\right)\). How can Lance rewrite the expression using both the Associative and Commutative Properties of Addition?
Options:
a. \(5+4 \frac{1}{2}\)
b. \(\left(3 \frac{1}{2}+2\right)+4 \frac{1}{2}\)
c. \(2+\left(3 \frac{1}{2}+4 \frac{1}{2}\right)\)
d. \(3 \frac{1}{2}+\left(4 \frac{1}{2}+2\right)\)

Answer: She can write as (3 1/2 + 2) + 4 1/2

Question 6.
Which of the following statements is true?
Options:
a. \(\frac{5}{8}>\frac{9}{10}\)
b. \(\frac{5}{12}>\frac{1}{3}\)
c. \(\frac{3}{6}>\frac{4}{5}\)
d. \(\frac{1}{2}>\frac{3}{4}\)

Answer: \(\frac{1}{2}>\frac{3}{4}\)

Explanation:
0.625 > 0.9
0.416 > 0.333
0.5 > 0.8
0.5 > 0.75
Thus the correct answer is option d.

Common Core – Multiply Fractions by Whole Numbers – Page No. 163

Multiply a Fraction or Mixed Number by a Whole Number.

Multiply. Write the product as a mixed number.

Question 1.

Answer:
1  5/10

Explanation:
5 × 3/10 = 15/10 = 1 and remainder is 5. So, the mixed fraction is 1  5/10

Question 2.
3 × \(\frac{3}{5}\) =
_____ \(\frac{□}{□}\)

Answer:
1 × 4/5

Explanation:
3 × 3/5 = 9/5 = 1 and remainder is 4. So, the mixed fraction is 1  4/5

Question 3.
5 × \(\frac{3}{4}\) =
_____ \(\frac{□}{□}\)

Answer:
3  3/4
Explanation:
15/4 = 3 and the remainder is 3. So, the mixed fraction is 3  3/4

Question 4.
4 × 1 \(\frac{1}{5}\) =
_____ \(\frac{□}{□}\)

Answer:
4  4/5
Explanation:
1 ×15 = 6/5.
4 x 6/5 = 24/5 = 4 and the remainder is 4. So, the mixed fraction is 4× 4/5

Question 5.
2 × 2 \(\frac{1}{3}\) =
_____ \(\frac{□}{□}\)

Answer:
4  2/3
Explanation:
2 13 = 7/3.
2 x 7/3 = 14/3.
14/3 = 4 and the remainder is 2. So, the mixed fraction is 4 2/3

Question 6.
5 × 1 \(\frac{1}{6}\) =
_____ \(\frac{□}{□}\)

Answer: 5 5/6

Explanation:
1 1/6 = 7/6
5 x 7/6 = 35/6.
35/6 = 5 and the remainder is 5.
So, the mixed fraction is 5 5/6

Question 7.
2 × 2 \(\frac{7}{8}\) =
_____ \(\frac{□}{□}\)

Answer: 6 1/1

Explanation:
2 7/8 = 23/8
2 x 23/8 = 46/8 = 6 1/1

Question 8.
7 × 1 \(\frac{3}{4}\) =
_____ \(\frac{□}{□}\)

Answer: 9 3/4

Explanation:
1 3/4 = 7/4
7 x 7/4 = 39/4
39/4 = 9 and the remainder is 3.
So, the mixed fraction is 9 3/4

Question 9.
8 × 1 \(\frac{3}{5}\) =
_____ \(\frac{□}{□}\)

Answer: 12 4/5

Explanation:
1 3/5 = 8/5
8 x 8/5 = 64/5
64/5 = 12 and the remainder is 4.
So, the mixed fraction is 12 4/5

Problem Solving

Question 10.
Brielle exercises for \(\frac{3}{4}\) hour each day for 6 days in a row. Altogether, how many hours does she exercise during the 6 days?
_____ \(\frac{□}{□}\)

Answer: 4 2/4

Explanation:
6 x 3/4 = 18/4 = 4 and the remainder is 2.
So, the mixed fraction is 4 2/4.

Question 11.
A recipe for quinoa calls for 2 \(\frac{2}{3}\) cups of milk. Conner wants to make 4 batches of quinoa. How much milk does he need?
_____ \(\frac{□}{□}\)

Answer: 10 2/3

Explanation:
quinoa calls for 8/3 cups of milk. Conner wants to make 4 batches of quinoa.
So, 4 x 8/3 = 32/3 = 10 and the remainder is 2.
So, the mixed fraction is 10 2/3

Common Core – Multiply Fractions by Whole Numbers – Page No. 164

Lesson Check

Question 1.
A mother is 1 \(\frac{3}{4}\) times as tall as her son. Her son is 3 feet tall. How tall is the mother?
Options:
a. 4 \(\frac{3}{4}\) feet
b. 5 \(\frac{1}{4}\) feet
c. 5 \(\frac{1}{2}\) feet
d. 5 \(\frac{3}{4}\) feet

Answer: b. 5 1/4 feet

Explanation:
A mother is 1 3/4 times as tall as her son. Her son is 3 feet tall.
So, 3 x 7/4 = 21/4 = 5 and the remainder is 1.
The mixed fraction is 5 1/4 feet.
Thus the correct answer is option b.

Question 2.
The cheerleaders are making a banner that is 8 feet wide. The length of the banner is 1 \(\frac{1}{3}\) times the width of the banner. How long is the banner?
Options:
a. 8 \(\frac{1}{3}\) feet
b. 8 \(\frac{3}{8}\) feet
c. 10 \(\frac{1}{3}\) feet
d. 10 \(\frac{2}{3}\) feet

Answer: d. 10 2/3 feet

Explanation:
The cheerleaders are making a banner that is 8 feet wide. The length of the banner is 1 1/3 times the width of the banner.
So, 8 x 4/3 = 32/3 =10 and the remainder is 2.
The mixed fraction is 10 2/3 feet.
Thus the correct answer is option d.

Spiral Review

Question 3.
Karleigh walks \(\frac{5}{8}\) mile to school every day. How far does she walk to school in 5 days?
Options:
a. \(\frac{5}{40}\) mile
b. \(\frac{25}{40}\) mile
c. \(\frac{10}{8}\) miles
d. \(\frac{25}{8}\) miles

Answer: d. 25/8 miles

Explanation:
5 x 5/8 = 25/8.
Thus the correct answer is option d.

Question 4.
Which number is a multiple of \(\frac{4}{5}\)?
Options:
a. \(\frac{8}{10}\)
b. \(\frac{12}{15}\)
c. \(\frac{16}{20}\)
d. \(\frac{12}{5}\)

Answer: d. 12/5

Explanation:
The multiple of 45 has the denominator 5.
So, 12/5 is the correct answer.
Thus the correct answer is option d.

Question 5.
Jo cut a key lime pie into 8 equal-size slices. The next day, \(\frac{7}{8}\) of the pie is left. Jo puts each slice on its own plate. How many plates does she need?
Options:
a. 5
b. 6
c. 7
d. 8

Answer: c. 7

Explanation:
Jo cut a key lime pie into 8 equal-size slices.
The next day, 78 of the pie is left. Jo puts each slice on its own plate.
She needs 7 plates.
Thus the correct answer is option c.

Question 6.
Over the weekend, Ed spent 1 \(\frac{1}{4}\) hours doing his math homework and 1 \(\frac{3}{4}\) hours doing his science project. Altogether, how much time did Ed spend doing homework over the weekend?
Options:
a. 3 hours
b. 2 \(\frac{3}{4}\) hours
c. 2 \(\frac{1}{2}\) hours
d. 2 hours

Answer: a. 3 hours

Explanation:
Given,
Over the weekend, Ed spent 1 \(\frac{1}{4}\) hours doing his math homework and 1 \(\frac{3}{4}\) hours doing his science project.
5/4 + 7/4 = 12/4 = 3 hours
Thus the correct answer is option a.

Common Core – Multiply Fractions by Whole Numbers – Page No. 165

Problem Solving Comparison

Problems with Fractions

Read each problem and solve.

Question 1.
A shrub is 1 \(\frac{2}{3}\) feet tall. A small tree is 3 times as tall as the shrub. How tall is the tree?

Answer: 5 feet

Explanation:

Question 2.
You run 1 \(\frac{3}{4}\) miles each day. Your friend runs 4 times as far as you do. How far does your friend run each day?
_________ miles

Answer: 7 miles

Explanation:
Given,
You run 1 \(\frac{3}{4}\) miles each day.
Your friend runs 4 times as far as you do.
4 x 7/4 = 7 miles each day

Question 3.
At the grocery store, Ayla buys 1 \(\frac{1}{3}\) pounds of ground turkey. Tasha buys 2 times as much ground turkey as Ayla. How much ground turkey does Tasha buy?
_____ \(\frac{□}{□}\) pounds

Answer: 2 2/3 pounds

Explanation:
Given,
At the grocery store, Ayla buys 1 \(\frac{1}{3}\) pounds of ground turkey.
Tasha buys 2 times as much ground turkey as Ayla.
2 x 4/3 = 8/3 = 2 and the remainder is 2.
The mixed fraction is 2 2/3 pounds.

Question 4.
When Nathan’s mother drives him to school, it takes \(\frac{1}{5}\) hour. When Nathan walks to school, it takes him 4 times as long to get to school. How long does it take Nathan to walk to school?
\(\frac{□}{□}\) hours

Answer: 4/5 hours

Explanation:
Given,
When Nathan’s mother drives him to school, it takes \(\frac{1}{5}\) hour.
When Nathan walks to school, it takes him 4 times as long to get to school.
4 x 1/5 = 4/5 hour
It takes 4/5 hour Nathan to walk to school.

Common Core – Multiply Fractions by Whole Numbers – Page No. 166

Lesson Check

Question 1.
A Wilson’s Storm Petrel is a small bird with a wingspan of 1 \(\frac{1}{3}\) feet. A California Condor is a larger bird with a wingspan almost 7 times as wide as the wingspan of the petrel. About how wide is the wingspan of the California Condor?
Options:
a. \(\frac{4}{21}\) foot
b. 2 \(\frac{1}{3}\) feet
c. 7 \(\frac{1}{3}\) feet
d. 9 \(\frac{1}{3}\) feet

Answer: d. 9 1/3 feet

Explanation:
Given,
A Wilson’s Storm Petrel is a small bird with a wingspan of 1 \(\frac{1}{3}\) feet.
A California Condor is a larger bird with a wingspan almost 7 times as wide as the wingspan of the petrel.
Convert from mixed fraction to the improper fraction.
1 1/3 = 4/3.
7 x 4/3 = 28/3 feet = 9 and the remainder is 1.
The mixed fraction is 9 1/3
Thus the correct answer is option d.

Question 2.
The walking distance from the Empire State Building in New York City to Times Square is about \(\frac{9}{10}\) mile. The walking distance from the Empire State Building to Sue’s hotel is about 8 times as far. About how far is Sue’s hotel from the Empire State Building?
Options:
a. \(\frac{9}{80}\) mile
b. \(\frac{72}{80}\) mile
c. 1 \(\frac{7}{10}\) miles
d. 7 \(\frac{2}{10}\) miles

Answer: d. 7 2/10 miles

Explanation:
Given,
The walking distance from the Empire State Building in New York City to Times Square is about \(\frac{9}{10}\) mile.
The walking distance from the Empire State Building to Sue’s hotel is about 8 times as far.
8 x 9/10 mile = 72/10 mile = 7 and the remainder is 2.
The mixed fraction is 7 2/10 miles.
Thus the correct answer is option d.

Spiral Review

Question 3.
Which of the following expressions is NOT equal to 3 × 2 \(\frac{1}{4}\)?
Options:
a. \(3 \times \frac{9}{4}\)
b. (3 × 2) + (3 × \(\frac{1}{4}\))
c. 6 \(\frac{3}{4}\)
d. 3 × 2 + \(\frac{1}{4}\)

Answer: d. 3 × 2 + 14

Explanation:
3 × 2 14 = 3 x 9/4 = 27/4
a. 3 × 94 = 27/4
b. (3 × 2) + (3 × 14) = 6 + 3/4 = 27/4
c. 6 3/4 = 27/4
d. 3 × 2 + 14 = 6 + 1/4 = 25/4
Thus the correct answer is option d.

Question 4.
At a bake sale, Ron sells \(\frac{7}{8}\) of an apple pie and \(\frac{5}{8}\) of a cherry pie. Altogether, how much pie does he sell at the bake sale?
Options:
a. \(\frac{2}{8}\)
b. \(\frac{12}{16}\)
c. \(\frac{12}{8}\)
d. \(\frac{35}{8}\)

Answer: c. 12/8

Explanation:
Given,
At a bake sale, Ron sells \(\frac{7}{8}\) of an apple pie and \(\frac{5}{8}\) of a cherry pie.
7/8 + 5/8 = 12/8
The bake sale 12/8 pie.
Thus the correct answer is option c.

Question 5.
On a ruler, which measurement is between \(\frac{3}{16}\) inch and \(\frac{7}{8}\) inch?
Options:
a. \(\frac{1}{16}\) inch
b. \(\frac{1}{8}\) inch
c. \(\frac{11}{16}\) inch
d. \(\frac{15}{16}\) inch

Answer: c. 11/16 inch

Explanation:
Subtract \(\frac{3}{16}\) inch and \(\frac{7}{8}\)
Make denominators as common.
\(\frac{7}{8}\) × \(\frac{2}{2}\) = \(\frac{14}{16}\)
\(\frac{14}{16}\) – \(\frac{3}{16}\) = \(\frac{11}{16}\) inch.
Thus the correct answer is option c.

Question 6.
Which of the following numbers is composite?
Options:
a. 4
b. 3
c. 2
d. 1

Answer:
a. 4

Explanation:
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself.
The factors of 4 are 1, 2, 4.
4 has more than 2 factors.
Thus the correct answer is option a.

Common Core – Multiply Fractions by Whole Numbers – Page No. 167

Lesson 8.1

Write the fraction as a product of a whole number and a unit fraction.

Question 1.
\(\frac{5}{6}\) =
Type below:
________

Answer: 5 x 1/6

Explanation:
Given that 5/6 or 5 sixth-size parts.
Each sixth-size part of the given fraction can be shown by the unit fraction 1/6.
You can use unit fractions to show 5/6
\(\frac{5}{6}\) = 5 x 1/6.

Question 2.
\(\frac{7}{8}\) =
Type below:
________

Answer: 7 x 1/8

Explanation:
Given that 7/8 or 7 eighth-size parts.
Each eighth-size part of the given fraction can be shown by the unit fraction 1/8.
You can use unit fractions to show 7/8
\(\frac{7}{8}\) = 7 x 1/8.

Question 3.
\(\frac{3}{5}\) =
Type below:
________

Answer: 5 x 1/3

Explanation:
Given that 5/3 or 5 third-size parts.
Each third-size part of the given fraction can be shown by the unit fraction 1/3.
You can use unit fractions to show 5/6
5/3 = 5 x 1/3.

List the next four multiples of the unit fraction

Question 4.
\(\frac{1}{2}\),
Type below:
________

Answer: 2/2, 3/2, 4/2, 5/2

Explanation:
1 x 1/2 = 1/2.
2 x 1/2 = 2/2.
3 x 1/2 = 3/2.
4 x 1/2 = 4/2.
5 x 1/2 = 5/2.
The next four multiples of 1/2 are 2/2, 3/2, 4/2, 5/2.

Question 5.
\(\frac{1}{6}\),
Type below:
________

Answer: 2/6, 3/6, 4/6, 5/6,6/6.

Explanation:
1 x 1/6 = 1/6.
2 x 1/6 = 2/6.
3 x 1/6 = 3/6.
4 x 1/6 = 4/6.
5 x 1/6 = 5/6.
6 x 1/6 = 6/6.
The next four multiples of 1/6 are 2/6, 3/6, 4/6, 5/6,6/6.

Lesson 8.2

List the next four multiples of the fraction.

Question 6.
\(\frac{3}{10}\),
Type below:
________

Answer: 6/10, 9/10, 12/10, 15/10

Explanation:
1 × 3/10 = 3/10
2 × 3/10 = 6/10
3 × 3/10 = 9/10
4 × 3/10 = 12/10
5 × 3/10 = 15/10

Question 7.
\(\frac{7}{12}\),
Type below:
________

Answer: 7/12, 14/12, 21/12, 28/12, 35/12

Explanation:
1 × 7/12 = 7/12
2 × 7/12 = 14/12
3 × 7/12 = 21/12
4 × 7/12 = 28/12
5 × 7/12 = 35/12

Write the product as the product of a whole number and a unit fraction.

Question 8.

2 × \(\frac{3}{6}\) =
Type below:
________

Answer:
1 group of \(\frac{3}{6}\) is \(\frac{3}{6}\)
2 groups of \(\frac{3}{6}\) is \(\frac{6}{6}\)
2 × \(\frac{3}{6}\) = \(\frac{6}{6}\)

Question 9.

3 × \(\frac{2}{8}\) =
Type below:
________

Explanation:
1 group of \(\frac{2}{8}\) is \(\frac{2}{8}\)
2 group of \(\frac{2}{8}\) is \(\frac{4}{8}\)
3 group of \(\frac{2}{8}\) is \(\frac{6}{8}\)
3 × \(\frac{2}{8}\) = \(\frac{6}{8}\)

Common Core – Multiply Fractions by Whole Numbers – Page No. 168

Lesson 8.3

Multiply.

Question 1.
3 × \(\frac{7}{10}\) =
\(\frac{□}{□}\)

Answer: \(\frac{21}{10}\)

Explanation:
Multiply 7 and 3
3 × 7 = 21
3 × \(\frac{7}{10}\) = \(\frac{21}{10}\)

Question 2.
5 × \(\frac{4}{8}\) =
\(\frac{□}{□}\)

Answer: 20/8

Explanation:
Multiply 5 and 4
5 × 4 = 20
5 × \(\frac{4}{8}\) = \(\frac{20}{8}\)

Question 3.
4 × \(\frac{6}{12}\) =
\(\frac{□}{□}\)

Answer: 24/12

Explanation:
Multiply 4 and 6
4 × 6 = 24
4 × \(\frac{6}{12}\) = \(\frac{24}{12}\)

Question 4.
2 × \(\frac{3}{4}\) =
\(\frac{□}{□}\)

Answer: 6/4

Explanation:
Multiply 2 and 3
2 × 3 = 6
2 × \(\frac{3}{4}\) = \(\frac{6}{4}\)

Question 5.
6 × \(\frac{3}{5}\) =
\(\frac{□}{□}\)

Answer: 18/5

Explanation:
Multiply 6 and 3
6 × 3 =18
6 × \(\frac{3}{5}\) = \(\frac{18}{5}\)

Question 6.
7 × \(\frac{2}{10}\) =
\(\frac{□}{□}\)

Answer: 14/10

Explanation:
Multiply 7 and 2.
7 × 2 =14
7 × \(\frac{2}{10}\) = \(\frac{14}{10}\)

Lesson 8.4

Multiply. Write the product as a mixed number.

Question 7.
4 × \(\frac{8}{10}\) =
_____ \(\frac{□}{□}\)

Answer: 3 2/10

Explanation:
Given,
4 × \(\frac{8}{10}\)
First multiply 4 and 8
4 × 8 = 32
4 × \(\frac{8}{10}\) = 32/10
Now convert from improper fraction to the mixed fraction.
32/10 = 3 \(\frac{2}{10}\)

Question 8.
3 × \(\frac{5}{6}\) =
_____ \(\frac{□}{□}\)

Answer: 2 3/6

Explanation:
Given,
3 × \(\frac{5}{6}\)
First multiply 3 and 5.
3 × 5 =15
3 × \(\frac{5}{6}\) = 15/6
Now convert from improper fraction to the mixed fraction.
15/6 = 2 3/6

Question 9.
2 × 3 \(\frac{1}{3}\) =
_____ \(\frac{□}{□}\)

Answer: 6 2/3

Explanation:
Given,
2 × 3 \(\frac{1}{3}\)
3 \(\frac{1}{3}\) = 10/3
2 × 10/3 = 20/3
Now convert from improper fraction to the mixed fraction.
20/3 = 6 2/3

Question 10.
4 × 2 \(\frac{2}{5}\) =
_____ \(\frac{□}{□}\)

Answer: 9 3/5

Explanation:
Given,
4 × 2 \(\frac{2}{5}\)
2 \(\frac{2}{5}\) = 4/5
4 × 12/5 = 48/5
Now convert from improper fraction to the mixed fraction.
48/5 = 9 3/5

Question 11.
5 × 1 \(\frac{7}{8}\) =
_____ \(\frac{□}{□}\)

Answer: 9 3/8

Explanation:
Given,
5 × 1 \(\frac{7}{8}\)
5 × 15/5 = 75/5
Now convert from improper fraction to the mixed fraction.
75/5 = 9 3/8

Question 12.
3 × 3 \(\frac{3}{4}\) =
_____ \(\frac{□}{□}\)

Answer: 11 1/4

Explanation:
Given,
3 × 3 \(\frac{3}{4}\)
3 × 15/4 = 45/4
Now convert from improper fraction to the mixed fraction.
45/4 = 11 1/4

Lesson 8.5

Question 13.
A shrub in Pam’s back yard is about 1 \(\frac{3}{8}\) feet tall. A small tree in her back yard is 7 times as tall as the shrub. About how tall is the tree?
_____ \(\frac{□}{□}\) feet

Answer: 9 5/2 feet.
Explanation:
Given,
A shrub in Pam’s back yard is about 1 \(\frac{3}{8}\) feet tall.
A small tree in her back yard is 7 times as tall as the shrub.
9.625 ft because 1 3/8 × 7 is equal to 9 5/2 feet
Therefore the tree is 9 5/2 feet.

Question 14.
A puppy weighs \(\frac{9}{10}\) pound. Its mother weighs 8 times as much. How much does the mother weigh?
_____ \(\frac{□}{□}\) pounds

Answer: 7 \(\frac{2}{10}\) pounds

Explanation:
Given,
A puppy weighs \(\frac{9}{10}\) pound. Its mother weighs 8 times as much.
\(\frac{9}{10}\) × 8 = 72/10
Convert from improper fraction to the mixed fraction.
72/10 = 7 \(\frac{2}{10}\) pounds
Thus the mother weigh 7 \(\frac{2}{10}\) pounds.

Conclusion:

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Go Math Grade 4 Answer Key Homework Practice FL Chapter 11 Angles

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Lesson: 1 – Angles and Fractional Parts of a Circle

• Common Core – Angles – Page No. 207
• Common Core – Angles Lesson Check – Page No. 208

Lesson: 2 – Degrees

• Common Core – Angles – Page No. 209
• Common Core – Angles Lesson Check – Page No. 210

Lesson: 3 – Measure and Draw Angles

• Common Core – Angles – Page No. 211
• Common Core – Angles Lesson Check – Page No. 212

Lesson: 4 – Join and Separate Angles

• Common Core – Angles – Page No. 213
• Common Core – Angles Lesson Check – Page No. 214

Lesson: 5 – Problem Solving Unknown Angle Measures

• Common Core – Angles – Page No. 215
• Common Core – Angles Lesson Check – Page No. 216

Lesson: 11.1 

• Common Core – Angles – Page No. 217
• Common Core – Angles Lesson Check – Page No. 218

Common Core – Angles – Page No. 207

Angles and Fractional Parts of a Circle

Tell what fraction of the circle the shaded angle represents.

Question 1.

Explanation:
By seeing the above figure we can say that the fraction of the shaded part is \(\frac{1}{4}\)

Question 2.

\(\frac{□}{□}\)

Answer: \(\frac{1}{2}\)

Explanation:
Half of the circle is shaded in the above figure. The fraction of the shaded part is \(\frac{1}{2}\).

Question 3.

\(\frac{□}{□}\)

Answer: \(\frac{1}{1}\)

Explanation:
The above circle is completely shaded. So, the fraction of the shaded part is \(\frac{1}{1}\).

Tell whether the angle on the circle shows a \(\frac{1}{4}, \frac{1}{2}, \frac{3}{4}\), or 1 full turn clockwise or counterclockwise.

Question 4.

\(\frac{□}{□}\)

Answer: \(\frac{1}{2}\)

Explanation:
By seeing the above figure we can say that the circle turns \(\frac{1}{2}\) counterclockwise.

Question 5.

\(\frac{□}{□}\)

Answer: \(\frac{3}{4}\)

Explanation:
By seeing the above figure we can say that the circle turns \(\frac{3}{4}\) counterclockwise.

Question 6.

__________

Answer: \(\frac{1}{1}\)

Explanation:
The above circle turns \(\frac{1}{1}\) counterclockwise.

Problem Solving

Question 7.
Shelley exercised for 15 minutes. Describe the turn the minute hand made.

Type below:
__________

Answer: \(\frac{1}{4}\) Clockwise
The minute hand is on 3 which means the minute hand made \(\frac{1}{4}\) Clockwise.

Question 8.
Mark took 30 minutes to finish lunch. Describe the turn the minute hand made.

Type below:
__________

Answer: \(\frac{1}{2}\) Clockwise
The minute hand is on 6 which means the minute hand made \(\frac{1}{2}\) Clockwise.

Common Core – Angles – Page No. 208

Lesson Check

Question 1.
What fraction of the circle does the shaded angle represent

Options:
a. \(\frac{1}{1}\) or 1
b. \(\frac{3}{4}\)
c. \(\frac{1}{2}\)
d. \(\frac{1}{4}\)

Answer: \(\frac{1}{4}\)

Explanation:
The above figure shows that the fraction of the shaded part is \(\frac{1}{4}\)
Thus the correct answer is option D.

Question 2.
Which describes the turn shown below?

Options:
a. \(\frac{1}{4}\) turn clockwise
b. \(\frac{1}{2}\) turn clockwise
c. \(\frac{1}{4}\) turn counterclockwise
d. \(\frac{1}{2}\) turn counterclockwise

Answer: \(\frac{1}{2}\) turn clockwise

Explanation:
The circle made half turn. The fraction of the circle is \(\frac{1}{2}\) turn clockwise.
Thus the correct answer is option B.

Spiral Review

Question 3.
Which shows \(\frac{2}{3}\) and \(\frac{3}{4}\) written as a pair of fractions with a common denominator?
Options:
a. \(\frac{2}{3} \text { and } \frac{4}{3}\)
b. \(\frac{6}{9} \text { and } \frac{6}{8}\)
c. \(\frac{2}{12} \text { and } \frac{3}{12}\)
d. \(\frac{8}{12} \text { and } \frac{9}{12}\)

Answer: \(\frac{8}{12} \text { and } \frac{9}{12}\)

Explanation:
Given the fraction \(\frac{2}{3}\) and \(\frac{3}{4}\)
LCM of 3 and 4 is 12
\(\frac{2}{3}\) × \(\frac{4}{4}\) = \(\frac{8}{12}\)
\(\frac{3}{4}\) × \(\frac{3}{3}\) = \(\frac{9}{12}\)
Thus the correct answer is option D.

Question 4.
Raymond bought \(\frac{3}{4}\) of a dozen rolls. How many rolls did he buy?
Options:
a. 3
b. 6
c. 7
d. 9

Answer: 9

Explanation:
Given that,
Raymond bought \(\frac{3}{4}\) of a dozen rolls.
\(\frac{3}{4}\) × 12 = 3 × 3 = 9
Thus the correct answer is option D.

Question 5.
Which of the following lists all the factors of 18?
Options:
a. 1, 2, 4, 9, 18
b. 1, 2, 3, 6, 9, 18
c. 2, 3, 6, 9
d. 1, 3, 5, 9, 18

Answer: 1, 2, 3, 6, 9, 18

Explanation:
The factors of 18 are
1 × 18 = 18
2 × 9 = 18
3 × 6 = 18
6 × 3 = 18
9 × 2 = 18
18 × 1 = 18
The factors are 1, 2, 3, 6, 9, 18.
Thus the correct answer is option B.

Question 6.
Jonathan rode 1.05 miles on Friday, 1.5 miles on Saturday, 1.25 miles on Monday, and 1.1 miles on Tuesday. On which day did he ride the shortest distance?
Options:
a. Monday
b. Tuesday
c. Friday
d. Saturday

Answer: Friday

Explanation:
Given that,
Jonathan rode 1.05 miles on Friday, 1.5 miles on Saturday, 1.25 miles on Monday, and 1.1 miles on Tuesday.
1.05 < 1.1 < 1.5
Thus the shortest distance is 1.05 miles that is on Friday.
Thus the correct answer is option C.

Common Core – Angles – Page No. 209

Degrees

Tell the measure of the angle in degrees.

Question 1.

60°

Question 2.

_____°

Answer: 180°

Explanation:
The complete angle of the circle is 360°
The above circle made half turn
1/2 × 360° = 180°

Question 3.

_____°

Answer: 90°

Explanation:
The complete angle of the circle is 360°
The above circle made 1/4 turn.
1/4 × 360° = 90°

Classify the angle. Write acute, obtuse, right, or straight.

Question 4.

__________

Answer: acute

Explanation:
The acute angle is the small angle which is less than 90°. The above angle is 25° which is less than 90°. Thus the above angle is an acute angle.

Question 5.

__________

Answer: obtuse

Explanation:
An obtuse angle has a measurement greater than 90 degrees but less than 180 degrees. The above angle is 110° which is greater than 90° and less than 180°. Thus the angle of the above figure is an obtuse angle.

Question 6.

__________

Answer: acute

Explanation:
The acute angle is the small angle which is less than 90°. The above angle is 60° which is less than 90°. Thus the above angle is an acute angle.

Classify the triangle. Write acute, obtuse, or right.

Question 7.

__________

Answer: right

Explanation:
In geometry and trigonometry, a right angle is an angle of exactly 90°, corresponding to a quarter turn.

Question 8.

__________

Answer: obtuse

Explanation:
An obtuse angle has a measurement greater than 90 degrees but less than 180 degrees. The above angle is 110° which is greater than 90° and less than 180°. Thus the angle of the above figure is an obtuse angle.

Question 9.

__________

Answer: acute

Explanation:
The acute angle is the small angle which is less than 90°. The above triangle is less than 90 degrees. Thus the above triangle is acute.

Problem Solving

Ann started reading at 4:00 P.M. and finished at 4:20 P.M.

Question 10.
Through what fraction of a circle did the minute hand turn?
\(\frac{□}{□}\)

Answer: \(\frac{1}{3}\)

Explanation:
The complete angle of the circle is 360°.
The minute hand is on 4. That means the clock turn 1/3 clockwise.

Question 11.
How many degrees did the minute hand turn?
_____°

Answer: 120°

Explanation:
1/3 × 360° = 120°
Thus the minute hand turn 120°.

Common Core – Angles – Page No. 210

Lesson Check

Question 1.
What kind of angle is shown?

Options:
a. acute
b. obtuse
c. right
d. straight

Answer: straight

Explanation:
180° is nothing but a straight angle.
Thus the correct answer is option D.

Question 2.
How many degrees are in an angle that turns through \(\frac{1}{4}\) of a circle?
Options:
a. 45°
b. 90°
c. 180°
d. 270°

Answer: 90°

Explanation:
The complete angle of the circle is 360°.
\(\frac{1}{4}\) × 360° = 90°
Thus the correct answer is option B.

Spiral Review

Question 3.
Mae bought 15 football cards and 18 baseball cards. She separated them into 3 equal groups. How many sports cards are in each group?
Options:
a. 5
b. 6
c. 11
d. 12

Answer: 11

Explanation:
Given that,
Mae bought 15 football cards and 18 baseball cards. She separated them into 3 equal groups.
The total cards = 15 + 18 = 33 cards
Divide 33 cards into 3 equal groups
33/3 = 11
Thus the correct answer is option C.

Question 4.
Each part of a race is \(\frac{1}{10}\) mile long. Marsha finished 5 parts of the race. How far did Marsha race?
Options:
a. \(\frac{1}{10}\) mile
b. \(\frac{5}{12}\) mile
c. \(\frac{1}{2}\) mile
d. 5 \(\frac{1}{10}\) miles

Answer: \(\frac{1}{2}\) mile

Explanation:
Each part of a race is \(\frac{1}{10}\) mile long. Marsha finished 5 parts of the race.
We have to divide \(\frac{1}{10}\) into 5 parts.
\(\frac{1}{10}\) ÷ 5 = \(\frac{1}{2}\) mile
Thus the correct answer is option C.

Question 5.
Jeff said his city got \(\frac{11}{3}\) inches of snow. Which shows this fraction written as a mixed number?
Options:
a. 3 \(\frac{2}{3}\)
b. 3 \(\frac{1}{3}\)
c. 2 \(\frac{2}{3}\)
d. 1 \(\frac{2}{3}\)

Answer: 3 \(\frac{2}{3}\)

Explanation:
Jeff said his city got \(\frac{11}{3}\) inches of snow.
Convert from improper fraction into the mixed fraction.
\(\frac{11}{3}\) = 3 \(\frac{2}{3}\)
Thus the correct answer is option A.

Question 6.
Amy ran \(\frac{3}{4}\) mile. Which decimal shows how many miles she ran?
Options:
a. 0.25 mile
b. 0.34 mile
c. 0.5 mile
d. 0.75 mile

Answer: 0.75 mile

Explanation:
Given,
Amy ran \(\frac{3}{4}\) mile.
The decimal form of \(\frac{3}{4}\) is 0.75
She ran 0.75 miles.
Thus the correct answer is option D.

Common Core – Angles – Page No. 211

Measure and Draw Angles

Use a protractor to find the angle measure.

Question 1.

m∠ABC= 120°

Question 2.

m∠MNP = _____°

Answer: 90°
By using the protractor we can measure the angle. m∠MNP = 90°

Question 3.

m∠RST = _____°

Answer: 55°
By using the protractor we can measure the angle m∠RST is 55°

Use a protractor to draw the angle.

Question 4.
40°

Answer:

Question 5.
170°

Answer:

Draw an example of each. Label the angle with its measure.

Question 6.
a right angle

Answer:

Question 7.
an acute angle

Answer:

Problem Solving

The drawing shows the angles a stair tread makes with a support board along a wall. Use your protractor to measure the angles.

Question 8.
What is the measure of ∠A?
_____°

Answer: 45°
By using the protractor we can measure the angle ∠A = 45°

Question 9.
What is the measure of ∠B?
_____°

Answer: 135°
By using the protractor we can measure the angle ∠B = 135°

Common Core – Angles – Page No. 212

Lesson Check

Question 1.
What is the measure of ∠ABC?

Options:
a. 15°
b. 25°
c. 155°
d. 165°

Answer: 15°
With the help of the protractor, we can measure the ∠ABC = 15°
The correct answer is option A.

Question 2.
What is the measure of ∠XYZ?

Options:
a. 20°
b. 30°
c. 150°
d. 160°

Answer: 150°
With the help of the protractor, we can measure the ∠XYZ = 150°
The correct answer is option C.

Spiral Review

Question 3.
Derrick earned $1,472 during the 4 weeks he had his summer job. If he earned the same amount each week, how much did he earn each week?
Options:
a. $360
b. $368
c. $3,680
d. $5,888

Answer: $368

Explanation:
Derrick earned $1,472 during the 4 weeks he had his summer job.
Divide 1472 by 4
1472/4 = $368
Therefore he earned $368 each week.
Thus the correct answer is option B.

Question 4.
Arthur baked 1 \(\frac{7}{12}\) dozen muffins. Nina baked 1 \(\frac{1}{12}\) dozen muffins. How many dozen muffins did they bake in all?
Options:
a. 3 \(\frac{2}{3}\)
b. 2 \(\frac{2}{3}\)
c. 2 \(\frac{1}{2}\)
d. \(\frac{6}{12}\)

Answer: 2 \(\frac{2}{3}\)

Explanation:
Arthur baked 1 \(\frac{7}{12}\) dozen muffins.
Nina baked 1 \(\frac{1}{12}\) dozen muffins.
Add both the fraction
1 \(\frac{7}{12}\) + 1 \(\frac{1}{12}\)
First add the whole numbers
1 + 1 = 2
\(\frac{7}{12}\) + \(\frac{1}{12}\) = \(\frac{8}{12}\)
2 \(\frac{8}{12}\) = 2 \(\frac{2}{3}\)
Thus the correct answer is option B.

Question 5.
Trisha drew the figure below. What figure did she draw?

Options:
a. line segment ST
b. ray ST
c. ray TS
d. line TS

Answer: ray TS
The name of the figure Trisha drew is ray TS.
The correct answer is option C.

Question 6.
Which describes the turn shown by the angle?

Options:
a. 1 full turn clockwise
b. \(\frac{3}{4}\) turn clockwise
c. \(\frac{1}{2}\) turn clockwise
d. \(\frac{1}{4}\) turn clockwise

Answer: \(\frac{1}{4}\) turn clockwise

Explanation:
The circle made a turn clockwise with a fraction \(\frac{1}{4}\).
Thus the correct answer is option D.

Common Core – Angles – Page No. 213

Join and Separate Angles

Add to find the measure of the angle. Write an equation to record your work.

Question 1.

50°+75°=125°
m∠ABD=125°

Question 2.

_____° + _____° = _____° ; m∠FGJ = _____°

Answer: 160°

Explanation:
m∠FGH = 140°
m∠HGJ = 20°
m∠FGJ = 140° + 20° = 160°

Question 3.

_____° + _____° + _____° = _____° ; m∠KLN = _____°

Answer: 165°

Explanation:
m∠KLM = 30°
m∠MLP = 90°
m∠PLN = 45°
m∠KLN = 30° + 90° + 45° = 165°

Use a protractor to find the measure of each angle in the circle.

Question 4.
m∠ABC = _____°

Answer: 115°
By using the protractor we can measure m∠ABC = 115°

Question 5.
m∠DBE = _____°

Answer: 90°
By using the protractor we can measure m∠DBE = 90°

Question 6.
m∠CBD = _____°

Answer: 75°
By using the protractor we can measure m∠CBD = 75°

Question 7.
m∠EBA = _____°

Answer: 80°
By using the protractor we can measure m∠EBA = 80°

Question 8.
Write the sum of the angle measures as an equation.
_____° + _____° + _____° + _____° = _____°

Answer: 115° + 75° + 90° + 80° = 360°

Explanation:
m∠ABC + m∠DBE + m∠CBD + m∠EBA
115° + 75° + 90° + 80° = 360°

Problem Solving

Question 9.
Ned made the design at the right. Use a protractor. Find and write the measure of each of the 3 angles.
_____° ; _____° ; _____° ;

Answer: 50°; 60°; 70°
By using the protractor we can measure each of the 3 angles i.e, 50°; 60°; 70°

Question 10.
Write an equation to find the measure of the total angle.
_____° + _____° + _____° = _____°

Answer: 50° + 60° + 70° =180°

Explanation:
Add all the three angles = 50° + 60° + 70° =180°

Common Core – Angles – Page No. 214

Lesson Check

Question 1.
What is the measure of m∠WXZ?

Options:
a. 32°
b. 83°
c. 88°
d. 97°

Answer: 83°

Explanation:
m∠WXY = 58°
m∠ZXY = 25°
m∠WXZ = m∠WXY + m∠ZXY
m∠WXZ = 58° + 25°
m∠WXZ = 83°
Thus the correct answer is option B.

Question 2.
Which equation can you use to find the m∠MNQ?

Options:
a. 148° – 24° = ■
b. 148° × 24° = ■
c. 148° ÷ 24° = ■
d. 148° + 24° = ■

Answer: 148° + 24° = ■

Explanation:
m∠MNQ = m∠MNP + m∠PNQ
m∠MNP + m∠PNQ = 148° + 24°
m∠MNQ = ■
148° + 24° = ■
Thus the correct answer is option D.

Spiral Review

Question 3.
Joe bought 6 packages of envelopes. Each package contains 125 envelopes. How many envelopes did he buy?
Options:
a. 750
b. 723
c. 720
d. 650

Answer: 750

Explanation:
Given,
Joe bought 6 packages of envelopes. Each package contains 125 envelopes.
Multiply the number of packages and number of envelopes
= 6 × 125 = 750
Thus the correct answer is option A.

Question 4.
The Lake Trail is \(\frac{3}{10}\) mile long and the Rock Trail is \(\frac{5}{10}\) long. Bill hiked each trail once. How many miles did he hike in all?
Options:
a. \(\frac{1}{5}\) mile
b. \(\frac{4}{10}\) mile
c. \(\frac{1}{2}\) mile
d. \(\frac{8}{10}\) mile

Answer: \(\frac{8}{10}\) mile

Explanation:
The Lake Trail is \(\frac{3}{10}\) mile long and the Rock Trail is \(\frac{5}{10}\) long.
\(\frac{3}{10}\) + \(\frac{5}{10}\) = \(\frac{8}{10}\) mile
Thus the correct answer is option D.

Question 5.
Ron drew a quadrilateral with 4 right angles and 4 sides with the same length. Which best describes the figure he drew?
Options:
a. square
b. rhombus
c. trapezoid
d. parallelogram

Answer: square

Explanation:
A quadrilateral with 4 right angles and 4 sides with the same length is known as a square.

Question 6.
How many degrees are in an angle that turns through \(\frac{3}{4}\) of a circle?
Options:
a. 45°
b. 90°
c. 180°
d. 270°

Answer: 270°

Explanation:
\(\frac{3}{4}\) of a circle is 3/4 × 360° = 3 × 90° = 270°
Thus the correct answer is option D.

Common Core – Angles – Page No. 215

Problem Solving Unknown Angle Measures
Solve each problem. Draw a diagram to help.

Question 1.

Question 2.
An artist is cutting a piece of metal as shown. What is the angle measure of the piece left over?

x = _____°

Answer: 95°

Explanation:
x  + 130° = 225
x = 225° – 130°
x = 95°

Question 3.
Joan has a piece of material for making a costume. She needs to cut it as shown. What is the angle measure of the piece left over?

x = _____°

Answer: 50°

Explanation:
x + 40° = 90°
x = 90° – 40°
x = 50°

Common Core – Angles – Page No. 216

Lesson Check

Question 1.
Angelo cuts a triangle from a sheet of paper as shown. What is the measure of ∠x in the triangle?

Options:
a. 15°
b. 25°
c. 75°
d. 105°

Answer: 15°

Explanation:
The above figure is a right triangle.
x + 75° = 90°
x = 90° – 75°
x = 15°
Thus the correct answer is option A.

Question 2.
Cindy cuts a piece of wood as shown. What is the angle measure of the piece left over?

Options:
a. 30°
b. 90°
c. 120°
d. 150°

Answer: 120°

Explanation:
x + 90° = 210°
x = 210° – 90
x = 120°
Thus the correct answer is option C.

Spiral Review

Question 3.
Tyronne worked 21 days last month. He earned $79 each day. How much did Tyronne earn last month?
Options:
a. $869
b. $948
c. $1,659
d. $2,169

Answer: $1,659

Explanation:
Given that,
Tyronne worked 21 days last month. He earned $79 each day.
21 × $79 = $1659
Thus the correct answer is option C.

Question 4.
Meg inline skated for \(\frac{7}{10}\) mile. Which shows this distance written as a decimal?
Options:
a. 0.07 mile
b. 0.1 mile
c. 0.7 mile
d. 7.1 miles

Answer: 0.7 mile

Explanation:
Meg inline skated for \(\frac{7}{10}\) mile.
The decimal form of \(\frac{7}{10}\) is 0.7 mile.
Thus the correct answer is option C.

Question 5.
Kerry ran \(\frac{3}{4}\) mile. Sherrie ran \(\frac{1}{2}\) mile. Marcie ran \(\frac{2}{3}\) mile. Which list orders the friends from least to greatest distance
run?
Options:
a. Kerry, Sherrie, Marcie
b. Kerry, Marcie, Sherrie
c. Sherrie, Kerry, Marcie
d. Sherrie, Marcie, Kerry

Answer: Sherrie, Marcie, Kerry

Explanation:
Kerry ran \(\frac{3}{4}\) mile. Sherrie ran \(\frac{1}{2}\) mile. Marcie ran \(\frac{2}{3}\) mile.
Put the fractions from least to greatest.
\(\frac{1}{2}\), \(\frac{2}{3}\), \(\frac{3}{4}\)
Thus the correct answer is option D.

Question 6.
What is the measure of m∠ABC?

Options:
a. 32°
b. 84°
c. 88°
d. 94°

Answer: 84°

Explanation:
m∠ABC = m∠ABD + m∠DBC
m∠ABC = 58° + 26°
m∠ABC = 84°
Thus the correct answer is option B.

Common Core – Angles – Page No. 217

Lesson 11.1

Tell whether the angle on the circle shows \(\frac{1}{4}, \frac{1}{2}, \frac{3}{4}\), or 1 full turn clockwise or counterclockwise.

Question 1.

\(\frac{□}{□}\)

Answer: \(\frac{1}{4}\)

Explanation:
The angle on the above circle shows \(\frac{1}{4}\) turn counterclockwise.

Question 2.

_____

Answer: 1
The angle on the above circle shows 1 full turn clockwise.

Question 3.

\(\frac{□}{□}\)

Answer: \(\frac{1}{2}\)
The angle on the above circle shows \(\frac{1}{2}\) turn clockwise.

Lesson 11.2

Tell the measure of the angle in degrees.

Question 4.

_____

Answer: 90°
The complete angle of the circle = 360°
The fraction of the shaded part is 1/4
1/4 × 360° = 90°

Question 5.

_____

Answer: 130°
The complete angle of the circle = 360°
The fraction of the shaded part is 130/360
130/360 × 360 = 130°

Question 6.

_____

Answer: 270°

Explanation:
The complete angle of the circle = 360°
The fraction of the shaded part is 3/4
3/4 × 360° = 270°

Classify the triangle. Write acute, obtuse, or right.

Question 7.

_____

Answer: Obtuse

Explanation:
An obtuse angle has a measurement greater than 90 degrees but less than 180 degrees. The above angle is 110° which is greater than 90° and less than 180°. Thus the angle of the above figure is an obtuse angle.

Question 8.

_____

Answer: Acute

Explanation:
The acute angle is the small angle which is less than 90°. The above angle is 60° which is less than 90°. Thus the above angle is an acute angle.

Question 9.

_____

Answer: Right

Explanation:
In geometry and trigonometry, a right angle is an angle of exactly 90°, corresponding to a quarter turn.

Common Core – Angles – Page No. 218

Lesson 11.3

Question 1.
Use a protractor to find the angle measure.

m ∠PQR = _____°

Answer: 15°
By using the protractor we can measure the angle m ∠PQR = 15°

Question 2.
Use a protractor to draw an angle with the measure 72º.

Answer:

Lesson 11.4

Add to find the measure of the angle. Write an equation to record your work.

Question 3.

m ∠NML = _____°

Answer: 140°

Explanation:
m ∠NML = m ∠LMX + m ∠NMX
m ∠NML = 50° + 90°
m ∠NML = 140°

Question 4.

m ∠UTS = _____°

Answer: 55°

Explanation:
m ∠UTS = m ∠STX + m ∠UTX
m ∠UTS = 25° + 30°
m ∠UTS = 55°

Question 5.

m ∠HGF = _____°

Answer: 165°

Explanation:
m ∠HGF = m ∠HGX + m ∠HGY + m ∠FGY
m ∠HGF = 45° + 50° + 70° = 165°
m ∠HGF = 165°

Lesson 11.5

Use the diagram for 1–2.

Question 6.
Luke is cutting a board to make a trapezoid for a project. What is the angle measure of the piece left over after Cut A?
x = _____°

Answer: 35°

Explanation:
By seeing the above figure we can find Cut A.
x + 55° = 90°
x = 90° – 55°
x = 35°

Question 7.
What is the angle measure of the piece left over after Cut B?
y = _____°

Answer: 60°

Explanation:
By seeing the above figure we can find Cut B.
70° + y = 130°
y = 130° – 70°
y = 60°

Conclusion:

We wish the data given about Go Math Grade 4 Answer Key Homework Practice FL Chapter 11 Angles helps you a lot. These detailed solutions can explain the concepts more in a simple and concise way. Hence, practicing from the Go Math Grade 4 Answer Key Homework Practice FL Chapter 11 Angles will make students find out the related questions of angles and score the highest marks in the exams.

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Go Math Grade 3 Answer Key Chapter 5 Use Multiplication Facts Extra Practice

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Common Core – Page No. 101000

Lesson 5.1

Describe a pattern for the table. Then complete the table.

Question 1.

Teams	2	3	4	5	6
Players	12	18	24	_________	_________

Answer:

Teams	2	3	4	5	6
Players	12	18	24	30	36

Explanation:

Multiply 6 with a number of tables.
Multiply 6 with 5 teams = 6 × 5 = 30
Multiply 6 with 6 teams = 6 × 6 = 36

Question 2.

Tables	4	5	6	7	8
Chairs	16	20	_________	28	_________

Answer:

Tables	4	5	6	7	8
Chairs	16	20	24	28	32

Explanation:

Multiply 4 with number of tables.
Number of chairs for 6 tables = x
Number of chairs for 8 tables = y
Now multiply number of tables with 4 = 6 × 4 = 24
And then multiply 8 tables with 4 = 8 × 4 = 32
Therefore the missing numbers in the table are 24 and 32

Lesson 5.2

Find the unknown factor.

Question 3.
72 = 9 × t
t = _______

Answer: 8

Explanation:

t × 9 = 72
t = 72/9 = 8
The unknown factor t is 8.

Question 4.
4 × ★ = 28
★ = _______

Answer: 7

Explanation:

4 × ★ = 28
★ = 28/4 = 7
★ = 7

Question 5.
b × 5 = 30
b = _______

Answer: 6

Explanation:

b × 5 = 30
b = 30/5 = 6
Thus the unknown factor b is 6.

Question 6.
d × 3 = 24
d = _______

Answer: 8

Explanation:

d × 3 = 24
d = 24/3 = 8
Therefore the unknown factor d is 8.

Question 7.
48 = 8 × p
p = _______

Answer: 6

Explanation:

8 × p = 48
p = 48/8
p = 6
Thus the unknown factor p is 6.

Question 8.
6 × ▲ = 24
▲= _______

Answer: 4

6 × ▲= 24
▲= 24/6
▲= 4
So the unknown factor▲is 4.

Question 9.
56 = 7 × ■
■ = _______

Answer: 8

Explanation:

7 × ■ = 56
■ = 56/7
7 divides 56 eight times.
So the unknown factor ■ is 8.

Question 10.
2 × g = 20
g = _______

Answer: 10

Explanation:

2 × g = 20
g = 20/2 = 10
Therefore the unknown factor g is 10.

Question 11.
h × 7 = 35
h = _______

Answer: 5

Explanation:

h × 7 = 35
h = 35/7
h = 5
Thus the unknown factor h is 5.

Question 12.
9 = 9 × a
a = _______

Answer: 1

Explanation:

9 × a = 9
a = 9/9
a = 1
So the unknown factor a is 1.

Question 13.
c × 4 = 36
c = _______

Answer: 9

Explanation:

c × 4 = 36
c = 36/4
4 divides 36 nine times.
c = 9
Therefore the unknown factor is 9.

Question 14.
5 × y = 40
y = _______

Answer: 8

Explanation:

5 × y = 40
y = 40/5
y = 8
Thus the unknown factor is 8.

Common Core – Page No. 102000

Lesson 5.3

Solve.

Question 1.
Hailey plants 6 rows of marigolds. Each row has 20 marigolds. How many marigolds does Hailey plant in all?
_______ marigolds

Answer: 120

Explanation:

Given that, Hailey plants 6 rows of marigolds.
Each row contains 20 marigolds.
Total number of marigolds that Hailey planted in all = x
x = 20 × 6 = 120
Therefore Hailey planted 120 marigolds.

Question 2.
A meeting room has 8 rows of chairs. Each row has 10 chairs. The first people to arrive fill 2 rows. How many chairs are not filled?
_______ chairs

Answer: 60

Explanation:

Given, A meeting room has 8 rows of chairs.
Each row has 10 chairs.
Total number of chairs = 8 × 10 = 80 chairs
The first people to arrive fill 2 rows.
That means 2 × 10 = 20 chairs
Number of chairs that are not filled = total number of chairs – number of filled chairs
= 80 – 20 = 60 chairs.

Lesson 5.4

Question 3.
1. Use a number line to find the product.

4 × 30 = _______

Answer: 120

Step 1:

Starts at 0.

Step 2:

Make a jump of 30s until you reach 120.

Step 3:

Count the number of jumps till you reach 120.
Number of jumps = 4
4 × 30 = 120

Use place value to find the product.

Question 4.
40 × 8 = _______ tens × 8
= _______ tens = _______

Answer:

i. 4
ii. 32
iii. 320

Explanation:

4 × tens = 4 tens = 40
4 tens × 8 = 32 tens
32 tens = 32 × 10 = 320

Question 5.
5 × 60 = 5 × _______ tens
= _______ tens = _______

Answer:

i. 6
ii. 30 tens
iii. 300

Explanation:

60 = 6 × tens = 6 tens
5 × 6 tens = 30 tens
30 tens = 30 × 10 = 300

Lesson 5.5

Find the product.

Question 6.
9 0
× 3
——
_______

Answer: 270

Explanation:

First multiply 3 with ones = 3 × 0 = 0
Next multiply 3 with tens = 3 × 90 = 270
So the product of 90 and 3 is 270.

Question 7.
5 0
× 8
——
_______

Answer: 400

Explanation:

First multiply 8 with ones = 8 × 0 = 0
Now multiply 8 with tens = 8 × 50 = 400
The product of 50 and 8 is 400.

Question 8.
7 0
× 9
——
_______

Answer: 630

Explanation:

Multiply 9 with ones = 9 × 0 = 0
Multiply 9 with tens = 9 × 70 = 630
The product of 9 and 70 is 630.

Question 9.
8 0
× 7
——
_______

Answer: 560

Explanation:

Multiply 7 with ones = 7 × 0 = 0
And then multiply 7 with tens = 7 × 80 = 560
Thus the product of 80 and 7 is 560.

Solve.

Question 10.
During the summer, Jayden volunteers at the library for 20 hours each week for 7 weeks. How many hours does Jayden volunteer in all?
_______ hours

Answer: 140 hours

Explanation:

During the summer, Jayden volunteers at the library for 20 hours each week for 7 weeks.
For each week he worked 20 hours
Number of hours he worked for 7 weeks = y
y = 7 × 20 = 140 hours
Therefore Jayden volunteers at the library for 20 hours.

Question 11.
Trisha teaches 8 different cooking classes. There are 20 students in each class. How many students in all are in Trisha’s cooking classes?
_______ students

Answer: 160 students

Explanation:

Given,
Trisha teaches 8 different cooking classes.
There are 20 students in each class.
Total number of students = number of classes × number of students in each class
= 8 × 20 = 160 students.
Therefore the total number of students in all the cooking classes area 120.

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Grade 3 Go Math Answer Key Chapter 9 Compare Fractions Extra Practice

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Common Core – Page No. 189000

Lesson 9.1

Solve. Show your work.

Question 1.
Nick finished \(\frac{4}{8}\) of his homework before dinner. Ed finished \(\frac{7}{8}\) of his homework before dinner. Who finished the greater part of his homework?

_____

Answer: Ed

Explanation:

Compare the fractions \(\frac{4}{8}\) and \(\frac{7}{8}\)
The denominator of both the fractions is the same. So, compare the numerators.
The numerator with the greatest number will be the greatest fraction.
7 is greater than 4.
\(\frac{7}{8}\) > \(\frac{4}{8}\)
Therefore Ed finished the greater part of his homework.

Question 2.
Rafael walked \(\frac{2}{3}\) mile and then rode his scooter \(\frac{2}{6}\) mile. Which distance is farther?

\(\frac{□} {□}\) mile is farther

Answer: \(\frac{2}{3}\)

Explanation:

Rafael walked \(\frac{2}{3}\) mile and then rode his scooter \(\frac{2}{6}\) mile.
The numerator of both the fractions is the same but the denominators are different.
The fraction is smaller if the denominator is greater.
Thus \(\frac{2}{3}\) > \(\frac{2}{6}\)
\(\frac{2}{3}\) mile is farther.

Lessons 9.2–9.3

Compare. Write <, >, or =.

Question 3.
\(\frac{2}{6}\) _____ \(\frac{3}{6}\)

Answer: \(\frac{2}{6}\) < \(\frac{3}{6}\)

Explanation:

Compare the fractions \(\frac{2}{6}\) and \(\frac{3}{6}\)
The denominators are the same and the numerators are different.
So compare the numerators of two fractions.
2 is less than 3.
So, \(\frac{2}{6}\) < \(\frac{3}{6}\)

Question 4.
\(\frac{6}{8}\) _____ \(\frac{1}{8}\)

Answer: \(\frac{6}{8}\) > \(\frac{1}{8}\)

Explanation:

Compare \(\frac{6}{8}\) and \(\frac{1}{8}\)
The denominators are the same and the numerators are different.
6 is greater than 1.
\(\frac{6}{8}\) > \(\frac{1}{8}\)

Question 5.
\(\frac{3}{8}\) _____ \(\frac{3}{4}\)

Answer: \(\frac{3}{8}\) < \(\frac{3}{4}\)

Explanation:

Compare the fractions \(\frac{3}{8}\) and \(\frac{3}{4}\)
The numerators are the same and denominators are different.
Compare the denominators of two fractions.
The fraction with lesser number will be the greatest.
\(\frac{3}{8}\) < \(\frac{3}{4}\)

Question 6.
\(\frac{1}{6}\) _____ \(\frac{1}{8}\)

Answer: \(\frac{1}{6}\) > \(\frac{1}{8}\)

Explanation:

The numerator of both the fractions is the same.
The denominator with the greatest number will be the smallest fraction.
So, \(\frac{1}{6}\) > \(\frac{1}{8}\)

Question 7.
\(\frac{2}{3}\) _____ \(\frac{2}{6}\)

Answer: \(\frac{2}{3}\) > \(\frac{2}{6}\)

Explanation:

The numerator of both the fractions is the same.
The denominator with the greatest number will be the smallest fraction.
\(\frac{2}{3}\) > \(\frac{2}{6}\)

Question 8.
\(\frac{1}{8}\) _____ \(\frac{3}{8}\)

Answer: \(\frac{1}{8}\) < \(\frac{3}{8}\)

Explanation:

The denominator of both the fractions is the same.
So, compare the numerators. The fraction with the small number will be the smallest fraction.
\(\frac{1}{8}\) < \(\frac{3}{8}\)

Lesson 9.4

Compare. Write <, >, or = . Write the strategy you used.

Question 9.
\(\frac{2}{8}\) _____ \(\frac{2}{3}\)

Answer: \(\frac{2}{8}\) < \(\frac{2}{3}\)

Explanation:

The numerator of both the fractions is the same.
Compare the denominators.
The denominator with the greatest number will be the smallest fraction.
\(\frac{2}{8}\) < \(\frac{2}{3}\)

Question 10.
\(\frac{5}{6}\) _____ \(\frac{1}{6}\)

Answer: \(\frac{5}{6}\) > \(\frac{1}{6}\)

Explanation:

The denominator of both the fractions is the same.
The fraction with the small number will be the smallest fraction.
5 is greater than 1.
\(\frac{5}{6}\) > \(\frac{1}{6}\)

Question 11.
\(\frac{7}{8}\) _____ \(\frac{3}{4}\)

Answer: \(\frac{7}{8}\) > \(\frac{3}{4}\)

Explanation:

Compare \(\frac{7}{8}\) and \(\frac{3}{4}\)
Make the denominators equal to compare the fractions.
\(\frac{3}{4}\) × \(\frac{8}{8}\) = \(\frac{24}{32}\)
\(\frac{7}{8}\) × \(\frac{4}{4}\) = \(\frac{28}{32}\)
\(\frac{28}{32}\) > \(\frac{24}{32}\)
\(\frac{7}{8}\) > \(\frac{3}{4}\)

Common Core – Page No. 190000

Lesson 9.5

Write the fractions in order from greatest to least.

Question 1.
\(\frac{1}{2}, \frac{1}{4}, \frac{1}{3}\)
Type below:
__________

Answer: \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\)

Explanation:

The numerator of the three fractions is the same.
So, the order from greatest to least is \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\)

Question 2.
\(\frac{4}{6}, \frac{1}{6}, \frac{2}{6}\)
Type below:
__________

Answer: \(\frac{4}{6}, \frac{2}{6}, \frac{1}{6}\)

Explanation:

The denominator of the three fractions is the same.
Compare the numerator of the fraction.
4 > 2 > 1
\(\frac{4}{6}, \frac{2}{6}, \frac{1}{6}\)

Question 3.
\(\frac{3}{6}, \frac{3}{4}, \frac{3}{8}\)
Type below:
__________

Answer: \(\frac{3}{4}, \frac{3}{6}, \frac{3}{8}\)

Explanation:

The numerator of the three fractions is the same.
So, the order is \(\frac{3}{4}, \frac{3}{6}, \frac{3}{8}\)

Question 4.
\(\frac{6}{8}, \frac{3}{8}, \frac{5}{8}\)
Type below:
__________

Answer: \(\frac{6}{8}, \frac{5}{8}, \frac{3}{8}\)

Explanation:

The denominator of the three fractions is the same.
Compare the numerator and write the order from greatest to least fraction.
\(\frac{6}{8}, \frac{5}{8}, \frac{3}{8}\)

Lessons 9.6–9.7

Shade the model. Then divide the pieces to find the equivalent fraction.

Question 5.

\(\frac{1}{4}=\frac{■}{8}\)
\(\frac{1}{4}\) = \(\frac{□} {□}\)

Answer: \(\frac{1}{4}\) = \(\frac{2} {8}\)

Explanation:

\(\frac{1}{4}\) = \(\frac{2} {8}\)

Question 6.

\(\frac{2}{3}=\frac{■}{6}\)
\(\frac{2}{3}\) = \(\frac{□} {□}\)

Answer: \(\frac{2}{3}\) = \(\frac{4} {6}\)

Explanation:

\(\frac{2}{3}\) = \(\frac{4} {6}\)

Use the number line to find the equivalent fraction.

Question 7.

\(\frac{1}{2}=\frac{■}{8}\)
\(\frac{1}{2}\) = \(\frac{□} {□}\)

Answer: \(\frac{1}{2}\) = \(\frac{4} {8}\)

Explanation:

Question 8.

\(\frac{2}{2}=\frac{■}{6}\)
\(\frac{2}{2}\) = \(\frac{□} {□}\)

Answer: \(\frac{2}{2}\) = \(\frac{6} {6}\)

Explanation:

Each shape is 1 whole. Shade the model to find the equivalent fraction.

Question 9.

\(\frac{3}{4}=\frac{■}{8}\)
\(\frac{3}{4}\) = \(\frac{□} {□}\)

Answer: \(\frac{3}{4}\) = \(\frac{6} {8}\)

Explanation:

\(\frac{3}{4}\) = \(\frac{6} {8}\)

Question 10.

\(\frac{1}{2}=\frac{■}{6}\)
\(\frac{1}{2}\) = \(\frac{□} {□}\)

Answer: \(\frac{1}{2}\) = \(\frac{3} {6}\)

Explanation:

\(\frac{1}{2}\) = \(\frac{3} {6}\)

Conclusion

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3rd Grade Go Math Answer Key Chapter 9 Compare Fractions

You will have topics like Comparing Fractions with the Same Numerator and Denominators, Equivalent Fractions, Compare and order fractions, and so on. You will not feel the Concept of Comparing Fractions difficult anymore with our HMH Go Math Grade 3 Answer Key Chapter 9 Compare Fractions. Make the most out of the 3rd Grade Go Math Solution Key Chapter 9 and solve various questions in it and master the subject.

Lesson 1: Compare Fractions 

• Compare Fractions – Page No. 509
• Compare Fractions Lesson Check – Page No. 510

Lesson 2: Problem Solving • Compare Fractions 

• Problem Solving Compare Fractions – Page No. 511
• Problem Solving Compare Fractions Lesson Check – Page No. 512

Lesson 3: Compare Fractions with the Same Denominator 

• Compare Fractions with the Same Denominator – Page No. 517
• Compare Fractions with the Same Denominator Lesson Check – Page No. 518

Lesson 4: Compare Fractions with the Same Numerator 

• Compare Fractions with the Same Numerator – Page No. 523
• Compare Fractions with the Same Numerator Lesson Check – Page No. 524

Lesson 5: Compare Fractions 

• Compare Fractions – Page No. 529
• Compare Fractions Lesson Check – Page No. 530

Mid -Chapter Checkpoint

• Mid -Chapter Checkpoint – Page No. 531
• Mid -Chapter Checkpoint Lesson Check – Page No. 532

Lesson 6: Compare and Order Fractions

• Compare and Order Fractions – Page No. 537
• Compare and Order Fractions Lesson Check – Page No. 538

Lesson 7: Model Equivalent Fractions 

• Model Equivalent Fractions – Page No. 543
• Model Equivalent Fractions Lesson Check – Page No. 544

Lesson 9.7 – Page No. 548

Lesson 9: Equivalent Fractions 

• Equivalent Fractions – Page No. 549
• Equivalent Fractions Lesson Check – Page No. 550

Review/ Test

• Review/Test – Page No. 551
• Review/Test – Page No. 552
• Review/Test – Page No. 553
• Review/Test – Page No. 554
• Review/Test – Page No. 555
• Review/Test – Page No. 556

Compare Fractions – Page No. 509

Share and Show

Question 1.
At the park, people can climb a rope ladder to its top. Rosa climbed \(\frac{2}{8}\) of the way up the ladder. Justin climbed \(\frac{2}{6}\) of the way up the ladder. Who climbed higher on the rope ladder?
First, what are you asked to find?
Type below:
____________

Answer: Justin climbed higher on the rope ladder.

Explanation:

Given,
Rosa climbed \(\frac{2}{8}\) of the way up the ladder
Justin climbed \(\frac{2}{6}\) of the way up the ladder
We are asked to find who climbed higher on the rope ladder
By comparing the denominators we can say that Justin Climbed higher than Rosa on the rope ladder.

Question 2.
Then, model and compare the fractions.
Type below:
____________

Answer:

Question 3.
Last, find the greater fraction.
\(\frac{2}{6}\) _____ \(\frac{2}{8}\)

Answer: \(\frac{2}{6}\) > \(\frac{2}{8}\)

Explanation:

When comparing fractions such as \(\frac{2}{8}\) and \(\frac{2}{6}\), you could also convert the fractions (if necessary) so they have the same denominator and then compare which numerator is larger.

Question 4.
___________ climbed higher on the rope ladder

Answer: Justin climbed higher on the rope ladder.

Question 5.
What if Cara also tried the rope ladder and climbed \(\frac{2}{4}\) of the way up? Who climbed highest on the rope ladder: Rosa, Justin, or Cara? Explain how you know.
___________

Answer: If Cara also tried the rope ladder and climbed \(\frac{2}{4}\) of the way up then Cara would be climbed highest on the rope ladder.
Because comparing fractions \(\frac{2}{4}\), \(\frac{2}{6}\), \(\frac{2}{8}\) Cara climbed high among the three. The fraction \(\frac{2}{4}\) is the greater than other 2 fractions. So by seeing this we can say that Cara climbed hhighest on the rope ladder.

Compare Fractions – Page No. 510

Use the table for 4–5.

Question 1.
Suri is spreading jam on 8 biscuits for breakfast. The table shows the fraction of biscuits spread with each jam flavor. Which flavor did Suri use on the most biscuits?
___________

Answer: Raspberry

Explanation:

The above table shows the fraction of jam frosted on the biscuits.
First, check the denominators to compare the fractions.
The denominators are the same. So, Compare with the numerators. The numerator of Raspberry is larger than other two flavors. So, Suri used Raspberry flavor on the most biscuits.

Question 2.
What’s the Question? The answer is strawberry
Type below:
___________

Answer:

Suri is spreading jam on 8 biscuits for breakfast. The table shows the fraction of biscuits spread with each jam flavor. She frosted \(\frac{3}{8}\) of the biscuits with peach jam, \(\frac{4}{8}\) with raspberry jam, and \(\frac{1}{8}\) with strawberry jam. Which flavor of jam did Suri use least on the biscuits?

Question 3.
Suppose Suri had also used plum jam on the biscuits. She frosted \(\frac{1}{2}\) of the biscuits with peach jam, \(\frac{1}{4}\) with raspberry jam, \(\frac{1}{8}\) with strawberry jam, and \(\frac{1}{8}\) with plum jam. Which flavor of jam did Suri use on the most biscuits?
___________

Answer: Peach

Explanation:

The fraction of peach jam is greater than raspberry jam, strawberry jam, and plum jam.
So, the answer is the peach jam.

Question 4.
Ms. Gordon has many snack bar recipes. One recipe uses \(\frac{1}{3}\) cup oatmeal, \(\frac{1}{4}\) vcup of milk, and \(\frac{1}{2}\) cup flour. Which ingredient will Ms. Gordon use the most of?
___________

Answer: flour

\(\frac{1}{2}\) > \(\frac{1}{3}\) and \(\frac{1}{4}\)
So, by comparing fractions we can say that Ms. Gordon use the most of flour for snack bar recipes.

Question 5.
Rick lives \(\frac{4}{6}\) mile from school. Noah lives \(\frac{3}{6}\) mile from school. Use the fractions and symbols to show which distance is longer.

\(\frac{4}{6}\) _____ \(\frac{3}{6}\)

Answer: \(\frac{4}{6}\) > \(\frac{3}{6}\)

Explanation:

First of all, compare the denominators. If the denominators are the same then check the numerators.
Here 4 is greater than 3. So, \(\frac{4}{6}\) > \(\frac{3}{6}\)

Problem Solving Compare Fractions – Page No. 511

Solve.

Question 1.
Luis skates \(\frac{2}{3}\) mile from his home to school. Isabella skates \(\frac{2}{4}\) mile to get to school. Who skates farther?
Think: Use fraction strips to act it out.
Luis

Answer: Luis

Explanation:

Given,
Luis skates \(\frac{2}{3}\) mile from his home to school.
Isabella skates \(\frac{2}{4}\) mile to get to school.
To find Who stakes farther we have to compare the fractions.
\(\frac{2}{3}\), \(\frac{2}{4}\)
The numerator of both the fractions is the same and the denominators are different.
So, first, make the denominators equal.
\(\frac{2}{3}\) × \(\frac{4}{4}\) = \(\frac{8}{12}\)
\(\frac{2}{4}\) × \(\frac{3}{3}\) = \(\frac{6}{12}\)
Now denominators are same.
Compare fractions \(\frac{8}{12}\) and \(\frac{6}{12}\)
8 is greater than 6. So, \(\frac{8}{12}\) > \(\frac{6}{12}\)
Therefore Luis Skates farther to school.

Question 2.
Sandra makes a pizza. She puts mushrooms on \(\frac{2}{8}\) of the pizza. She adds green peppers to \(\frac{5}{8}\) of the pizza. Which topping covers more of the pizza?
___________

Answer: Green Peppers

Explanation:

Sandra makes a pizza. She puts mushrooms on \(\frac{2}{8}\) of the pizza.
She adds green peppers to \(\frac{5}{8}\) of the pizza.
Compare the fractions of mushrooms and green peppers.
\(\frac{2}{8}\), \(\frac{5}{8}\)
The denominators are the same. So compare the numerators.
2 is lesser than 5. Thus \(\frac{2}{8}\) < \(\frac{5}{8}\)
Thus Green Peppers covers more of the pizza.

Question 3.
The jars of paint in the art room have different amounts of paint. The green paint jar is \(\frac{4}{8}\) full. The purple paint jar is \(\frac{4}{6}\) full. Which paint jar is less full?
The _______ paint jar

Answer: The green paint jar

Explanation:

The jars of paint in the art room have different amounts of paint.
The green paint jar is \(\frac{4}{8}\) full.
The purple paint jar is \(\frac{4}{6}\) full.
The numerators of both the fractions are the same.
Compare the denominators of green paint and purple paint jars.
The denominator with the greatest number will be the smallest fraction.
Therefore \(\frac{4}{8}\) < \(\frac{4}{6}\)
Thus green paint jar is less full.

Question 4.
Jan has a recipe for bread. She uses \(\frac{2}{3}\) cup of flour and \(\frac{1}{3}\) cup of chopped onion. Which ingredient does she use more of, flour or onion?
_______

Answer: Flour

Explanation:

Jan has a recipe for bread. She uses \(\frac{2}{3}\) cup of flour and \(\frac{1}{3}\) cup of chopped onion.
Compare the fraction of flour and onion.
The denominators of both the fractions are the same. So, compare the numerators.
2 is greater than 1. Thus \(\frac{2}{3}\) > \(\frac{1}{3}\)
That means Jan used more flour for bread.

Question 5.
Edward walked \(\frac{3}{4}\) mile from his home to the park. Then he walked \(\frac{2}{4}\) mile from the park to the library. Which distance is shorter?
_______

Answer: \(\frac{2}{4}\) mile

Explanation:

Edward walked \(\frac{3}{4}\) mile from his home to the park.
Then he walked \(\frac{2}{4}\) mile from the park to the library.
To find the shorter distance we have to compare the fractions of Edward from home to park and from park to library.
\(\frac{3}{4}\), \(\frac{2}{4}\)
The denominators of both the fractions are the same.
So compare the numerators.
3 is greater than 2. Thus \(\frac{3}{4}\) > \(\frac{2}{4}\)
Thus the distance from the park to the library is shorter.

Problem Solving Compare Fractions – Page No. 512

Lesson Check

Question 1.
Ali and Jonah collect seashells in identical buckets. When they are finished, Ali’s bucket is \(\frac{2}{6}\) full and Jonah’s bucket is \(\frac{3}{6}\) full. Which of the following correctly compares the fractions?
Options:
a. \(\frac{2}{6}\) = \(\frac{3}{6}\)
b. \(\frac{2}{6}\) > \(\frac{3}{6}\)
c. \(\frac{3}{6}\) < \(\frac{2}{6}\)
d. \(\frac{3}{6}\) > \(\frac{2}{6}\)

Answer: \(\frac{3}{6}\) > \(\frac{2}{6}\)

Explanation:

Given that, Ali and Jonah collect seashells in identical buckets.
When they are finished, Ali’s bucket is \(\frac{2}{6}\) full and Jonah’s bucket is \(\frac{3}{6}\) full
Compare fractions \(\frac{2}{6}\) and \(\frac{3}{6}\)
We observe that the denominators are the same. So, compare the numerators of both the fractions.
3 is greater than 2.
Thus \(\frac{3}{6}\) > \(\frac{2}{6}\)
So, the correct answer is option D.

Question 2.
Rosa paints a wall in her bedroom. She puts green paint on \(\frac{5}{8}\) of the wall and blue paint on \(\frac{3}{8}\) of the wall. Which of the following correctly compares the fractions?
Options:
a. \(\frac{5}{8}\) > \(\frac{3}{8}\)
b. \(\frac{5}{8}\) < \(\frac{3}{8}\)
c. \(\frac{3}{8}\) > \(\frac{5}{8}\)
d. \(\frac{3}{8}\) = \(\frac{5}{8}\)

Answer: \(\frac{5}{8}\) > \(\frac{3}{8}\)

Explanation:

Given:
Rosa paints a wall in her bedroom.
She puts green paint on \(\frac{5}{8}\) of the wall and blue paint on \(\frac{3}{8}\) of the wall.
The denominators are same so compare the numerators of both the fractions.
5 is greater than 3. So, \(\frac{5}{8}\) > \(\frac{3}{8}\)
Thus the correct answer is option A.

Spiral Review

Question 3.
Dan divides a pie into eighths. How many equal parts are there?
Options:
a. 3
b. 6
c. 8
d. 10

Answer: 8

Dan divides a pie into eighths.
Eighths are nothing but the name of the parts. Eighths is equal to 8.
So, the correct answer is option C.

Question 4.
Which shows equal parts?
a.
b.
c.
d.

Answer:

Explanation:

Among all the figures circle is equally divided into 6 parts.
So, the answer is option B.

Question 5.
Charles places 30 pictures on his bulletin board in 6 equal rows. How many pictures are in each row?
Options:
a. 3
b. 4
c. 5
d. 6

Answer: 5

Explanation:

Given, Charles places 30 pictures on his bulletin board in 6 equal rows.
Number of pictures in each row = x
x × 6 = 30
x = 30/6 = 5
Therefore there are 5 pictures in each row.

Question 6.
Which of the following describes a pattern in the table?

Options:
a. Add 1.
b. Add 4.
c. Multiply by 2.
d. Multiply by 5.

Answer: Multiply by 5

Explanation:

The above table shows that number of tables is multiplied by 5.
So, the correct answer is option D.

Compare Fractions with the Same Denominator – Page No. 517

Compare. Write <, >, or =.

Question 1.

Answer: \(\frac{3}{4}\) > \(\frac{1}{4}\)

Explanation:

Check whether the denominators of the two fractions are the same.
Here the denominators of \(\frac{3}{4}\) and \(\frac{1}{4}\) are same. So compare the numerators.
3 is greater than 1.
Therefore, \(\frac{3}{4}\) > \(\frac{1}{4}\)

Question 2.
\(\frac{3}{6}\) ______ \(\frac{0}{6}\)

Answer: \(\frac{3}{6}\) > \(\frac{0}{6}\)

Explanation:

First, check whether the denominators of the two fractions are the same or not.
After that compare the numerators.
3 > 0
So, \(\frac{3}{6}\) > \(\frac{0}{6}\)

Question 3.
\(\frac{1}{2}\) ______ \(\frac{1}{2}\)

Answer: \(\frac{1}{2}\) = \(\frac{1}{2}\)

Explanation:

First, compare fractions with the same denominators.
If both are the same, then compare the numerators of both fractions.
The denominators and numerators are same for \(\frac{1}{2}\)
Thus \(\frac{1}{2}\) = \(\frac{1}{2}\)

Question 4.
\(\frac{5}{6}\) ______ \(\frac{6}{6}\)

Answer: \(\frac{5}{6}\) < \(\frac{6}{6}\)

Explanation:

Compare the denominators of the fractions
The denominators of \(\frac{5}{6}\) and \(\frac{6}{6}\)
Now compare the numerators of the fractions.
5 < 6
So, \(\frac{5}{6}\) < \(\frac{6}{6}\)

Question 5.
\(\frac{7}{8}\) ______ \(\frac{5}{8}\)

Answer: \(\frac{7}{8}\) > \(\frac{5}{8}\)

Explanation:

Check whether the denominators are the same or not.
The denominator of \(\frac{7}{8}\) and \(\frac{5}{8}\) are same.
Now check the numerators 7 > 5.
Thus \(\frac{7}{8}\) > \(\frac{5}{8}\)

Question 6.
\(\frac{2}{3}\) ______ \(\frac{2}{3}\)

Answer: \(\frac{2}{3}\) = \(\frac{2}{3}\)

Explanation:

Compare the denominators of 2 fractions.
Here numerators and denominators are the same.
So, \(\frac{2}{3}\) = \(\frac{2}{3}\)

Question 7.
\(\frac{8}{8}\) ______ \(\frac{0}{8}\)

Answer: \(\frac{8}{8}\) > \(\frac{0}{8}\)

Explanation:

Check whether the denominators are the same. Now compare the numerators of two fractions.
8 > 0.
So, \(\frac{8}{8}\) > \(\frac{0}{8}\)

Question 8.
\(\frac{1}{6}\) ______ \(\frac{1}{6}\)

Answer: \(\frac{1}{6}\) = \(\frac{1}{6}\)

Explanation:

When the denominators are the same, the whole is divided into the same size pieces. Now compare the numerators of both the fractions.
\(\frac{1}{6}\) = \(\frac{1}{6}\)

Question 9.
\(\frac{3}{4}\) ______ \(\frac{2}{4}\)

Answer: \(\frac{3}{4}\) > \(\frac{2}{4}\)

Explanation:

Check whether the denominators are the same. If same that means the whole is divided into the same size pieces.
The denominators of \(\frac{3}{4}\) and \(\frac{2}{4}\)
Now compare the numerators of both fractions.
3 is greater than 2.
Thus \(\frac{3}{4}\) > \(\frac{2}{4}\)

Question 10.
\(\frac{1}{6}\) ______ \(\frac{2}{6}\)

Answer: \(\frac{1}{6}\) < \(\frac{2}{6}\)

Explanation:

Check whether the denominators are the same. If same that means the whole is divided into the same size pieces.
The denominators of \(\frac{1}{6}\) and \(\frac{2}{6}\)
Now check the numerators 1 is less than 2.
Therefore, \(\frac{1}{6}\) < \(\frac{2}{6}\)

Question 11.
\(\frac{1}{2}\) ______ \(\frac{0}{2}\)

Answer: \(\frac{1}{2}\) > \(\frac{0}{2}\)

Explanation:

When the denominators are same, the whole is divided into the same pieces. Now check the numerators.
1 is greater than 0
Thus \(\frac{1}{2}\) > \(\frac{0}{2}\)

Question 12.
\(\frac{3}{8}\) ______ \(\frac{3}{8}\)

Answer: \(\frac{3}{8}\) = \(\frac{3}{8}\)

Explanation:

Check the denominators of two fractions. If both are equal then compare the numerators.
The numerators of both fractions are equal.
So, \(\frac{3}{8}\) = \(\frac{3}{8}\)

Question 13.
\(\frac{1}{4}\) ______ \(\frac{4}{4}\)

Answer: \(\frac{1}{4}\) < \(\frac{4}{4}\)

Explanation:

Compare fractions with the same denominators.
The denominators of \(\frac{1}{4}\) and \(\frac{4}{4}\) are same.
Compare numerators 1 and 4.
1 is less than 4.
Thus \(\frac{1}{4}\) < \(\frac{4}{4}\)

Question 14.
\(\frac{5}{8}\) ______ \(\frac{4}{8}\)

Answer: \(\frac{5}{8}\) > \(\frac{4}{8}\)

Explanation:

Check whether the denominators are the same or not.
Now compare the numerators.
5 is greater than 4.
\(\frac{5}{8}\) > \(\frac{4}{8}\)

Question 15.
\(\frac{4}{6}\) ______ \(\frac{6}{6}\)

Answer: \(\frac{4}{6}\) < \(\frac{6}{6}\)

Explanation:

Check whether the denominators of both the fractions are the same or not.
The denominators of \(\frac{4}{6}\) and \(\frac{6}{6}\) are the same.
Now compare the numerators 4 and 6.
4 is lesser than 6. So, \(\frac{4}{6}\) < \(\frac{6}{6}\)

Problem Solving

Question 16.
Ben mowed \(\frac{5}{6}\) of his lawn in one hour. John mowed \(\frac{4}{6}\) of his lawn in one hour. Who mowed less of his lawn in one hour?
___________

Answer: John

Explanation:

Given,
Ben mowed \(\frac{5}{6}\) of his lawn in one hour.
John mowed \(\frac{4}{6}\) of his lawn in one hour.
Compare the denominators of both the fractions.
As the denominators are the same compare the numerators of the fractions.
4 is less than 5.
\(\frac{4}{6}\) < \(\frac{5}{6}\)
So, John mowed less of his lawn in one hour.

Question 17.
Darcy baked 8 muffins. She put blueberries in \(\frac{5}{8}\) of the muffins. She put raspberries in \(\frac{3}{8}\) of the muffins. Did more muffins have blueberries or raspberries?
___________

Answer: Blueberries

Explanation:

Given,
Darcy baked 8 muffins.
She put blueberries in \(\frac{5}{8}\) of the muffins.
She put raspberries in \(\frac{3}{8}\) of the muffins.
\(\frac{5}{8}\) is greater than \(\frac{3}{8}\)
Thus there are more blueberries in muffins.

Compare Fractions with the Same Denominator – Page No. 518

Lesson Check

Question 1.
Julia paints \(\frac{2}{6}\) of a wall in her room white. She paints more of the wall green. Which fraction could show the part of the wall that is green?
Options:
a. \(\frac{1}{6}\)
b. \(\frac{2}{6}\)
c. \(\frac{3}{6}\)
d. \(\frac{0}{6}\)

Answer: \(\frac{3}{6}\)

Explanation:

First compare the denominators of given options and then compare the numerators
A. \(\frac{3}{6}\) < \(\frac{2}{6}\)
B. \(\frac{2}{6}\) = \(\frac{2}{6}\)
C. \(\frac{3}{6}\) > \(\frac{2}{6}\)
D. \(\frac{0}{6}\) < \(\frac{2}{6}\)
So, the answer is option C.

Question 2.
Liam is comparing fraction circles. Which of the following statements is true?
Options:
a. \(\frac{1}{2}\) = \(\frac{1}{2}\)
b. \(\frac{3}{4}\) > \(\frac{4}{4}\)
c. \(\frac{4}{6}\) < \(\frac{3}{6}\)
d. \(\frac{2}{8}\) = \(\frac{3}{8}\)

Answer: \(\frac{1}{2}\) = \(\frac{1}{2}\)

Explanation:

Check whether the denominators are same. If both are same then compare the numerators.
\(\frac{1}{2}\) = \(\frac{1}{2}\)
Option A is the correct answer.

Spiral Review

Question 3.
Mr. Edwards buys 2 new knobs for each of his kitchen cabinets. The kitchen has 9 cabinets. How many knobs does he buy?
Options:
a. 20
b. 18
c. 16
d. 12

Answer: 18

Explanation:

Given, Mr. Edwards buys 2 new knobs for each of his kitchen cabinets.
The kitchen has 9 cabinets.
Number of knobs he buys = x
x = 9 × 2 = 18
Thus the correct answer is option B.

Question 4.
Allie builds a new bookcase with 8 shelves. She can put 30 books on each shelf. How many books can the bookcase hold?
Options:
a. 30
b. 38
c. 240
d. 300

Answer: 240

Explanation:

Given that Allie builds a new bookcase with 8 shelves.
She can put 30 books on each shelf.
Let the number of books can the bookcase hold = y
y = 30 × 8
y = 240
Thus the correct answer is option C.

Question 5.
The Good Morning Café has 28 customers for breakfast. There are 4 people sitting at each table. How many tables are filled?
Options:
a. 8
b. 7
c. 6
d. 4

Answer: 7

Explanation:

The Good Morning Café has 28 customers for breakfast.
There are 4 people sitting at each table.
Number of tables be t
t ×4 = 28
t = 28/4 = 4
Thus the number of tables filled = 7

Question 6.
Ella wants to use the Commutative Property of Multiplication to help find the product 5 × 4. Which number sentence can she use?
Options:
a. 5 + 4 = 10
b. 5 × 5 = 25
c. 5 − 4 = 1
d. 4 × 5 = 20

Answer: 4 × 5 = 20

Explanation:

According to the commutative property of multiplication, changing the order of the numbers we are multiplying, does not change the product.
a × b = b × a
5 × 4 = 4 × 5 = 20
So, the correct answer is option D.

Compare Fractions with the Same Numerator – Page No. 523

Compare. Write <, >, or =.

Question 1.

Question 2.
\(\frac{3}{8}\) ______ \(\frac{3}{6}\)

Answer: \(\frac{3}{8}\) < \(\frac{3}{6}\)

Explanation:

When comparing fractions with the same numerator, the fraction with the smaller denominator is greater.
So, \(\frac{3}{8}\) < \(\frac{3}{6}\)

Question 3.
\(\frac{2}{3}\) ______ \(\frac{2}{4}\)

Answer: \(\frac{2}{3}\) > \(\frac{2}{4}\)

Explanation:

Compare the fractions \(\frac{2}{3}\) and \(\frac{2}{4}\)
The numerators of both the fractions are the same. So compare the denominators.
The fraction with the smaller denominator is greater
So, \(\frac{2}{3}\) > \(\frac{2}{4}\)

Question 4.
\(\frac{2}{8}\) ______ \(\frac{2}{3}\)

Answer: \(\frac{2}{8}\) < \(\frac{2}{3}\)

Explanation:

Compare \(\frac{2}{8}\) and \(\frac{2}{3}\)
When comparing fractions with the same numerator, the fraction with the smaller denominator is greater.
\(\frac{2}{8}\) < \(\frac{2}{3}\)

Question 5.
\(\frac{3}{6}\) ______ \(\frac{3}{4}\)

Answer: \(\frac{3}{6}\) < \(\frac{3}{4}\)

Explanation:

Compare the fractions \(\frac{3}{6}\) and \(\frac{3}{4}\)
The numerators are the same and the denominators are different.
The number with the smallest number will be the greatest.
So, \(\frac{3}{6}\) < \(\frac{3}{4}\)

Question 6.
\(\frac{1}{2}\) ______ \(\frac{1}{6}\)

Answer: \(\frac{1}{2}\) > \(\frac{1}{6}\)

Explanation:

When comparing fractions with the same numerator, the fraction with the smaller denominator is greater.
2 is greater than 6.
\(\frac{1}{2}\) > \(\frac{1}{6}\)

Question 7.
\(\frac{5}{6}\) ______ \(\frac{5}{8}\)

Answer: \(\frac{5}{6}\) > \(\frac{5}{8}\)

Explanation:

We observe that numerators are the same and the denominators are different.
The fraction with the smallest number will be the greatest.
So, \(\frac{5}{6}\) > \(\frac{5}{8}\)

Question 8.
\(\frac{4}{8}\) ______ \(\frac{4}{8}\)

Answer: \(\frac{4}{8}\) = \(\frac{4}{8}\)

Explanation:

The numerators and denominators of both the fractions are the same.
So, \(\frac{4}{8}\) = \(\frac{4}{8}\)

Question 9.
\(\frac{6}{8}\) ______ \(\frac{6}{6}\)

Answer: \(\frac{6}{8}\) < \(\frac{6}{6}\)

Explanation:

Compare the fractions \(\frac{6}{8}\) and \(\frac{6}{6}\)
We observe that numerators are the same and the denominators are different.
So, \(\frac{6}{8}\) < \(\frac{6}{6}\)

Problem Solving

Question 10.
Javier is buying food in the lunch line. The tray of salad plates is \(\frac{3}{8}\) full. The tray of fruit plates is \(\frac{3}{4}\) full. Which tray is more full?
The tray of ______ plates

Answer: The fruit plate tray

Explanation:

Javier is buying food in the lunch line. The tray of salad plates is \(\frac{3}{8}\) full.
The tray of fruit plates is \(\frac{3}{4}\) full.
Compare the fraction of salad plates and fruit plates.
\(\frac{3}{8}\) and \(\frac{3}{4}\)
The numerators are same. So compare the denominators.
So, \(\frac{3}{8}\) <\(\frac{3}{4}\)
Thus the fruit plate tray is more full than salad plate tray.

Question 11.
Rachel bought some buttons. Of the buttons, \(\frac{2}{4}\) are yellow and \(\frac{2}{8}\) are red. Rachel bought more of which color buttons?
More _______ buttons

Answer: Yellow

Explanation:

Rachel bought some buttons. Of the buttons, \(\frac{2}{4}\) are yellow and \(\frac{2}{8}\) are red.
Compare \(\frac{2}{4}\) and \(\frac{2}{8}\)
The fraction with the smaller denominator is greater.
\(\frac{2}{4}\) >\(\frac{2}{8}\)
Therefore there are more yellow buttons.

Compare Fractions with the Same Numerator – Page No. 524

Lesson Check

Question 1.
Which symbol makes the statement true?
\(\frac{3}{4}\) O \(\frac{3}{8}\)
a. >
b. <
c. =
d. none

Answer: >

Explanation:

In the above statement, the fractions are of the same numerators. So, we need to check the denominators.
The number with the highest number will be the least fraction.
So, \(\frac{3}{4}\) > \(\frac{3}{8}\)
Thus the correct answer is option A.

Question 2.
Which symbol makes the statement true?
\(\frac{2}{4}\) O \(\frac{2}{3}\)
a. >
b. <
c. =
d. none

Answer: <

Explanation:

The fractions are of the same numerators. So, we need to see the denominators.
The number with the highest number will be the least fraction.
So, \(\frac{2}{4}\) < \(\frac{2}{3}\)
So, the correct answer is option B.

Spiral Review

Question 3.
Anita divided a circle into 6 equal parts and shaded 1 of the parts. Which fraction names the part she shaded?
Options:
a. \(\frac{1}{6}\)
b. \(\frac{1}{5}\)
c. \(\frac{5}{6}\)
d. \(\frac{1}{1}\)

Answer: \(\frac{1}{6}\)

Explanation:

Given that, Anita divided a circle into 6 equal parts and shaded 1 of the parts.
So, the fraction of the shaded part is \(\frac{1}{6}\)
Thus the correct answer is option A.

Question 4.
Which fraction names the shaded part of the rectangle?

Options:
a. \(\frac{1}{8}\)
b. \(\frac{2}{8}\)
c. \(\frac{6}{8}\)
d. \(\frac{8}{8}\)

Answer: \(\frac{2}{8}\)

Explanation:

The rectangle is divided into 8 equal parts. Out of 8 two parts are shaded.
So, the fraction name of the shaded part is \(\frac{2}{8}\)
The correct answer is option B.

Question 5.
Chip worked at the animal shelter for 6 hours each week for several weeks. He worked for a total of 42 hours. Which of the following can be used to find the number of weeks Chip worked at the animal shelter?
Options:
a. 6 + 42
b. 42 − 6
c. 42 ÷ 6
d. 42 × 6

Answer: 42 ÷ 6

Explanation:

Chip worked at the animal shelter for 6 hours each week for several weeks.
Number of hours he worked = 42 hours
Number of weeks he worked at the animal shelter = x
x × 6 = 42
x = 42 ÷ 6
Thus the correct answer is option C.

Question 6.
Mr. Jackson has 20 quarters. If he gives 4 quarters to each of his children, how many children does Mr. Jackson have?
Options:
a. 3
b. 4
c. 5
d. 6

Answer: 5

Explanation:

Given, Mr. Jackson has 20 quarters.
If he gives 4 quarters to each of his children
Number of children Mr. Jackson have = y
y × 4 = 20
y = 20/4 = 5
Therefore, Mr. Jackson has 5 children.

Compare Fractions – Page No. 529

Compare. Write <, >, or =. Write the strategy you used.

Question 1.

Answer: Same Numerator

Question 2.
\(\frac{2}{3}\) ______ \(\frac{7}{8}\)

Answer: \(\frac{2}{3}\) < \(\frac{7}{8}\)

Missing pieces

Explanation:

Compare the fractions \(\frac{2}{3}\), \(\frac{7}{8}\)
The numerators and denominators are different here.
\(\frac{2}{3}\) × \(\frac{8}{8}\) = \(\frac{16}{24}\)
\(\frac{7}{8}\) × \(\frac{3}{3}\) = \(\frac{21}{24}\)
16 is less than 24.
So, \(\frac{16}{24}\) < \(\frac{21}{24}\)
That means \(\frac{2}{3}\) < \(\frac{7}{8}\)

Question 3.
\(\frac{3}{4}\) ______ \(\frac{1}{4}\)

Answer: \(\frac{3}{4}\) > \(\frac{1}{4}\)

Explanation:

The Denominator is the same here. So compare the numerators.
\(\frac{3}{4}\), \(\frac{1}{4}\)
3 is greater than 1.
Thus \(\frac{3}{4}\) > \(\frac{1}{4}\)

Name a fraction that is less than or greater than the given fraction. Draw to justify your answer.

Question 4.
greater than \(\frac{1}{3}\)
Type below:
___________

Answer: \(\frac{2}{3}\)

Explanation:

\(\frac{2}{3}\) is greater than \(\frac{1}{3}\)

Question 5.
less than \(\frac{3}{4}\)
Type below:
___________

Answer: \(\frac{2}{4}\)

Explanation:

\(\frac{2}{4}\) is less than \(\frac{3}{4}\)

Problem Solving

Question 6.
At the third-grade party, two groups each had their own pizza. The blue group ate \(\frac{7}{8}\) pizza. The green group ate \(\frac{2}{8}\) pizza. Which group ate more of their pizza?
The _______ group

Answer: The blue group

Explanation:

Given,
At the third-grade party, two groups each had their own pizza.
The blue group ate \(\frac{7}{8}\) pizza.
The green group ate \(\frac{2}{8}\) pizza.
Compare the fractions of the blue group and green group.
\(\frac{7}{8}\) and \(\frac{2}{8}\)
The denominators are the same here. So compare the numerators.
The numerator with the greatest number will be the greatest fraction.
Therefore \(\frac{7}{8}\) > \(\frac{2}{8}\)
So, the blue group ate more pizza.

Question 7.
Ben and Antonio both take the same bus to school. Ben’s ride is \(\frac{7}{8}\) mile. Antonio’s ride is \(\frac{3}{4}\) mile. Who has a longer bus ride?
___________

Answer: Ben

Explanation:

Ben and Antonio both take the same bus to school.
Ben’s ride is \(\frac{7}{8}\) mile.
Antonio’s ride is \(\frac{3}{4}\) mile.
Compare the fractions \(\frac{7}{8}\), \(\frac{3}{4}\)
Make the denominators equal to compare the fractions.
\(\frac{3}{4}\) × \(\frac{8}{8}\) = \(\frac{24}{32}\)
\(\frac{7}{8}\) × \(\frac{4}{4}\) = \(\frac{28}{32}\)
\(\frac{28}{32}\) > \(\frac{24}{32}\)
\(\frac{7}{8}\) > \(\frac{3}{4}\)
Thus Ben has longer bus ride.

Compare Fractions – Page No. 530

Lesson Check

Question 1.
Which statement is correct?
Options:
a. \(\frac{2}{3}\) > \(\frac{7}{8}\)
b. \(\frac{2}{3}\) < \(\frac{7}{8}\)
c. \(\frac{2}{3}\) = \(\frac{7}{8}\)
d. \(\frac{7}{8}\) = \(\frac{2}{3}\)

Answer: \(\frac{2}{3}\) < \(\frac{7}{8}\)

Explanation:

A. \(\frac{2}{3}\) > \(\frac{7}{8}\)
Here the numerator of one fraction is greater than the numerator of the other fraction.
So, \(\frac{2}{3}\) is not greater than \(\frac{7}{8}\)
B. \(\frac{2}{3}\) < \(\frac{7}{8}\)
Here the numerator of one fraction is greater than the numerator of the other fraction.
2 is less than 7.
Thus the statement \(\frac{2}{3}\) < \(\frac{7}{8}\) is true.
Option B is the answer.

Question 2.
Which symbol makes the statement true?
\(\frac{2}{4}\) O \(\frac{2}{6}\)
a. >
b. <
c. =
d. none

Answer: >

Explanation:

Compare the fractions \(\frac{2}{4}\) & \(\frac{2}{6}\)
The numerator of both the fractions are the same.
So we need to compare the denominators.
The denominator with the greater number will the smallest fraction.
Therefore, \(\frac{2}{4}\) > \(\frac{2}{6}\)
The correct answer is option A.

Spiral Review

Question 3.
Cam, Stella, and Rose each picked 40 apples. They put all their apples in one crate. How many apples are in the crate?
Options:
a. 40
b. 43
c. 120
d. 123

Answer: 120

Explanation:

Given that, Cam, Stella, and Rose each picked 40 apples.
They put all their apples in one crate.
That means each person picked 40 apples = 40 + 40 + 40 = 120 apples
Therefore there are 120 apples in the crate.
The correct answer is option C.

Question 4.
Each shape is 1 whole. Which fraction is represented by the shaded part of the model?

Options:
a. \(\frac{2}{4}\)
b. \(\frac{4}{4}\)
c. \(\frac{8}{4}\)
d. \(\frac{8}{1}\)

Answer: \(\frac{8}{4}\)

Explanation:

From the figure we observe that there are 2 squares.
Each square is divided into 4 equal parts.
Total number of shaded parts = 4
So, the fraction of 1 whole shaded part is \(\frac{8}{4}\)
Thus the correct answer is option C.

Question 5.
Which related multiplication fact can you use to find
16 ÷ ■ = 2?
Options:
a. 4 × 4 = 16
b. 8 × 2 = 16
c. 8 × 1 = 8
d. 4 × 2 = 8

Answer: 8 × 2 = 16

Explanation:

16 ÷ ■ = 2
■ = 16/2 = 8
So, the related multiplication fact of 16 ÷ ■ = 2 is 8 × 2 = 16.
The correct answer is option B.

Question 6,
What is the unknown factor?
9 × ■ = 36
Options:
a. 7
b. 6
c. 4
d. 3

Answer: 4

Explanation:

■ is the unknown factor
9 × ■ = 36
■ = 36/9 = 4
Thus the correct answer is option C.

Mid -Chapter Checkpoint – Page No. 531

Concepts and Skills

Question 1.
When two fractions refer to the same whole, explain why the fraction with a lesser denominator has larger pieces than the fraction with a greater denominator.
Type below:
___________

Answer: If two fractions have the same numerator but different denominators the fraction with greater denominator is smaller.
Example: Let us consider an apple that is divided into equal parts.
If the apple is divided among 2 people.
Then each get \(\frac{1}{2}\) part of the apple.
If the apple is divided among 4 people.
Then each get \(\frac{1}{4}\) part of an apple.
Hence, in the first case, people get more amount of apple than the second.
Hence, if as a whole the denominator is less the fraction is greater.

Question 2.
When two fractions refer to the same whole and have the same denominators, explain why you can compare only the numerators
Type below:
___________

Answer: If the denominators are the same, then the fraction with the greater numerator is the greater fraction. The fraction with the lesser numerator is the lesser fraction.
Example:
Let us consider a pizza which is cut into 4 parts.
One person ate 3 pieces then the fraction is \(\frac{3}{4}\)
And the other person ate 1 piece then the fraction is \(\frac{1}{4}\)
Now compare the fractions \(\frac{1}{4}\) and \(\frac{3}{4}\)
First person ate 2 pieces more than the second person.
Hence the fraction with the greater numerator is the greater fraction.

Compare. Write <, >, or =.

Question 3.
\(\frac{1}{6}\) ______ \(\frac{1}{4}\)

Answer: \(\frac{1}{6}\) < \(\frac{1}{4}\)

Explanation:

\(\frac{1}{6}\), \(\frac{1}{4}\)
In this case the numerators are same and the denominators are different.
We know that the two fractions have the same numerator but different denominators the fraction with greater denominator is smaller.
So, \(\frac{1}{6}\) < \(\frac{1}{4}\)

Question 4.
\(\frac{1}{8}\) ______ \(\frac{1}{8}\)

Answer: \(\frac{1}{8}\) = \(\frac{1}{8}\)

Explanation:

Compare the fractions \(\frac{1}{8}\) & \(\frac{1}{8}\)
The numerators and the denominators are same here. Thus these are the equivalent fractions.
Hence, \(\frac{1}{8}\) = \(\frac{1}{8}\)

Question 5.
\(\frac{2}{8}\) ______ \(\frac{2}{3}\)

Answer: \(\frac{2}{8}\) < \(\frac{2}{3}\)

Explanation:

Compare the fractions \(\frac{2}{8}\) & \(\frac{2}{3}\)
The numerators are same and denominators are different.
As we know the denominators with the greatest number will be the smallest fraction.
\(\frac{2}{8}\) < \(\frac{2}{3}\)

Question 6.
\(\frac{4}{2}\) ______ \(\frac{1}{2}\)

Answer: \(\frac{4}{2}\) > \(\frac{1}{2}\)

Explanation:

Compare both the fractions \(\frac{4}{2}\) and \(\frac{1}{2}\)
In this case, the denominators are the same but the numerators are different.
So compare the numerators.
4 is greater than 1.
Thus \(\frac{4}{2}\) > \(\frac{1}{2}\)

Question 7.
\(\frac{7}{8}\) ______ \(\frac{3}{8}\)

Answer: \(\frac{7}{8}\) > \(\frac{3}{8}\)

Explanation:

Comparing the fractions \(\frac{7}{8}\) and \(\frac{3}{8}\)
The denominators are same but the numerators are different.
We know that the denominators are the same, then the fraction with the greater numerator is the greater fraction. The fraction with the lesser numerator is the lesser fraction.
7 is greater than 3.
So, \(\frac{7}{8}\) > \(\frac{3}{8}\)

Question 8.
\(\frac{5}{6}\) ______ \(\frac{2}{3}\)

Answer: \(\frac{5}{6}\) > \(\frac{2}{3}\)

Explanation:

Compare the fractions \(\frac{5}{6}\) and \(\frac{2}{3}\)
In this case the numerators and the denominators are different.
So, we have to make the denominators equal.
\(\frac{5}{6}\) × \(\frac{3}{3}\) = \(\frac{15}{18}\)
\(\frac{2}{3}\) × \(\frac{6}{6}\) = \(\frac{12}{18}\)
Now the denominators are same. So compare the numerators 15 is greater than 12.
So, \(\frac{15}{18}\) > \(\frac{12}{18}\)
That means \(\frac{5}{6}\) > \(\frac{2}{3}\)

Question 9.
\(\frac{2}{4}\) ______ \(\frac{3}{4}\)

Answer: \(\frac{2}{4}\) < \(\frac{3}{4}\)

Explanation:

The denominators are the same. So compare the fractions with the numerators.
2 is less than 3.
So, \(\frac{2}{4}\) < \(\frac{3}{4}\)

Question 10.
\(\frac{6}{6}\) ______ \(\frac{6}{8}\)

Answer: \(\frac{6}{6}\) > \(\frac{6}{8}\)

Explanation:

Here the numerators are same but the denominators are different.
We know that denominators with the greatest number will be the smallest fraction.
Therefore, \(\frac{6}{6}\) > \(\frac{6}{8}\)

Question 11.
\(\frac{3}{4}\) ______ \(\frac{7}{8}\)

Answer: \(\frac{3}{4}\) < \(\frac{7}{8}\)

Explanation:

Compare the fractions \(\frac{3}{4}\) and \(\frac{7}{8}\)
The numerators and denominators are different.
So, we have to make the denominators equal.
\(\frac{3}{4}\) × \(\frac{8}{8}\) = \(\frac{24}{32}\)
\(\frac{7}{8}\) × \(\frac{4}{4}\) = \(\frac{28}{32}\)
Now the denominators are equal. So compare the numerators of both the fractions.
\(\frac{24}{32}\) < \(\frac{28}{32}\)
Therefore \(\frac{3}{4}\) < \(\frac{7}{8}\)

Name a fraction that is less than or greater than the given fraction. Draw to justify your answer.

Question 12.
greater than \(\frac{2}{6}\)
Type below:
___________

Answer: \(\frac{4}{6}\)
\(\frac{4}{6}\) > \(\frac{2}{6}\)

Question 13.
less than \(\frac{2}{3}\)
Type below:
___________

Answer: \(\frac{1}{3}\)
\(\frac{1}{3}\) < \(\frac{2}{3}\)

Mid -Chapter Checkpoint – Page No. 532

Question 14.
Two walls in Tiffany’s room are the same size. Tiffany paints \(\frac{1}{4}\) of one wall. Roberto paints \(\frac{1}{8}\) of the other wall. Who painted a greater amount in Tiffany’s room?
___________

Answer: Tiffany

Explanation:

Given that, Two walls in Tiffany’s room are the same size. Tiffany paints \(\frac{1}{4}\) of one wall.
Roberto paints \(\frac{1}{8}\) of the other wall.
The numerators are the same and the denominators are different here.
So, we have to make the denominators same.
\(\frac{1}{4}\) × \(\frac{8}{8}\) = \(\frac{8}{32}\)
\(\frac{1}{8}\) × \(\frac{4}{4}\) = \(\frac{4}{32}\)
Now compare the fractions \(\frac{8}{32}\) and \(\frac{4}{32}\)
8 is greater than 4.
\(\frac{8}{32}\) > \(\frac{4}{32}\)
Therefore, Tiffany painted greater amount than Roberto.

Question 15.
Matthew ran \(\frac{5}{8}\) mile during track practice. Pablo ran \(\frac{5}{6}\) mile. Who ran farther?
___________

Answer: Pablo

Explanation:

Given,
Matthew ran \(\frac{5}{8}\) mile during track practice.
Pablo ran \(\frac{5}{6}\) mile.
Compare the fractions \(\frac{5}{8}\) and \(\frac{5}{6}\)
Numerators are the same and denominators are different.
The denominator with the greatest number will be the smallest fraction.
Thus \(\frac{5}{8}\) < \(\frac{5}{6}\)
Pablo ran farther than Matthew.

Question 16.
Mallory bought 6 roses for her mother. Two-sixths of the roses are red and \(\frac{4}{6}\) is yellow. Did Mallory buy fewer red roses or yellow roses?
___________

Answer: Red Roses

Explanation:

Mallory bought 6 roses for her mother.
Two-sixths of the roses are red and \(\frac{4}{6}\) is yellow.
Compare fractions \(\frac{4}{6}\) and \(\frac{2}{6}\)
The denominators of both the fractions are the same and numerators are different.
4 is greater than 2. So, \(\frac{4}{6}\) > \(\frac{2}{6}\)
Therefore Mallory buys fewer red roses.

Question 17.
Lani used \(\frac{2}{3}\) cup of raisins, \(\frac{3}{8}\) cup of cranberries, and \(\frac{3}{4}\) cup of oatmeal to bake cookies. Which ingredient did Lani use the least amount of?
___________

Answer: Cranberries

Explanation:

Lani used \(\frac{2}{3}\) cup of raisins, \(\frac{3}{8}\) cup of cranberries, and \(\frac{3}{4}\) cup of oatmeal to bake cookies.
Compare the fractions \(\frac{2}{3}\), \(\frac{3}{8}\) and \(\frac{3}{4}\)
The numerators and denominators are different in this case.
The denominator with the highest number will be the smallest fraction.
Therefore Lani used the least amount of cranberries.

Compare and Order Fractions – Page No. 537

Write the fractions in order from greatest to least.

Question 1.

Question 2.
\(\frac{2}{8}\), \(\frac{5}{8}\), \(\frac{1}{8}\)
Type below:
___________

Answer: \(\frac{5}{8}\), \(\frac{2}{8}\), \(\frac{1}{8}\)

Explanation:

The denominators of three fractions are same. So compare the numerators of the fractions.
5 is greater than 2 is greater than 1.
Thus the order of the fraction is \(\frac{5}{8}\), \(\frac{2}{8}\), \(\frac{1}{8}\)

Question 3.
\(\frac{1}{3}\), \(\frac{1}{6}\), \(\frac{1}{2}\)
Type below:
___________

Answer: \(\frac{1}{2}\), \(\frac{1}{3}\), \(\frac{1}{6}\)

Explanation:

Compare the three fractions \(\frac{1}{3}\), \(\frac{1}{6}\), \(\frac{1}{2}\)
We observe that the numerators of the fractions are same and the denominators are different.
We know that the denominators with the smallest number will be the greater fraction.
Therefore, \(\frac{1}{2}\), \(\frac{1}{3}\), \(\frac{1}{6}\)

Question 4.
\(\frac{2}{3}\), \(\frac{2}{6}\), \(\frac{2}{8}\)
Type below:
___________

Answer: \(\frac{2}{3}\), \(\frac{2}{6}\), \(\frac{2}{8}\)

Explanation:

Comparing the fractions \(\frac{2}{3}\), \(\frac{2}{6}\), \(\frac{2}{8}\)
The numerators are the same but the denominators are different.
We know that the denominators with the greatest number will be the smallest fraction.
3 is greater than 6 is greater than 8.
So, the order of the fraction is \(\frac{2}{3}\), \(\frac{2}{6}\), \(\frac{2}{8}\)

Write the fractions in order from least to greatest.

Question 5.
\(\frac{2}{4}\), \(\frac{4}{4}\), \(\frac{3}{4}\)
Type below:
___________

Answer: \(\frac{2}{4}\), \(\frac{3}{4}\), \(\frac{4}{4}\)

Explanation:

The denominators are same but the numerators are different.
So compare the numerators of three fractions.
2 < 3 < 4
\(\frac{2}{4}\), \(\frac{3}{4}\), \(\frac{4}{4}\)

Question 6.
\(\frac{4}{6}\), \(\frac{5}{6}\), \(\frac{2}{6}\)
Type below:
___________

Answer: \(\frac{2}{6}\), \(\frac{4}{6}\), \(\frac{5}{6}\)

Explanation:

Compare the fractions \(\frac{4}{6}\), \(\frac{5}{6}\), \(\frac{2}{6}\)
The denominators are same but the numerators are different.
So compare the numerators of the three fractions.
The order of fractions from least to greatest is \(\frac{2}{6}\), \(\frac{4}{6}\), \(\frac{5}{6}\)

Question 7.
\(\frac{7}{8}\), \(\frac{0}{8}\), \(\frac{3}{8}\)
Type below:
___________

Answer: \(\frac{0}{8}\), \(\frac{3}{8}\), \(\frac{7}{8}\)

Explanation:

Compare the fractions \(\frac{7}{8}\), \(\frac{0}{8}\), \(\frac{3}{8}\)
The numerators of the fractions are different. But the denominators are same.
0 < 3 < 7
The order from least to greatest is \(\frac{0}{8}\), \(\frac{3}{8}\), \(\frac{7}{8}\)

Question 8.
\(\frac{3}{4}\), \(\frac{3}{6}\), \(\frac{3}{8}\)
Type below:
___________

Answer: \(\frac{3}{8}\), \(\frac{3}{6}\), \(\frac{3}{4}\)

Explanation:

Compare the fractions \(\frac{3}{4}\), \(\frac{3}{6}\), \(\frac{3}{8}\)
The numerators are same but the denominators of the three fractions are different.
So, compare the denominators.
The denominators with the greatest number will be the smallest fraction.
So, the order of fractions from least to greatest is \(\frac{3}{8}\), \(\frac{3}{6}\), \(\frac{3}{4}\)

Problem Solving

Question 9.
Mr. Jackson ran \(\frac{7}{8}\) mile on Monday. He ran \(\frac{3}{8}\) mile on Wednesday and \(\frac{5}{8}\) mile on Friday. On which day did Mr. Jackson run the shortest distance?
On ___________

Answer: Wednesday

Explanation:

Mr. Jackson ran \(\frac{7}{8}\) mile on Monday.
He ran \(\frac{3}{8}\) mile on Wednesday and \(\frac{5}{8}\) mile on Friday
The denominators of the fractions are the same. So, compare the numerators.
Compare to all Mr. Jackson run the shortest distance on Wednesday.

Question 10.
Delia has three pieces of ribbon. Her red ribbon is \(\frac{2}{4}\) foot long. Her green ribbon is \(\frac{2}{3}\) foot long. Her yellow ribbon is \(\frac{2}{6}\) foot long. She wants to use the longest piece for a project. Which color ribbon should Delia use?
The _______ ribbon

Answer: Green

Explanation:

Delia has three pieces of ribbon. Her red ribbon is \(\frac{2}{4}\) foot long.
Her green ribbon is \(\frac{2}{3}\) foot long.
Her yellow ribbon is \(\frac{2}{6}\) foot long.
Compare the fractions to know which color should Delia use.
\(\frac{2}{4}\), \(\frac{2}{3}\) and \(\frac{2}{6}\)
The numerators of the three fractions are the same but the denominators are different.
\(\frac{2}{3}\) is longest among all.
so, the answer is Green ribbon.

Compare and Order Fractions – Page No. 538

Lesson Check

Question 1.
Which list orders the fractions from least to greatest?
Options:
a. \(\frac{1}{8}\), \(\frac{1}{3}\), \(\frac{1}{6}\)
b. \(\frac{1}{3}\), \(\frac{1}{6}\), \(\frac{1}{8}\)
c. \(\frac{1}{8}\), \(\frac{1}{6}\), \(\frac{1}{3}\)
d. \(\frac{1}{6}\), \(\frac{1}{8}\), \(\frac{1}{3}\)

Answer: \(\frac{1}{8}\), \(\frac{1}{6}\), \(\frac{1}{3}\)

Explanation:

When the numerators are the same, think about the denominators to compare and order fractions.
The denominator with the greatest number is the smallest fraction.
\(\frac{1}{8}\) < \(\frac{1}{6}\) < \(\frac{1}{3}\)
So, the order is \(\frac{1}{8}\), \(\frac{1}{6}\), \(\frac{1}{3}\)

Question 2.
Which list orders the fractions from greatest to least?
Options:
a. \(\frac{3}{8}\), \(\frac{3}{6}\), \(\frac{3}{4}\)
b. \(\frac{3}{4}\), \(\frac{3}{6}\), \(\frac{3}{8}\)
c. \(\frac{3}{4}\), \(\frac{3}{8}\), \(\frac{3}{4}\)
d. \(\frac{3}{6}\), \(\frac{3}{4}\), \(\frac{3}{8}\)

Answer: \(\frac{3}{4}\), \(\frac{3}{6}\), \(\frac{3}{8}\)

Explanation:

If the numerators are the same, think about the denominators to compare and order fractions.
The denominators with the smallest number will be the greatest fraction.
\(\frac{3}{4}\) > \(\frac{3}{6}\) > \(\frac{3}{8}\)
Thus the fractions from greatest to least are \(\frac{3}{4}\), \(\frac{3}{6}\), \(\frac{3}{8}\)

Spiral Review

Question 3.
What fraction of the group of cars is shaded?

Options:
a. \(\frac{3}{8}\)
b. \(\frac{1}{2}\)
c. \(\frac{5}{8}\)
d. \(\frac{3}{5}\)

Answer: \(\frac{3}{8}\)

Explanation:

Total number of cars = 8
Number of shaded cars among those 8 cars = 3
So, the fraction of the shaded cars = 3/8
Thus the answer is option A.

Question 4.
Wendy has 6 pieces of fruit. Of these, 2 pieces are bananas. What fraction of Wendy’s fruit is bananas?
Options:
a. \(\frac{2}{6}\)
b. \(\frac{2}{4}\)
c. \(\frac{4}{6}\)
d. \(\frac{2}{2}\)

Answer: \(\frac{2}{6}\)

Explanation:

Given that, Wendy has 6 pieces of fruit.
Of these, 2 pieces are bananas.
The fraction of Wendy’s fruit is 2/6
Thus the correct answer is \(\frac{2}{6}\) i.e., option A.

Question 5.
Toby collects data and makes a bar graph about his classmates’ pets. He finds that 9 classmates have dogs, 2 classmates have fish, 6 classmates have cats, and 3 classmates have gerbils. Which pet will have the longest bar on the bar graph?
Options:
a. dog
b. fish
c. cat
d. gerbil

Answer: dog

Explanation:

Number of classmates who have dogs = 9
Number of classmates who have fish = 2
Number of classmates who have cats = 6
Number of classmates who have gerbils = 3
So, dogs will have the longest bar on the bar graph.

Question 6.
The number sentence is an example of which multiplication property?
6 × 7 = (6 × 5) + (6 × 2)
Options:
a. Associative
b. Commutative
c. Distributive
d. Identity

Answer: Distributive

Explanation:

6 × 7 = (6 × 5) + (6 × 2)
Here 7 is distributed into 5 + 2
According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
So, the answer is option C.

Model Equivalent Fractions – Page No. 543

Shade the model. Then divide the pieces to find the equivalent fraction.

Question 1.

Answer: \(\frac{4}{8}\)
Explanation:

The figure shows that there are 8 equal parts and 4 of them are shaded.
The Fraction of the shaded part is \(\frac{4}{8}\)
Thus, \(\frac{4}{8}\) = \(\frac{2}{4}\)

Question 2.

\(\frac{1}{3}\) = \(\frac{■}{6}\)
\(\frac{□}{□}\)

Answer: \(\frac{2}{6}\)

Explanation:

There are 6 equal parts in which 2 parts are shaded. Now the fraction for the shaded part is \(\frac{2}{6}\)

\(\frac{1}{3}\) = \(\frac{2}{6}\)

Use the number line to find the equivalent fraction.

Question 3.

\(\frac{1}{2}\) = \(\frac{■}{4}\)
\(\frac{□}{□}\)

Answer: \(\frac{2}{4}\)

The fraction \(\frac{1}{2}\) and \(\frac{2}{4}\) lies on the same point.

Therefore, \(\frac{1}{2}\) = \(\frac{2}{4}\)

Question 4.

\(\frac{3}{4}\) = \(\frac{■}{8}\)
\(\frac{□}{□}\)

Answer: \(\frac{6}{8}\)

The above figure shows that the point \(\frac{6}{8}\) and \(\frac{3}{4}\) lies on the same point on the number line.

Thus \(\frac{3}{4}\) = \(\frac{6}{8}\)

Problem Solving

Question 5.
Mike says that \(\frac{3}{3}\) of his fraction model is shaded blue. Ryan says that \(\frac{6}{6}\) of the same model is shaded blue. Are the two fractions equivalent? If so, what is another equivalent fraction?
___________

Answer: \(\frac{2}{2}\)

Explanation:

Mike says that \(\frac{3}{3}\) of his fraction model is shaded blue.
Ryan says that \(\frac{6}{6}\) of the same model is shaded blue.
The two fractions are equivalent.
\(\frac{3}{3}\) = \(\frac{6}{6}\) = \(\frac{2}{2}\)

Question 6.
Brett shaded \(\frac{4}{8}\) of a sheet of notebook paper. Aisha says he shaded \(\frac{1}{2}\) of the paper. Are the two fractions equivalent? If so, what is another equivalent fraction?
___________

Answer: \(\frac{2}{4}\)

Explanation:

\(\frac{1}{2}\) = \(\frac{4}{8}\)
So, the two fractions are equivalent.
The another equivalent fraction is \(\frac{2}{4}\).

Model Equivalent Fractions – Page No. 544

Lesson Check

Question 1.
Find the fraction equivalent to \(\frac{2}{3}\).

Options:
a. \(\frac{3}{2}\)
b. \(\frac{4}{6}\)
c. \(\frac{3}{6}\)
d. \(\frac{1}{3}\)

Answer: \(\frac{4}{6}\)

\(\frac{2}{3}\) = \(\frac{4}{6}\)

Question 2.
Find the fraction equivalent to \(\frac{1}{4}\).

Options:
a. \(\frac{1}{2}\)
b. \(\frac{2}{4}\)
c. \(\frac{2}{8}\)
d. \(\frac{6}{8}\)

Answer: \(\frac{2}{8}\)

Explanation:

The fugure shows that the \(\frac{1}{4}\) and \(\frac{2}{8}\) lies on the same point.
So, the equivalent fraction of \(\frac{1}{4}\) is \(\frac{2}{8}\)
Thus the correct answer is option C.

Spiral Review

Question 3.
Eric practiced piano and guitar for a total of 8 hours this week. He practiced the piano for \(\frac{1}{4}\) of that time. How many hours did Eric practice the piano this week?
Options:
a. 6 hours
b. 4 hours
c. 3 hours
d. 2 hours

Answer: 2 hours

Explanation:

Eric practiced piano and guitar for a total of 8 hours this week.
He practiced the piano for \(\frac{1}{4}\) of that time.
To find how many hours did Eric practice the piano this week
You need to multiply the total number of hours with a fraction of the time he practiced.
8 ×  \(\frac{1}{4}\) = 2 hours
Thus the correct answer is option D.

Question 4.
Kylee bought a pack of 12 cookies. One-third of the cookies are peanut butter. How many of the cookies in the pack are peanut butter?
Options:
a. 9
b. 6
c. 4
d. 3

Answer: 4

Explanation:

Given,
Kylee bought a pack of 12 cookies.
One-third of the cookies are peanut butter.
To find the number of cookies in the pack is peanut butter.
Multiply number of cookies with a fraction of cookies are peanut butter
12 × \(\frac{1}{3}\) = 4
So, the correct answer is option C.

Question 5.
There are 56 students going to the game. The coach puts 7 students in each van. Which number sentence can be used to find how many vans are needed to take the students to the game?
Options:
a. 56 + 7 = ■
b. ■ + 7 = 56
c. ■ × 7 = 56
d. 56 − 7 = ■

Answer: ■ × 7 = 56

Explanation:

There are 56 students going to the game.
The coach puts 7 students in each van.
Let ■ be the number of vans
56 ÷ 7 = ■
■ × 7 = 56
■ = 8
Thus the correct answer is option C.

Question 6.
Which number sentence can be used to describe the picture?

Options:
a. 2 + 4 = 6
b. 4 − 2 = 2
c. 4 × 1 = 4
d. 8 ÷ 2 = 4

Answer: 8 ÷ 2 = 4

Explanation:

Number of counters = 8
Number of equal groups = 4
Number in each group = 2
The division equation is 8 ÷ 2 = 4
So, the answer is option D.

Lesson 9.7 – Page No. 548

Question 13.
Christy bought 8 muffins. She chose 2 apple, 2 banana, and 4 blueberry. She and her family ate the apple and banana muffins for breakfast. What fraction of the muffins did they eat? Write an equivalent fraction. Draw a picture.
\(\frac{□}{□}\)

Answer: \(\frac{4}{8}\)

Explanation:

Given:
Christy bought 8 muffins.
She chose 2 apple, 2 banana, and 4 blueberries. She and her family ate the apple and banana muffins for breakfast.
They had 2 apples and 2 banana muffins for their breakfast.
Only 4 blueberries are left out of 8 muffins.
The fraction of the muffins they ate = \(\frac{4}{8}\) or \(\frac{1}{2}\)

Question 14.
After dinner, \(\frac{2}{3}\) of the cornbread is left. Suppose 4 friends want to share it equally. What fraction names how much of the whole pan of corn bread each friend will get? Use the model on the right. Explain your answer.

\(\frac{□}{□}\)

Answer: \(\frac{1}{6}\)

Explanation:

To know the fraction of the whole pan of cornbread that each friend get. I divide each third into 2 equal pieces to get 4 pieces in all.
\(\frac{2}{3}\) = \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\)
That means each friend gets \(\frac{1}{6}\) of cornbread of whole pan.

Question 15.
There are 16 people having lunch. Each person wants \(\frac{1}{4}\) of a pizza. How many whole pizzas are needed? Draw a picture to show your answer.
______ pizzas

Answer: 4 pizzas

Explanation:

Given that, There are 16 people having lunch.
Each person wants \(\frac{1}{4}\) of a pizza.
Multiply the total number of people with fraction of each pizza for one person.
= 16 × \(\frac{1}{4}\)
= 16/4 = 4
Therefore 4 pizzas are needed for 16 people.

Question 16.
Lucy has 5 oatmeal bars, each cut in half. What fraction names all of the oatmeal bar halves?

\(\frac{□}{□}\)

Answer: \(\frac{10}{2}\)

Explanation:

Lucy has 5 oatmeal bars, each cut in half.
Total number of oatmeal bars = 5
5 oatmeal bars are divided into halves = 5 + 5 = 10
So. the fraction name for all of the oatmeal bar halves = \(\frac{10}{2}\)

Question 16.
What if Lucy cuts each part of the oatmeal bar into 2 equal pieces to share with friends? What fraction names all of the oatmeal bar pieces now?
\(\frac{□}{□}\)

Answer: \(\frac{10}{2}\)

Explanation:

The above figure shows that there are 5 oatmeal bars.
And each oatmeal bar is divided into halves = 5 × 2 = 10
The fraction for the all of the oatmeal bar halves = \(\frac{10}{2}\)
The equivalent fraction of \(\frac{10}{2}\) is \(\frac{20}{4}\)

Question 17.
Mr. Peters made a pizza. There is \(\frac{4}{8}\) of the pizza left over. Select the fractions that are equivalent to the part of the pizza that is left over. Mark all that apply.

Options:
a. \(\frac{5}{8}\)
b. \(\frac{3}{4}\)
c. \(\frac{2}{4}\)
d. \(\frac{1}{2}\)

Answer: \(\frac{2}{4}\)

Explanation:

Mr. Peters made a pizza. There is \(\frac{4}{8}\) of the pizza left over.
The equivalent fraction of \(\frac{4}{8}\) is \(\frac{2}{4}\)
So, the correct answer is option C.

Equivalent Fractions – Page No. 549

Each shape is 1 whole. Shade the model to find the equivalent fraction.

Question 1.

Answer: \(\frac{3}{6}\)

Explanation:

The circle is divided into 6 equal groups. Each group is \(\frac{1}{6}\) of the whole circle.
There are 3 shaded parts in the circle.
So, the fraction of the shaded part is \(\frac{3}{6}\).
\(\frac{1}{2}\) = \(\frac{3}{6}\)

Question 2.

\(\frac{3}{4}\) = \(\frac{6}{■}\)
\(\frac{□}{□}\)

Answer: \(\frac{6}{8}\)

Explanation:

The square is divided into 8 equal parts. Each group is \(\frac{1}{8}\) of the whole square.
There are 6 shaded parts in the square.
Thus the fraction of the shaded part is 6/8
So, \(\frac{3}{4}\) = \(\frac{6}{8}\)

Circle equal groups to find the equivalent fraction.

Question 3.

\(\frac{2}{4}\) = \(\frac{■}{2}\)
\(\frac{□}{□}\)

Answer: \(\frac{1}{2}\)

Explanation:

Rectangle is divided into 4 equal parts. The fraction of each group is 1/4.
There are 2 shaded parts out of 4 = \(\frac{2}{4}\)
latex]\frac{2}{4}[/latex] = \(\frac{1}{2}\)

Question 4

\(\frac{4}{6}\) = \(\frac{■}{3}\)
\(\frac{□}{□}\)

Answer: \(\frac{2}{3}\)

Explanation:

The figure shows that the rectangle is divided into 6 equal parts and 4 are shaded among them.
The fraction of the shaded part is \(\frac{4}{6}\)
We can also write it as \(\frac{2}{3}\)
Thus, \(\frac{4}{6}\) = \(\frac{2}{3}\)

Problem Solving

Question 5.
May painted 4 out of 8 equal parts of a poster board blue. Jared painted 2 out of 4 equal parts of a same-size poster board red. Write fractions to show which part of the poster board each person painted.
Type below:
____________

Answer: May \(\frac{4}{8}\); Jared \(\frac{2}{4}\)

Explanation:

Given that, May painted 4 out of 8 equal parts of a poster board blue.
4 parts are shaded out of 8 parts. So, the fraction of the shaded part is \(\frac{4}{8}\)
Jared painted 2 out of 4 equal parts of a same-size poster board red.
The fraction of the shaded part is \(\frac{2}{4}\)

Question 6.
Are the fractions equivalent? Draw a model to explain.
____________

Answer: Yes

Equivalent Fractions – Page No. 550

Lesson Check

Question 1.
Which fraction is equivalent to \(\frac{6}{8}\)?

Options:
a. \(\frac{1}{4}\)
b. \(\frac{1}{3}\)
c. \(\frac{3}{4}\)
d. \(\frac{4}{6}\)

Answer: \(\frac{3}{4}\)

Explanation:

\(\frac{6}{8}\) = \(\frac{3}{4}\)
So, the correct answer is option C.

Question 2.
Which fraction is equivalent to \(\frac{1}{3}\) ?

Options:
a. \(\frac{1}{6}\)
b. \(\frac{2}{8}\)
c. \(\frac{2}{6}\)
d. \(\frac{2}{3}\)

Answer: \(\frac{2}{6}\)

Explanation:

\(\frac{1}{3}\) = \(\frac{2}{6}\)
The correct answer is option C.

Spiral Review

Question 3.
Which number sentence is shown by the array?

Options:
a. 8 − 2 = 6
b. 8 × 1 = 8
c. 2 + 8 = 10
d. 16 ÷ 2 = 8

Answer: 16 ÷ 2 = 8

Explanation:

Number of counters = 16
Number of rows = 2
Divide Number of counters by number of rows
= 16 ÷ 2 = 8
Thus the correct answer is option D.

Question 4.
Cody put 4 plates on the table. He put 1 apple on each plate. Which number sentence can be used to find the total number of apples on the table?
Options:
a. 4 + 1 = 5
b. 4 − 1 = 3
c. 4 × 1 = 4
d. 4 ÷ 2 = 2

Answer: 4 × 1 = 4

Explanation:

Cody put 4 plates on the table.
He put 1 apple on each plate.
The total number of apples on each table = 4 × 1 = 4
So, the correct answer is option C.

Question 5.
Which number sentence is a related fact to 7 × 3 = 21?
Options:
a. 7 + 3 = 10
b. 7 − 3 = 4
c. 7 × 2 = 14
d. 21 ÷ 3 = 7

Answer: 21 ÷ 3 = 7

Explanation:

The related division fact of 7 × 3 = 21 is 21 ÷ 3 = 7
The correct answer is option D.

Question 6.
Find the quotient.
4)\(\bar{3 6}\)
Options:
a. 9
b. 8
c. 7
d. 6

Answer: 9

Explanation:

36 ÷ 4 = 9
4 divides 36 nine times. So the quotient is 9.
So, the correct answer is option A.

Review/Test – Page No. 551

Question 1.
Alexa and Rose read books that have the same number of pages. Alexa’s book is divided into 8 equal chapters. Rose’s book is divided into 6 equal chapters. Each girl has read 3 chapters of her book.
Write a fraction to describe what part of the book each girl read. Then tell who read more pages. Explain.
Type below:
_____________

Answer: Rose read more pages than Alexa

Explanation:

Given that,
Alexa and Rose read books that have the same number of pages.
Alexa’s book is divided into 8 equal chapters.
Rose’s book is divided into 6 equal chapters.
Each girl has read 3 chapters of her book.
The fraction of Alexa’s book = \(\frac{3}{8}\)
The fraction of Rose’s book = \(\frac{3}{6}\)
Now, compare the fractions to find who read more pages.
\(\frac{3}{8}\) & \(\frac{3}{6}\)
The numerators of the two fractions are the same. So compare the denominators.
The denominator of the greater number will be the smallest fraction.
\(\frac{3}{8}\) < \(\frac{3}{6}\)
By this, we can say that Rose read more pages than Alexa.

Question 2.
David, Maria, and Simone are shading same-sized index cards for a science project. David shaded \(\frac{2}{4}\) of his index card. Maria shaded \(\frac{2}{8}\) of her index card and Simone shaded \(\frac{2}{6}\) of her index card.
For 2a–2d, choose Yes or No to indicate whether the comparisons are correct.
a. \(\frac{2}{4}\) > \(\frac{2}{8}\)
i. yes
ii. no

Answer: Yes

Explanation:

\(\frac{2}{4}\) > \(\frac{2}{8}\)
The denominators with the smallest number will be the greatest fraction.
Thus the statement \(\frac{2}{4}\) > \(\frac{2}{8}\) is true.

Question 2.
b. \(\frac{2}{8}\) > \(\frac{2}{6}\)
i. yes
ii. no

Answer: No

Explanation:

\(\frac{2}{8}\) > \(\frac{2}{6}\)
The numerators are same so compare the denominators.
The denominator with the greatest number will be the smallest fraction.
\(\frac{2}{8}\) < \(\frac{2}{6}\)
Thus the statement is false.

Question 2.
c. \(\frac{2}{6}\) < \(\frac{2}{4}\)
i. yes
ii. no

Answer: Yes

Explanation:

\(\frac{2}{6}\), \(\frac{2}{4}\)
The numerators are same so compare the denominators.
The denominator with the greatest number will be the smallest fraction.
\(\frac{2}{6}\) < \(\frac{2}{4}\)
Thus the statement is correct.

Question 2.
d. \(\frac{2}{8}\) = \(\frac{2}{4}\)
i. yes
ii. no

Answer: No

Explanation:

\(\frac{2}{8}\) = \(\frac{2}{4}\)
The numerators and denominators are different.
So, \(\frac{2}{8}\) is not equal to \(\frac{2}{4}\)
The statement is false.

Question 3.
Dan and Miguel are working on the same homework assignment. Dan has finished \(\frac{1}{4}\) of the assignment. Miguel has finished \(\frac{3}{4}\) of the assignment. Which statement is correct? Mark all that apply.
Options:
a. Miguel has completed the entire assignment.
b. Dan has not completed the entire assignment.
c. Miguel has finished more of the assignment than Dan.
d. Dan and Miguel have completed equal parts of the assignment.

Answer: B & C are the correct statements.

Explanation:

Given, Dan and Miguel are working on the same homework assignment.
Dan has finished \(\frac{1}{4}\) of the assignment.
Miguel has finished \(\frac{3}{4}\) of the assignment.
A. Miguel has completed the entire assignment.
Miguel has finished \(\frac{3}{4}\) of the assignment. So the statement is false.
B. Dan has not completed the entire assignment.
Dan has finished \(\frac{1}{4}\) of the assignment. So the statement is true.
C. Miguel has finished more of the assignment than Dan.
\(\frac{3}{4}\) > \(\frac{1}{4}\)
So, the statement is true.
D. Dan and Miguel have completed equal parts of the assignment.
\(\frac{3}{4}\) is not equal to \(\frac{1}{4}\)
Thus the statement is false.
So the correct answer is B & C.

Review/Test – Page No. 552

Question 4.
Bryan cut two peaches that were the same size for lunch. He cut one peach into fourths and the other into sixths. Bryan ate \(\frac{3}{4}\) of the first peach. His brother ate \(\frac{5}{6}\) of the second peach. Who ate more peach? Explain the strategy you used to solve the problem.
___________

Answer: Bryan’s brother

Explanation:

Given that,
Bryan cut two peaches that were the same size for lunch.
He cut one peach into fourths and the other into sixths.
Bryan ate \(\frac{3}{4}\) of the first peach.
His brother ate \(\frac{5}{6}\) of the second peach.
Compare the fractions \(\frac{3}{4}\) and \(\frac{5}{6}\)
The numerators and denominators are different.
\(\frac{3}{4}\) × \(\frac{6}{6}\) = \(\frac{18}{24}\)
\(\frac{5}{6}\) × \(\frac{3}{4}\) = \(\frac{15}{24}\)
\(\frac{15}{24}\) < \(\frac{18}{24}\)
By this we can say that Bryan’s brother ate more peach.

Question 5.
A nature center offers 2 guided walks. The morning walk is \(\frac{2}{3}\) mile. The evening walk is \(\frac{3}{6}\) mile. Which walk is shorter? Explain how you can use the model to find the answer.

___________

Answer: Evening walk

Explanation:

Given, The morning walk is \(\frac{2}{3}\) mile
The evening walk is \(\frac{3}{6}\) mile.
The shorter among both is \(\frac{3}{6}\) i.e, evening walk

\(\frac{2}{3}\) > \(\frac{3}{6}\)

Question 6.
Chun lives \(\frac{3}{8}\) mile from school. Gail lives \(\frac{5}{8}\) mile from school. Use the fractions and symbols to show which distance is longer.

\(\frac{□}{□}\) mile

Answer: \(\frac{3}{8}\) < \(\frac{5}{8}\)

Explanation:

Given,
Chun lives \(\frac{3}{8}\) mile from school.
Gail lives \(\frac{5}{8}\) mile from school.
Denominators are the same so we have to compare the numerators.
3 is less than 5. \(\frac{3}{8}\) < \(\frac{5}{8}\)

Review/Test – Page No. 553

Question 7.
Mrs. Reed baked four pans of lasagna for a family party. Use the rectangles to represent the pans.

Part A
Draw lines to show how Mrs. Reed could cut one pan of lasagna into thirds, one into fourths, one into sixths, and one into eighths.
Type below:
___________

Answer:

Mrs. Reed could cut one pan of lasagna into thirds:

Mrs. Reed could cut one pan of lasagna into fourths:

Mrs. Reed could cut one pan of lasagna into sixths:

Mrs. Reed could cut one pan of lasagna into eighths:

Question 7.
Part B
At the end of the dinner, equivalent amounts of lasagna in two pans were left. Use the models to show the lasagna that might have been left over. Write two pairs of equivalent fractions to represent the models.
Type below:
___________

Answer:

\(\frac{1}{3}\) = \(\frac{2}{6}\)

\(\frac{1}{4}\) = \(\frac{2}{8}\)

Question 8.
Tom rode his horse for \(\frac{4}{6}\) mile. Liz rode her horse for an equal distance. What is an equivalent fraction that describes how far Liz rode? Use the models to show your work.

\(\frac{4}{6}\) = \(\frac{□}{□}\)

Answer: \(\frac{4}{6}\) = \(\frac{2}{3}\)

Explanation:

The above figure shows that the fraction of the first figure \(\frac{4}{6}\) is equal to the fraction of the second figure i.e., \(\frac{2}{3}\).

Question 9.
Avery prepares 2 equal-size oranges for the bats at the zoo. One dish has \(\frac{3}{8}\) of an orange. Another dish has \(\frac{1}{4}\) of an orange. Which dish has more orange? Show your work. \(\frac{□}{□}\)

Answer: First, we need to find an equivalent fraction to \(\frac{1}{4}\) so it would have the same denominator as \(\frac{3}{8}\)
\(\frac{1}{4}\) = \(\frac{2}{8}\) – equivalent fractions
Now we can compare the fractions:
\(\frac{2}{8}\) < \(\frac{3}{8}\)
Therefore \(\frac{1}{4}\) < \(\frac{3}{8}\)
So, the answer is \(\frac{3}{8}\)

Review/Test – Page No. 554

Question 10.
Jenna painted \(\frac{1}{8}\)of one side of a fence. Mark painted \(\frac{1}{6}\) of the other side of the same fence. Use >, =, or < to compare the parts that they painted.
\(\frac{1}{8}\) ______ \(\frac{1}{6}\)

Answer: \(\frac{1}{8}\) < \(\frac{1}{6}\)

Explanation:

Jenna painted \(\frac{1}{8}\)of one side of a fence.
Mark painted \(\frac{1}{6}\) of the other side of the same fence.
The numerators of both fractions are the same. So compare the denominators.
\(\frac{1}{8}\) & \(\frac{1}{6}\)
The denominator with the greatest number will be the smallest fraction.
So, \(\frac{1}{8}\) < \(\frac{1}{6}\)

Question 11.
Bill used \(\frac{1}{3}\) cup of raisins and \(\frac{2}{3}\) cup of banana chips to make a snack. For 11a–11d, select True or False for each comparison.
a. \(\frac{1}{3}\) > \(\frac{2}{3}\)
i. True
ii. False

Answer: False

Explanation:

The denominators are the same here. So check the numerators.
1 is less than 2.
\(\frac{1}{3}\) > \(\frac{2}{3}\)
The statement is false.

Question 11.
b. \(\frac{2}{3}\) = \(\frac{1}{3}\)
i. True
ii. False

Answer: False

Explanation:

The denominators and numerators are not equal in this equation.
So, the statement is false.

Question 11.
c. \(\frac{1}{3}\) < \(\frac{2}{3}\)
i. True
ii. False

Answer: True

Explanation:

The denominators of both the fractions are the same.
Compare the numerators. 1 is less than 2.
So, \(\frac{1}{3}\) < \(\frac{2}{3}\).
The statement is true.

Question 11.
d. \(\frac{2}{3}\) > \(\frac{1}{3}\)
i. True
ii. False

Answer: True

Explanation:

The denominators of both the fractions are the same.
Compare the numerators. 2 is greater than 1.
\(\frac{2}{3}\) > \(\frac{1}{3}\)
The statement is true.

Question 12.
Jorge, Lynne, and Crosby meet at the playground. Jorge lives \(\frac{5}{6}\) mile from the playground. Lynne lives \(\frac{4}{6}\) mile from the playground. Crosby lives \(\frac{7}{8}\) mile from the playground.
Part A
Who lives closer to the playground, Jorge or Lynne?
Explain how you know.
_____

Answer: Lynne

Explanation:

Jorge lives \(\frac{5}{6}\) mile from the playground.
Lynne lives \(\frac{4}{6}\) mile from the playground.
The denominators are the same. So, compare the numerators.
5 is greater than 4. So, \(\frac{5}{6}\) > \(\frac{4}{6}\)
Therefore, Lynne lives closer to the playground.

Question 12.
Part B
Who lives closer to the playground, Jorge or Crosby?
Explain how you know.
_____

Answer: Jorge

Explanation:

Jorge lives \(\frac{5}{6}\) mile from the playground.
Crosby lives \(\frac{7}{8}\) mile from the playground.
Compare the fraction of the both Jorge and Crosby.
\(\frac{5}{6}\) × \(\frac{8}{8}\) = \(\frac{40}{48}\)
\(\frac{7}{8}\) × \(\frac{6}{6}\) = \(\frac{42}{48}\)
\(\frac{40}{48}\) < \(\frac{42}{48}\)
Therefore, Jorge lives closer to the playground.

Review/Test – Page No. 555

Question 13.
Ming needs \(\frac{1}{2}\) pint of red paint for an art project. He has 6 jars that have the following amounts of red paint in them. He wants to use only 1 jar of paint. Mark all of the jars of paints that Ming could use.
Options:
a. \(\frac{2}{3}\) pint
b. \(\frac{1}{4}\) pint
c. \(\frac{4}{6}\) pint
d. \(\frac{3}{4}\) pint
e. \(\frac{3}{8}\) pint
f. \(\frac{2}{6}\) pint

Answer: \(\frac{2}{3}\) pint, \(\frac{3}{4}\) pint, \(\frac{4}{6}\) pint

Explanation:

We have to find all the jars that have an amount of paint greater than \(\frac{1}{2}\)
A. \(\frac{2}{3}\) pint > \(\frac{1}{2}\)
B. \(\frac{1}{4}\) pint < \(\frac{1}{2}\)
C. \(\frac{4}{6}\) pint > \(\frac{1}{2}\)
D. \(\frac{3}{4}\) pint < \(\frac{1}{2}\)
E. \(\frac{3}{8}\) pint < \(\frac{1}{2}\)
F. \(\frac{2}{6}\) pint < \(\frac{1}{2}\)

Question 14.
There are 12 people having lunch. Each person wants \(\frac{1}{3}\) of a sub sandwich. How many whole sub sandwiches are needed? Use the models to show your answer.

______ sub sandwiches

Answer: 4 sub sandwiches

Explanation:

Given that, There are 12 people having lunch.
Each person wants \(\frac{1}{3}\) of a sub sandwich.
Multiply the number of people with Each person wants of a sub sandwich.
12 × \(\frac{1}{3}\)
3 divides 12 four times. So, the answer is 4 sub sandwiches.

Question 15.
Mavis mixed \(\frac{2}{4}\) quart of apple juice with \(\frac{1}{2}\) quart of cranberry juice. Compare the fractions. Choose the symbol that makes the statement true.
\(\frac{2}{4}\) \(\frac{1}{2}\)
______

Answer:  \(\frac{2}{4}\) = \(\frac{1}{2}\)

Question 16.
Pat has three pieces of fabric that measure \(\frac{3}{6}\), \(\frac{5}{6}\), and \(\frac{2}{6}\) yards long. Write the lengths in order from least to greatest.
Type below:
___________

Answer: \(\frac{2}{6}\), \(\frac{3}{6}\), \(\frac{5}{6}\)

Explanation:

The denominators of \(\frac{3}{6}\), \(\frac{5}{6}\), and \(\frac{2}{6}\) are same. So, Compare the numerators 2 < 3, 5

Review/Test – Page No. 556

Question 17.
Cora measures the heights of three plants. Draw a line to match each height on the left to the word on the right that describes its place in the order of heights.

Type below:
___________

Answer:

Explanation:

\(\frac{4}{6}\) < \(\frac{4}{4}\)
\(\frac{4}{8}\) < \(\frac{4}{4}\)
\(\frac{4}{6}\) > \(\frac{4}{8}\)
The numerators are same. So, compare the denominators. The greatest fraction will have the lesser denominator.
\(\frac{4}{8}\) < \(\frac{4}{6}\) < \(\frac{4}{4}\).

Question 18.
Danielle drew a model to show equivalent fractions.

Use the model to complete the number sentence.
\(\frac{1}{2}\) = \(\frac{□}{□}\) = \(\frac{□}{□}\)
Type below:
___________

Answer: \(\frac{1}{2}\) = \(\frac{2}{4}\) = \(\frac{4}{8}\)

Total number of boxes are 4 and each are grouped into 2 = 8
Out of 4 boxes 2 boxes are shaded = \(\frac{2}{4}\)
\(\frac{2}{4}\) = \(\frac{1}{2}\)
Next out of 8 grouped squares 4 are shaded = \(\frac{4}{8}\)
\(\frac{4}{8}\) = \(\frac{1}{2}\)
Therefore the equivalent fractions are \(\frac{1}{2}\) = \(\frac{2}{4}\) = \(\frac{4}{8}\)

Question 19.
Floyd caught a fish that weighed \(\frac{2}{3}\) pound. Kira caught a fish that weighed \(\frac{7}{8}\) pound. Whose fish weighed more? Explain the strategy you used to solve the problem.
_____

Answer: Kira

Explanation:

We need to find equivalent fractions with the same denominator:
So Make the denominators of \(\frac{2}{3}\) and \(\frac{7}{8}\) equal.
\(\frac{2}{3}\) × \(\frac{8}{8}\) = \(\frac{16}{24}\)
\(\frac{7}{8}\) × \(\frac{3}{3}\) = \(\frac{21}{24}\)
\(\frac{16}{24}\) < \(\frac{21}{24}\)
Therefore \(\frac{2}{3}\) < \(\frac{7}{8}\)

Question 20.
Sam went for a ride on a sailboat. The ride lasted \(\frac{3}{4}\) hour.

What fraction is equivalent to \(\frac{3}{4}\)?
\(\frac{□}{□}\)

Answer: \(\frac{6}{8}\)

Explanation:

Total number of boxes are 4 and each is grouped into 2 = 8
Out of 4 boxes 3 boxes are shaded = \(\frac{3}{4}\)
Next out of 8 grouped squares 6 are shaded = \(\frac{6}{8}\)
Thus the fraction is equivalent to \(\frac{3}{4}\) is \(\frac{6}{8}\)

Conclusion

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Common Core – Page No. 171000

Lesson 8.1

Write the number of equal parts. Then write the name for the parts.

Question 1.

Equal parts: _________
Name: _________

Answer:

i. 4
ii. Fourths

Explanation:

The figure shows that the square is divided into 4 equal parts. So, the name for the parts is fourths.

Question 2.

Equal parts: _________
Name: _________

Answer:

i. 2
ii. Halves

Explanation:

The circle is divided into two equal parts. Thus the name for the parts is halves.

Question 3.

Equal parts: _________
Name: _________

Answer:

i. 6
ii. Sixths

Explanation:

The hexagon is divided into six equal parts. Thus the name for the parts is sixths.

Lesson 8.2

Draw lines to show how much each person gets. Write the answer.

Question 4.
4 friends share 3 oranges equally.

Type below:
___________

Answer: 3 fourths of an orange

Explanation:

There are 3 oranges and
The total number of friends = 4
We need to divide the 3 oranges for 4 friends equally
= 3/4
So, each friend gets 3 fourth of the orange.

Question 5.
6 sisters share 4 sandwiches equally.

Type below:
___________

Answer: 4 sixths of a sandwich

Explanation:

Total number of sandwiches = 4
Number of friends = 6
To share the sandwiches equally we need to divide the number of sandwiches by a number of friends.
4/6
So, each friend gets 4 sixths of the sandwich.

Lessons 8.3–8.4

Write the number of equal parts in the whole. Write a fraction in words and in numbers to name the shaded part.

Question 6.

_________ equal parts
_________ eighths

Question 6.
\(\frac{□} {□}\)

Answer:

i. 8
ii. Five
iii. \(\frac{5} {8}\)

Explanation:

The square is divided into 8 eight equal parts.
Among them, five parts are shaded.
So, the fraction name for the shaded part is \(\frac{5} {8}\).

Question 7.

_________ equal parts
_________ thirds

Question 7.
\(\frac{□} {□}\)

Answer:

i. 3
ii. Two
iii. \(\frac{2} {3}\)

Explanation:

The aboved figure shows that the rectangle is divided into 3 equal parts. And 2 parts are shaded among them.
The fraction name for the shaded part is 2 thirds i.e, \(\frac{2} {3}\)

Common Core – Page No. 172000

Lesson 8.5

Write the fraction that names the point.

Question 1.
point A: \(\frac{□} {□}\)

Answer: \(\frac{1} {6}\)

Explanation:

The number lies between 0 and 1. Each point is 1 sixth of the number line. So, it starts with 0/6 and ends on 6/6.
Now we have to locate the point A.
The point A lies between 0/6 and 2/6. The number between 0 and 2 is 1.
Thus the point A is \(\frac{1} {6}\)

Question 2.
point B: \(\frac{□} {□}\)

Answer: \(\frac{3} {6}\)

Explanation:

The point B lies between \(\frac{2} {6}\) and \(\frac{4} {6}\). The number between 2 and 4 is 3. Thus the location of point B is \(\frac{3} {6}\).

Question 3.
point C: \(\frac{□} {□}\)

Answer: \(\frac{5} {6}\)

Explanation:

The point C is located between \(\frac{4} {6}\) and \(\frac{6} {6}\).
The number between 4 and 6 is 5. Thus the location of Point C is \(\frac{5} {6}\)

Lesson 8.6

Each shape is 1 whole. Write a fraction greater than 1 for the parts that are shaded.

Question 4.

2 = \(\frac{□} {□}\)

Answer: \(\frac{8} {4}\)

Explanation:

There are 2 circles and each circle is equally divided into 4 groups.
Number in each group = 4
Number of equal parts = 8
The shaded part of the circle = \(\frac{8} {4}\)

Question 5.

3 = \(\frac{□} {□}\)

Answer: \(\frac{18} {6}\)

Explanation:

Number of circles = 3
Number of equal parts = 18
Number of shaded part in each circle = 6
So, the fraction of the shaded part is \(\frac{18} {6}\)

Lesson 8.7

Write a fraction to name the shaded part of each group.

Question 6.

\(\frac{□} {□}\)

Answer: \(\frac{3} {6}\) or \(\frac{1} {2}\)

Explanation:

There are 6 circles, in which 3 circles are shaded and 3 circles are not shaded.
So, the fraction name for the shaded part is \(\frac{3} {6}\) or \(\frac{1} {2}\)

Question 7.

\(\frac{□} {□}\)

Answer: \(\frac{1} {4}\) or \(\frac{2} {8}\)

Explanation:

The figure shows that there are 8 circles and in that 2 circles are shaded.
So, the fraction name for the shaded part is \(\frac{2} {8}\) or \(\frac{1} {4}\)

Lessons 8.8–8.9

Draw a quick picture to solve.

Question 8.
Charlotte has 12 T-shirts. One-fourth of her T-shirts is green. How many of Charlotte’s T-shirts are green?
_________ green T-shirts

Answer: 3 T-shirts

Explanation:

Given,
Charlotte has 12 T-shirts.
One-fourth of her T-shirts is green.
To know how many of Charlotte’s T-shirts are green we need to multiply 12 with 1/4
12 × \(\frac{1} {4}\)
12/4 = 3
Therefore there are 3 green T-shirts.

Question 9.
Josh walks 18 dogs each week. Today, he is walking \(\frac{1}{3}\) of the dogs. How many dogs is he walking today?
_________ dogs

Answer: 6 dogs

Explanation:

Given that Josh walks 18 dogs each week.
Today, he is walking \(\frac{1}{3}\) of the dogs.
To find how many dogs he walked today
We need to multiply 18 and \(\frac{1}{3}\)
18 × \(\frac{1}{3}\)
= 18/3 = 6
Thus he walked 6 dogs today.

Go Math Grade 3 Answer Key Chapter 8 Understand Fractions Extra Practice helps you to test your preparation standards. You can see the topics like Equal parts of a whole, unit fractions, relate fractions and whole numbers. We even considered images for a few questions for a better understanding of the concepts.

Go Math Grade 3 Answer Key Chapter 7 Division Facts and Strategies includes fundamentals of divisions using several methods. Those who want to improve their skills in Math can refer to HMH Go Math Grade 3 Chapter 7 Answer Key. You can Download Go Math Grade 3 Answer Key Chapter 7 Division Facts and Strategies PDF free of cost and use quick reference for all your queries.

3rd Grade Go Math Answer Key Chapter 7 Division Facts and Strategies

You can learn the fundamentals of multiplication and division using our Go Math Grade 3 Answer Key Chapter 7 Division Facts and Strategies. Before you begin your preparation learn the topics covered in the Chapter and learn accordingly. Click on the below-mentioned links to access different Lessons within the Chapter & Division Facts and Strategies. We even provided a short and crisp explanation for the Problems to help you understand the concepts easily. Make the most out of Go Math Grade 3 Solution Key and score better grades in your exams.

Lesson 1: Divide by 2

• Divide by 2 Page No. 369
• Divide by 2 Lesson Check Page No. 370

Lesson 2: Divide by 10

• Divide by 10 Page No. 375
• Divide by 10 Lesson Check Page No. 376

Lesson 3: Divide by 5

• Divide by 5 Page No. 381
• Divide by 5 Lesson Check Page No. 382

Lesson 4: Divide by 3

• Divide by 3 Page No. 387
• Divide by 3 Lesson Check Page No. 388

Lesson 5: Divide by 4

• Divide by 4 Page No. 393
• Divide by 4 Lesson Check Page No. 394

Lesson 6: Divide by 6

• Divide by 6 Page No. 399
• Divide by 6 Lesson Check Page No. 400

Mid -Chapter Checkpoint

• Mid -Chapter Checkpoint Page No. 401
• Mid -Chapter Checkpoint Lesson Check Page No. 402

Lesson 7: Divide by 7

• Divide by 7 Page No. 407
• Divide by 7 Lesson Check Page No. 408

Lesson 8: Divide by 8

• Divide by 8 Page No. 413
• Divide by 8 Lesson Check Page No. 413

Lesson 9: Divide by 9

• Divide by 9 Page No. 419
• Divide by 9 Lesson Check Page No. 420

Lesson 10: Problem Solving • Two-Step Problems

• Problem Solving Two-Step Problems Page No. 425
• Two-Step Problems Lesson Check Page No. 426

Lesson 11: Order of Operations

• Order of Operations Page No. 431
• Order of Operations Lesson Check Page No. 432

Chapter 7 Review/Test

• Review/Test Page No. 433
• Review/Test Page No. 434
• Review/Test Page No. 435
• Review/Test Page No. 436
• Review/Test Page No. 437
• Review/Test Page No. 438

Divide by 2 – Page No. 369

Write a division equation for the picture.

Question 1.

Answer: 12 ÷ 2 = 6 or 12 ÷ 6 = 2

Explanation:

Number of counters = 12
Number of equal groups = 2
Number of counters in each group = 6
The division equation is the number of counters by number in each group = 12 ÷ 6 = 2
Next, divide number of counters by number of rows = 12 ÷ 2 = 6

Question 2.

Type below:
__________

Answer: 18 ÷ 2 = 9 or 18 ÷ 9 = 2

Explanation:

Number of counters = 18
Number of groups = 2
Number of counters in each group = 9
So, the division equation is the number of counters by number of groups = 18 ÷ 2 =9
Next divide number of counters by number in each group = 18 ÷ 9 = 2

Question 3.

Type below:
__________

Answer: 10 ÷ 5 = 2 or 10 ÷ 2 = 5

Explanation:

No. of counters = 10
Number of groups = 5
No. of counters in each group = 2
The division equation is 10 ÷ 5 = 2 or 10 ÷ 2 = 5

Find the quotient. You may want to draw a quick picture to help.

Question 4.
______ = 14 ÷ 2

Answer: 7

Explanation:

14/2 = 7
So, the quotient is 7

Question 5.
______ = 4 ÷ 2

Answer: 2

Explanation:

4/2 = 2
The quotient is 2

Question 6.
16 ÷ 2 = ______

Answer: 8

Explanation:

16/2 = 8
The quotient is 8

Question 7.
2)\(\bar { 1 8 }\)
______

Answer: 9

Explanation:

18/2 = 9
The quotient is 9

Question 8.
2)\(\bar { 1 2 }\)
______

Answer: 6

Explanation:

12/2 = 6
So, the quotient is 6.

Question 9.
2)\(\bar { 1 4 }\)
______

Answer: 7

Explanation:

14/2 = 7
The quotient is 7

Problem Solving

Question 10.
Mr. Reynolds, the gym teacher, divided a class of 16 students into 2 equal teams. How many students were on each team?
______ students

Answer: 8 students

Explanation:

Number of students = 16
Number of equal teams = 2
Number of students in each team = x
To find the number of students in each team we need to divide the number of students by number of equal teams
= 16 ÷ 2 = 8 students

Question 11.
Sandra has 10 books. She divides them into groups of 2 each. How many groups can she make?
______ groups

Answer: 5 groups

Explanation:

Given,
Sandra has 10 books
She divides them into groups of 2 each
Divide the number of books by the number of books in each group
= 10 ÷ 2 = 5 groups
Therefore Sandra makes 5 groups.

Divide by 2 – Page No. 370

Lesson Check

Question 1.
Ava has 12 apples and 2 baskets. She puts an equal number of apples in each basket. How many apples are in a basket?
Options:
a. 2
b. 4
c. 6
d. 8

Answer: 6

Explanation:

Given that, Ava has 12 apples and 2 baskets
She puts an equal number of apples in each basket
Divide number of apples by number of baskets = 12 ÷ 2= 6
So, she puts 6 apples in each basket.
Thus the correct answer is option C

Question 2.
There are 8 students singing a song in the school musical. Ms. Lang put the students in 2 equal rows. How many students are in each row?
Options:
a. 2
b. 4
c. 6
d. 10

Answer: 4

Explanation:

There are 8 students singing a song in the school musical
Ms. Lang put the students in 2 equal rows
To find the number of students in each row
We have to divide the number of students by number of equal rows
= 8 ÷ 2 = 4

Spiral Review

Question 3.
Find the product.
2 × 6
Options:
a. 4
b. 8
c. 12
d. 18

Answer: 12

Question 4.
Jayden plants 24 trees. He plants the trees equally in 3 rows. How many trees are in each row?
Options:
a. 6
b. 8
c. 9
d. 27

Answer: 8

Explanation:

Given,
Jayden plants 24 trees
He plants the trees equally in 3 rows
To know the number of trees in each row we have to divide number of trees by number of trees
24 ÷ 3 = 8
Thus the correct answer is option B

Question 5.
Which of the following describes this pattern?
9, 12, 15, 18, 21, 24
Options:
a. Multiply by 3.
b. Multiply by 5.
c. Add 3.
d. Subtract 3.

Answer: Add 3

Explanation:

By seeing the above pattern we can say that every number is added by 3
9 + 3 = 12 + 3 = 15 + 3 = 18 + 3 = 21 + 3 = 24
So, the correct answer is option C

Question 6.
A tricycle has 3 wheels. How many wheels are there on 4 tricycles?
Options:
a. 7
b. 9
c. 12
d. 15

Answer: 12

Explanation:

Given,
A tricycle has 3 wheels
number of wheels are there on 4 tricycles = x
x = 4 × 3 = 12
So, the correct answer is option C

Divide by 10 – Page No. 375

Find the unknown factor and quotient.

Question 1.

Answer: 2, 2

Explanation:

Let the unknown factor be x
10 × x = 20
x = 20/10 = 2
20/10 = 2
The quotient is 2

Question 2.
10 × ______ = 70   70 ÷ 10 = ______

Answer: 7, 7

Explanation:

Let x be the unknown factor
10 × x = 70
x = 70/10 =  7
Since division is the opposite of multiplication, you can use a multiplication table to find a quotient

Question 3.
10 × ______ = 80   80 ÷ 10 = ______

Answer: 8, 8

Explanation:

Let a be the unknown factor
10 × a = 80
a = 80/10 = 8

Question 4.
10 × ______ = 30   30 ÷ 10 = ______

Answer: 3, 3

Explanation:

y be the unknown factor
10 × y = 30
y = 30/10 = 3
First, we need to check whether the divisor or dividend is the related multiplication fact or not.
Next check whether the divisor or the dividend the product in the related multiplication fact or not. If both are the same then the quotient is the unknown factor.

Find the quotient.

Question 5.
60 ÷ 10 = ______

Answer: 6

Explanation:

Question 6.
______ = 40 ÷ 4

Answer: 10

Explanation:

Question 7.
20 ÷ 2 = ______

Answer: 10

Explanation:

Question 8.
50 ÷ 10 = ______

Answer: 5

Explanation:

Question 9.
90 ÷ 10 = ______

Answer: 9

Explanation:

Question 10.
10 ÷ 10 = ______

Answer: 1

Explanation:

10/10 = 1
Any number divided by the same number is always 1. So, the quotient is 1.

Question 11.
______ = 30 ÷ 10

Answer: 3

Explanation:

Question 12.
40 ÷ 10 = ______

Answer: 4

Explanation:

40/10 = 4
So, the quotient is 4

Question 13.
10)\(\bar { 4 0 }\)
______

Answer: 4

Explanation:

40 ÷ 10 = 40/10 = 4
10 cancels 40 by 4 times. So, the quotient is 4

Question 14.
10)\(\bar { 7 0 }\)
______

Answer: 7

Explanation:

Question 15.
10)\(\bar { 1 0 0 }\)
______

Answer: 10

Explanation:

100 ÷ 10 = 100/10 = 10
So, the quotient is 10.

Question 16.
10)\(\bar { 2 0 }\)
______

Answer: 2

Explanation:

Problem Solving

Question 17.
Pencils cost 10¢ each. How many pencils can Brent buy with 90¢?
______ pencils

Answer: 9 pencils

Explanation:

Given:
Pencils cost 10¢ each
Number of pencils can Brent buy with 90¢ = x
x × 10¢ = 90¢
x = 90/10 = 9
Thus Brent can buy 9 pencils with 90¢

Question 18.
Mrs. Marks wants to buy 80 pens. If the pens come in packs of 10, how many packs does she need to buy?
______ packs

Answer: 8 packs

Explanation:

Mrs. Marks wants to buy 80 pens
The pens come in packs of 10
No. of packs she needs to buy =?
Divide the number of pens by number of pens in one pack
= 80 ÷ 10 = 8
Therefore Mrs. Marks needs to buy 8 packs.

Divide by 10 – Page No. 376

Lesson Check

Question 1.
Gracie uses 10 beads on each necklace she makes. She has 60 beads to use. How many necklaces can Gracie make?
Options:
a. 6
b. 10
c. 50
d. 70

Answer: 6

Explanation:

Given, Gracie uses 10 beads on each necklace she makes
She has 60 beads to use
How many necklaces can Gracie make?
Divide the number of beads by the number of beads on each necklace
= 60 ÷ 10 = 6
Thus the correct answer is option A.

Question 2.
A florist arranges 10 flowers in each vase. How many vases does the florist need to arrange 40 flowers?
Options:
a. 3
b. 4
c. 30
d. 50

Answer: 4

Explanation:

A florist arranges 10 flowers in each vase
Number of vases the florist need to arrange 40 flowers
To find the number of vases that florist need
We have to divide the number of flowers by number of flowers in each vase
= 40 ÷ 10 = 4
Thus the florist needs 4 vases to arrange 40 flowers

Spiral Review

Question 3.
What is the unknown factor?
7 × p = 14
Options:
a. 21
b. 7
c. 3
d. 2

Answer: 2

Explanation:

P is the unknown factor
7 × p = 14
p = 14/7
p= 2
So, the correct answer is option D

Question 4.
Aspen Bakery sold 40 boxes of rolls in one day. Each box holds 6 rolls. How many rolls in all did the bakery sell?
Options:
a. 24
b. 46
c. 240
d. 320

Answer: 240

Explanation:

Aspen Bakery sold 40 boxes of rolls in one day
Each box holds 6 rolls
To find the number of rolls in all did bakery sell, we have to multiply no. of boxed in 1 day with a number of rolls in each box
= 40 × 6 = 240 rolls
Thus the correct answer is option C

Question 5.
Mr. Samuels buys a sheet of stamps. There are 4 rows with 7 stamps in each row. How many stamps does Mr. Samuels buy?
Options:
a. 11
b. 14
c. 21
d. 28

Answer: 28

Explanation:

Mr. Samuels buys a sheet of stamps. There are 4 rows with 7 stamps in each row.
To know the number of stamps Mr. Samuels buy, we have to multiply no. of rows with the number of stamps in each row
= 7 × 4 = 28
Therefore, Mr. Samuels buy 28 stamps.

Question 6.
There are 56 students going on a field trip to the science center. The students tour the center in groups of 8. How many groups of students are there?
Options:
a. 6
b. 7
c. 9
d. 64

Answer: 7

Explanation:

There are 56 students going on a field trip to the science center.
The students tour the center in groups of 8.
The number of groups =?
Divide the number of students by the number of students in each group = 56 ÷ 8 = 7
So, the answer is option B

Divide by 5 – Page No. 381

Use count up or count back on a number line to solve.

Question 1.

Answer: 8

Explanation:

Step 1:

Start at 40

Step 2:

Count back by 5s until you reach point 0. Complete the jumps on the number line.

Step 3:

Count the number of times you jumped back 5.
You jumped 8 times to reach 0.
Thus, 40 ÷ 5 = 8

Question 2.

25 ÷ 5 = _______

Answer: 5

• Start at 25
• Count back by 5s until you reach point 0. Complete the jumps on the number line.
• Count the number of times you jumped back 5.
  You jumped 5 times to reach 0.
  Thus, 25 ÷ 5 = 5

Find the quotient.

Question 3.
_______ = 10 ÷ 5

Answer: 2

• Begin at 0.
• Count up 5s until you reach 10
• Count the number of times you count up.

5, 10
You counted by 5 two times. 10 ÷ 5 = 2

Question 4.
_______ = 30 ÷ 10

Answer: 3

• Begin at 0.
• Count up 10s until you reach 30
• Count the number of times you count up.

10, 20, 30
You counted by 10 three times. 30 ÷ 10 = 3

Question 5.
14 ÷ 2 = _______

Answer: 7

• Begin at 0.
• Count up 2s until you reach 14
• Count the number of times you count up.

2, 4, 6, 8, 10, 12, 14
You counted by 2 seven times.
Thus 14 ÷ 2 = 7

Question 6.
5 ÷ 5 = _______

Answer: 1

• Begin at 0.
• Count up 5s until you reach 5
• Count the number of times you count up.

5
You counted by 5 one time. 5 ÷ 5 = 1
Thus 1 is the quotient.

Question 7.
45 ÷ 5 = _______

Answer: 9

• Begin at 0.
• Count up 5s until you reach 45
• Count the number of times you count up.

5, 10, 15, 20, 25, 30, 35, 40, 45
You counted by 5 nine times. 45 ÷ 5 = 9
Thus the quotient is 9.

Question 8.
_______ = 60 ÷ 10

Answer: 6

• Begin at 0.
• Count up 10s until you reach 60
• Count the number of times you count up.

10, 20, 30, 40, 50, 60
You counted by 10 six times. 60 ÷ 10 = 6
So, the quotient is 6

Question 9.
_______ = 15 ÷ 5

Answer: 3

• Begin at 0.
• Count up 5s until you reach 15
• Count the number of times you count up.

5, 10, 15
You count 15 by 5 three times. 15 ÷ 5 = 3
So, the quotient is 3.

Question 10.
18 ÷ 2 = _______

Answer: 9

• Begin at 0.
• Count up 2s until you reach 18
• Count the number of times you count up.

2, 4, 6, 8, 10, 12, 14, 16, 18.
You count by 2 nine times. So, 18 ÷ 2 = 9

Question 11.
_______ = 0 ÷ 5

Answer: 0

0 divided by any number is always 0. So, the quotient is 0.

Question 12.
20 ÷ 5 = _______

Answer: 4

• Begin at 0.
• Count up 5s until you reach 20.
• Count the number of times you count up.

5, 10, 15, 20
You count by 5 four times. Thus 20 ÷ 5 = 4

Question 13.
25 ÷ 5 = _______

Answer: 5

• Begin at 0.
• Count up 5s until you reach 25.
• Count the number of times you count up.

5, 10, 15, 20, 25.
That means you counted 5 times to reach 25. 25 ÷ 5 = 5

Question 14.
_______ = 35 ÷ 5

Answer: 7

• Start at 0.
• Count up 5s until you reach 35.
• Count the number of times you count up to reach 35.

5, 10, 15, 20, 25, 30, 35.
You counted 5s seven times to reach 35. 35 ÷ 5 = 7
Thus the quotient is 7.

Question 15.
5)\(\bar { 2 0 }\)
_______

Answer: 4

20 ÷ 5 = 4

• Begins at 0.
• Count up 5s until you reach 20.
• Count the number of times you count up to reach 20.

5, 10, 15, 20
You counted 5s four times.
20 ÷ 5 = 4. 4 is the quotient.

Question 16.
10)\(\bar { 7 0 }\)
_______

Answer: 7

70 ÷ 10 = 7

• Begins at 0.
• Count up 10s until you reach 70.
• Count the number of times you count up to reach 70.

10, 20, 30, 40, 50, 60, 70.
You counted 10s seven times. So, the quotient is 7.

Question 17.
5)\(\bar { 1 5 }\)
_______

Answer: 3

15 ÷ 5 = _

• Begin at 0.
• Count up 5s until you reach 15
• Count the number of times you count up.

5, 10, 15
So, the quotient is 3.

Question 18.
5)\(\bar { 4 0 }\)
_______

Answer: 8

• Start at 40
• Count up by 5s until you reach40.
• Count the number of times you count up.

5, 10, 15, 20, 25, 30, 35, 40.
Thus, 40 ÷ 5 = 8. The quotient is 8.

Problem Solving

Question 19.
A model car maker puts 5 wheels in each kit. A machine makes 30 wheels at a time. How many packages of 5 wheels can be made from the 30 wheels?
_______

Answer: 6 packages

Explanation:

A model car maker puts 5 wheels in each kit.
A machine makes 30 wheels at a time.
Divide the number of wheels by the number of wheels in each kit
= 30 ÷ 5 = 6 packages
6 packages of 5 wheels can be made from the 30 wheels.

Question 20.
A doll maker puts a small bag with 5 hair ribbons inside each box with a doll. How many bags of 5 hair ribbons can be made from 45 hair ribbons?
_______

Answer: 9 bags

Explanation:

A doll maker puts a small bag with 5 hair ribbons inside each box with a doll.
Let Number of bags of 5 hair ribbons can be made from 45 hair ribbons = y
Divide the total number of hair ribbons by number of hair ribbons in each bag
45 ÷ 5
y = 45/5 = 9
Therefore 9 bags of 5 hair ribbons can be made from 45 hair ribbons.

Divide by 5 – Page No. 382

Lesson Check

Question 1.
A model train company puts 5 boxcars with each train set. How many sets can be completed using 35 boxcars?
Options:
a. 5
b. 6
c. 7
d. 8

Answer: 7

Explanation:

A model train company puts 5 boxcars with each train set
Number of sets can be completed using 35 boxcars = x
To know the number of sets we need to divide no. of boxcars by no. of boxcars with each train set
35 ÷ 5 = 7 sets
Thus the correct answer is option C

Question 2.
A machine makes 5 buttons at a time. Each doll shirt gets 5 buttons. How many doll shirts can be finished with 5 buttons?
Options:
a. 0
b. 1
c. 2
d. 5

Answer: 1

Explanation:

A machine makes 5 buttons at a time
Each doll shirt gets 5 buttons
Divide 5 ÷ 5 = 1
Thus 1 doll shirt can be finished with 5 buttons

Spiral Review

Question 3.
Julia earns $5 each day running errands for a neighbor. How much will Julia earn if she runs errands for 6 days in one month?
Options:
a. $40
b. $35
c. $30
d. $25

Answer: $30

Explanation:

Julia earns $5 each day running errands for a neighbor
How much will Julia earn if she runs errands for 6 days in one month = x
To know how much she earns in one month, we have to multiply number of days with the income she earns per day
= $5 × 6 = $30
Thus Julia earns $30 if she runs errands for 6 days in one month.

Question 4.
Marcus has 12 slices of bread. He uses 2 slices of bread for each sandwich. How many sandwiches can Marcus make?
Options:
a. 6
b. 7
c. 8
d. 9

Answer: 6

Explanation:

Marcus has 12 slices of bread
He uses 2 slices of bread for each sandwich
Divide no. of slices of bread by slices of bread for each sandwich
= 12 ÷ 2 = 6
Thus Marcus makes 6 sandwiches.

Use the line plot for 5–6.

Question 5.
How many students have no pets?
Options:
a. 0
b. 3
c. 4
d. 5

Answer: 4

Explanation:

The above line plot shows that there are no pets is 4

Question 6.
How many students answered the question “How many pets do you have?”
Options:
a. 10
b. 12
c. 14
d. 15

Answer: 15

Explanation:

Number of students who have 0 pets = 4
Number of students who have 1 pet = 5
Number of students who have 2 pets = 2
Number of students who have 3 pets = 0
Number of students who have 4 pets = 3
Number of students who have 5 pets = 1
Total = 4 + 5 + 2 + 0 + 3 + 1 = 15 students

Divide by 3 – Page No. 387

Find the quotient. Draw a quick picture to help.

Question 1.

Answer: 4

Question 2.
24 ÷ 3 = _______

Answer: 8

Question 3.
_______ = 6 ÷ 3

Answer: 2

6 ÷ 3 = 2

Question 4.
40 ÷ 5 = _______

Answer: 8

40 ÷ 5 = 8

Find the quotient.

Question 5.
_______ = 15 ÷ 3

Answer: 5

• Start at 0.
• Count by 3 until you reach 15.
• Count the number of times you count up to 15.

3, 6, 9, 12, 15.

So, 15 ÷ 3 = 5

Question 6.
_______ = 21 ÷ 3

Answer: 7

Explanation:

• Start at 0.
• Count by 3 until you reach 21
• Count the number of times you count up to 21.

3, 6, 9, 12, 15, 18, 21.
21 ÷ 3 = 7
Thus, the quotient is 7

Question 7.
16 ÷ 2 = _______

Answer: 8

Explanation:

• Start at 0.
• Count by 2 until you reach 16.
• Count the number of times you count up to 16.

2, 4, 6, 8, 10, 12, 14, 16.
16 ÷ 2 = 8
The quotient is 8.

Question 8.
27 ÷ 3 = _______

Answer: 9

Explanation:

• Start at 0.
• Count by 3 until you reach 27
• Count the number of times you count up to 27.

3, 6, 9, 12, 15, 18, 21, 24, 27.
27 ÷ 3 = 9
The quotient is 9.

Question 9.
0 ÷ 3 = _______

Answer: 0

Explanation:

0 divided by any number is always 0. Thus the quotient is 0.

Question 10.
9 ÷ 3 = _______

Answer: 3

• Start at 0.
• Count by 3 until you reach 9.
• Count the number of times you count up to 9.

3, 6, 9.
9 ÷ 3 = 3
the quotient is 3.

Question 11.
_______ = 30 ÷ 3

Answer: 10

Explanation:

• Start at 0.
• Count by 3 until you reach 30
• Count the number of times you count up to 30.

3, 6, 9, 12, 15, 18, 21, 24, 27, 30
30 ÷ 3 = 10
Thus quotient is 10.

Question 12.
_______ = 12 ÷ 4

Answer: 3

Explanation:

• Start at 0.
• Count by 4s until you reach 12
• Count the number of times you count up to 12.

4, 8, 12
12 ÷ 4 = 3
The quotient is 3.

Question 13.
3)\(\bar { 1 2 }\)
_______

Answer: 4

Explanation:

• Start at 0.
• Count by 3 until you reach 12
• Count the number of times you count up to 12.

12 ÷ 3 = 4
The quotient is 4.

Question 14.
3)\(\bar { 1 5 }\)
_______

Answer: 5

Explanation:

15 ÷ 3 = _

• Start at 0.
• Count by 3s until you reach 15
• Count the number of times you count up to 15.

3, 6, 9, 12, 15.
15 ÷ 3 = 5

Question 15.
3)\(\bar { 2 4 }\)
_______

Answer: 8

Explanation:

• Start at 0.
• Count by 3s until you reach 24
• Count the number of times you count up to 24.

3, 6, 9, 12, 15, 18, 21, 24.
The quotient is 8.

Question 16.
3)\(\bar { 9 }\)
_______

Answer: 3

Explanation:

9 ÷ 3 = 3
3 divides 9 three times. So, the quotient is 3.

Problem Solving

Question 17.
The principal at Miller Street School has 12 packs of new pencils. She will give 3 packs to each third-grade class. How many third-grade classes are there?
_______

Answer: 4 classes

Explanation:

The principal at Miller Street School has 12 packs of new pencils
She will give 3 packs to each third-grade class
Divide the number of packs by number of packs for each class
= 12  ÷ 3 = 12/3 = 4 classes.

Question 18.
Mike has $21 to spend at the mall. He spends all of his money on bracelets for his sisters. Bracelets cost $3 each. How many bracelets does he buy?
_______

Answer: 7 bracelets

Explanation:

Mike has $21 to spend at the mall
Bracelets cost $3 each
Divide total cost Mike spend by the cost of each bracelet
21 ÷ 3 = 7
Thus the answer is 7 bracelets.

Divide by 3 – Page No. 388

Lesson Check

Question 1.
There are 18 counters divided equally among 3 groups. How many counters are in each group?
Options:
a. 5
b. 6
c. 7
d. 8

Answer: 6

Explanation:

There are 18 counters divided equally among 3 groups
Number of counters in each group = x
x = Number of counters by number of groups
x = 18 ÷ 3 = 6 counters

Question 2.
Josh has 27 signed baseballs. He places the baseballs equally on 3 shelves. How many baseballs are on each shelf?
Options:
a. 6
b. 7
c. 8
d. 9

Answer: 9

Explanation:

Josh has 27 signed baseballs
He places the baseballs equally on 3 shelves
Number of baseballs are on each shelf = no. of signed baseballs ÷ baseballs equally on 3 shelves
= 27 ÷ 3 = 9 baseballs

Spiral Review

Question 3.
Each bicycle has 2 wheels. How many wheels do 8 bicycles have?
Options:
a. 10
b. 16
c. 24
d. 32

Answer: 16

Explanation:

Each bicycle has 2 wheels
Number of wheels do 8 bicycles have = x
x = 8 × 2 = 16 wheels
option B is the correct answer

Question 4.
How many students watch less than 3 hours of TV a day?

Options:
a. 3
b. 7
c. 8
d. 13

Answer: 7

Explanation:

Number of students who watch 0 hours of TV a day = 1
Number of students who watch 1 hour of TV a day = 2
Number of students who watch 2 hours of TV a day = 4
Total number of students who watch less than 3 hours = 1 + 2 + 4 = 7

Question 5.
Which of the following is an example of the Distributive Property?
Options:
a. 3 × 6 = 18
b. 6 × 3 = 15 + 3
c. 3 × 6 = 6 × 3
d. 6 × 3 = (3 × 2) + (3 × 4)

Answer: 6 × 3 = (3 × 2) + (3 × 4)

Explanation:

The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum.
6 × 3 = (3 × 2) + (3 × 4) is the example of the Distributive Property

Question 6.
Which unknown number completes the equations?
3 × □ = 21   21 ÷ 3 = □
Options:
a. 3
b. 6
c. 7
d. 18

Answer: 7

Explanation:

Let □ is the unknown factor
Check whether it is related fact for both multiplication and division
3 × □ = 21
□ = 21/3 = 7
The related multiplication and division facts of 21, 7 and 3 is 3 × 7 = 21 and 21 ÷ 3 = 7
Thus the correct answer is option C

Divide by 4 – Page No. 393

Draw tiles to make an array. Find the quotient.

Question 1.

Answer: 4

Explanation:

Question 2.
20 ÷ 4 = ______

Answer: 5

20 ÷ 4 = 5

Question 3.
12 ÷ 4 = ______

Answer: 3

12 ÷ 4 = 3

Question 4.
10 ÷ 2 = ______

Answer: 5

10 ÷ 2 = 5

Find the quotient.

Question 5.
24 ÷ 3 = ______

Answer: 8

Explanation:

24 ÷ 3
3 divides 24 by 8 times
So, the quotient is 8

Question 6.
______ = 8 ÷ 2

Answer: 4

Explanation:

2 divides 8 by four times. So, the quotient is 4.

Question 7.
32 ÷ 4 = ______

Answer: 8

Explanation:

4 divides 32 eight times. So the quotient is 8.

Question 8.
______ = 28 ÷ 4

Answer: 7

Explanation:

4 divides 28 seven times. You can also check the multiplication table to find the quotient.

28 ÷ 4 = 7

Thus the quotient is 7.

Question 9.
4)\(\bar { 3 6 }\)
______

Answer: 9

Explanation:

36 ÷ 4 = _

4 divides 36 nine times.

36 ÷ 4 = 9

So, the quotient is 9.

Question 10.
4)\(\bar { 8 }\)
______

Answer: 2

Explanation:

8 ÷ 4 = 2

4 divides 8 two times. So, the quotient is of 8 and 4 is 2.

Question 11.
4)\(\bar { 2 4 }\)
______

Answer: 6

Explanation:

24 ÷ 4
24/4 = 6
Thus the quotient is 6

Question 12.
3)\(\bar { 3 0 }\)
______

Answer: 10

Explanation:

30 ÷ 3
30/3 = 10
The quotient is 10

Find the unknown number.

Question 13.
20 ÷ 5 = a
a = ______

Answer: 4

Explanation:

a is the unknown number
20 ÷ 5 = a
a = 20/5
5 divides 20 four times
Thus the quotient is 4.

Question 14.
32 ÷ 4 = p
p = ______

Answer: 8

Explanation:

P is the unknown number.
P = 32 ÷ 4
P = 32/4 = 8
Therefore the unknown number p is 8.

Question 15.
40 ÷ 10 = □
□ = ______

Answer: 4

Explanation:

□ = 40 ÷ 10
10 dives 40 four times. Thus the unknown number is 4.

Question 16.
18 ÷ 3 = x
x = ______

Answer: 6

Explanation:

X = 18 ÷ 3
= 18/3 = 6
Thus the unknown value x is 6.

Problem Solving

Question 17.
Ms. Higgins has 28 students in her gym class. She puts them in 4 equal groups. How many students are in each group?
______

Answer: 7 students

Explanation:

Ms. Higgins has 28 students in her gym class.
She puts them in 4 equal groups.
Divide number of students by number of equal groups
= 28 ÷ 4
= 7
Therefore there are 7 students in each group.

Question 18.
Andy has 36 CDs. He buys a case that holds 4 CDs in each section. How many sections can he fill?
______

Answer: 9 CDs

Explanation:

Andy has 36 CDs.
He buys a case that holds 4 CDs in each section.
Divide the total number of CDs by number of CDs in each section
= 36 ÷ 4 = 9
Thus Andy can fill 9 sections.

Divide by 4 – Page No. 394

Lesson Check

Question 1.
Darion picks 16 grapefruits off a tree in his backyard. He puts 4 grapefruits in each bag. How many bags does he need?
Options:
a. 3
b. 4
c. 5
d. 6

Answer: 4

Explanation:

Given:

Darion picks 16 grapefruits off a tree in his backyard
He puts 4 grapefruits in each bag
Number of bags he needs = x
Divide the number of grapefruits by number of grapefruits in each bag
x = 16 ÷ 4 = 4
Thus Darion needs 4 bags to put grapefruits.

Question 2.
Tori has a bag of 32 markers to share equally among 3 friends and herself. How many markers will Tori and each of her friends get?
Options:
a. 6
b. 7
c. 8
d. 9

Answer: 8

Explanation:

Tori has a bag of 32 markers to share equally among 3 friends and herself
Total number of markers = 32
Number of equal groups = 3 friends and Tori = 3 + 1 = 4
To find the number of marks do they get, we need to divide the number of markers by number of people
= 32 ÷ 4 = 8
Therefore each friend gets 8 markers.
So, the correct answer is option C

Spiral Review

Question 3.
Find the product.
3 × 7
Options:
a. 18
b. 21
c. 24
d. 28

Answer: 21

Explanation:

We find the product of 7 and 3 by simply calculating 7 times 3 which equals 21.
So, the correct answer is option B.

Question 4.
Which of the following describes this pattern?
8, 12, 16, 20, 24, 28
Options:
a. Multiply by 4.
b. Add 4.
c. Multiply by 2.
d. Subtract 4.

Answer: Multiply by 4

Explanation:

We can see that sequence is formed by adding 4 each time
8
8 + 4 = 12
12 + 4 = 16
16 + 4 = 20
20 + 4 = 24
24 + 4 = 28
The pattern is formed by adding 4 to the previous number.
By seeing this we can say that it is the multiple of 4.
Thus the correct answer is option C

Question 5.
Which is an example of the Commutative Property of Multiplication?
Options:
a. 3 × 6 = 2 × 9
b. 2 × 4 = 5 + 3
c. 4 × 5 = 5 × 4
d. 2 × 5 = 5 + 5

Answer: 4 × 5 = 5 × 4

Explanation:

According to the commutative property of multiplication, changing the order of the numbers we are multiplying, does not change the product.
a × b = b × a
So, the perfect example of Commutative Property of Multiplication is 4 × 5 = 5 × 4.
Option C is the correct answer.

Question 6.
Jasmine has 18 model horses. She places the model horses equally on 3 shelves. How many model horses are on each shelf?
Options:
a. 6
b. 7
c. 15
d. 21

Answer: 6

Explanation:

Jasmine has 18 model horses
She places the model horses equally on 3 shelves
To find the model horses are on each shelf we have to write the division equation
= number of model horses by number of equal shelves
= 18 ÷ 3 = 6 model horses
Therefore there are 6 model horses are on each shelf.

Divide by 6 – Page No. 399

Find the unknown factor and quotient.

Question 1.

Answer: 7, 7

Explanation:

First, use a related multiplication fact
6 × _ = 42
Let _ be x
6 × x = 42
x = 42/6 = 7
Next use factors to divide 42 and 6
Factor of 6 are 3 and 2
So, first divide by 3
42 ÷ 3 = 14
14 ÷ 2 = 7
Thus 42 ÷ 6 = 7

Question 2.
6 × ______ = 18 18 ÷ 6 = ______

Answer: 3, 3

Explanation:

First, use a related multiplication fact
6 × _ = 18
Let x represents the unknown factor
6 × x = 18
x = 18/6 = 3
Next use factors to divide 18 and 6
Factor of 6 are 3 and 2
So, first divide by 3
18 ÷ 3 = 6
6 ÷ 2 = 3
18 ÷ 6 = 3

Question 3.
4 × ______ = 24 24 ÷ 4 = ______

Answer: 6, 6

Explanation:

First, use a related multiplication fact
4 × _ = 24
4 × x = 24
x =24/4 = 6
x = 6
Next use factors to divide 24 and 4
Factors of 4 are 2, 2
So, first divide by 2
24 ÷ 2 = 12
12 ÷ 2 = 6
24 ÷ 4 = 6

Question 4.
6 × ______ = 54 54 ÷ 6 = ______

Answer: 9, 9

Explanation:

First, use a related multiplication fact
6 × x = 54
x = 54/6 = 9
x = 9
Next use factors to divide 54 and 6
Factors of 6 are 3, 2
So, first divide by 3
54 ÷ 3 = 18
Next divide by 2
18 ÷ 2 = 9
54 ÷ 6 = 9

Question 5.
______ = 24 ÷ 6

Answer: 4

Explanation:

Use factors to divide 54 and 6
Factors of 6 are 3, 2
So, first divide by 3
24 ÷ 3 = 8
Next divide by 2
8 ÷ 2 = 4
Thus 24 ÷ 6 = 4

Question 6.
48 ÷ 6 = ______

Answer: 8

Explanation:

Use factors to divide 48 and 6
Factors of 6 are 3, 2
So, first divide by 3
48 ÷ 3 = 16
Next divide by 2
16 ÷ 2 = 8
Thus 48 ÷ 6 = 8

Question 7.
______ = 6 ÷ 6

Answer: 1

Explanation:

Any number divided by the same number will be 1. So, the quotient of 6/6 = 1.

Question 8.
12 ÷ 6 = ______

Answer: 2

Explanation:

Use factors to divide 12 and 6
Factors of 6 are 3, 2
So, first divide by 3
12 ÷ 3 = 4
Next divide by 2
4 ÷ 2 = 2
Thus 12 ÷ 6 = 2

Question 9.
6)\(\bar { 3 6 }\)
______

Answer: 6

Explanation:

36 ÷ 6
Factors of 6 are 3, 2
So, first divide by 3
36 ÷ 3 = 12
Next divide by 2
12 ÷ 2 = 6
Thus 36 ÷ 6 = 6

Question 10.
6)\(\bar { 5 4 }\)
______

Answer: 9

Explanation:

54 ÷ 6
Factors of 6 are 3, 2
So, first divide by 3
54 ÷ 3 = 18
Next divide by 2
18 ÷ 2 = 9
54 ÷ 6 = 9

Question 11.
6)\(\bar { 3 0 }\)
______

Answer: 5

Explanation:

30 ÷ 6
Factors of 6 are 3, 2
So, first divide by 3
30 ÷ 3 = 10
Next divide by 2
10 ÷ 2 = 5
Thus 30 ÷ 6 = 5

Question 12.
1)\(\bar { 6 }\)
______

Answer: 6

Explanation:

6 ÷ 1 = 6
Any number divided by 1 will be always the same number. So, the quotient is 6

Question 13.
p = 42 ÷ 6
p = ______

Answer: 7

Explanation:

Factor of 6 are 3 and 2
So, first divide by 3
42 ÷ 3 = 14
14 ÷ 2 = 7
Thus 42 ÷ 6 = 7

Question 14.
18 ÷ 3 = q
q = ______

Answer: 6

Explanation:

18 ÷ 3 = q
q = 18 ÷ 3
q = 18/3
3 divides 18 by 6 times. So, the quotient is 6

Question 15.
r = 30 ÷ 6
r = ______

Answer: 5

Explanation:

r = 30 ÷ 6
r = 30/6
6 divides 30 by 5 times. So, the quotient is 5

Question 16.
60 ÷ 6 = s
s = ______

Answer: 10

Explanation:

60 ÷ 6 = s
s = 60/6
6 divides 60 by 10 times. So, the quotient is 10.

Problem Solving

Question 17.
Lucas has 36 pages of a book left to read. If he reads 6 pages a day, how many days will it take Lucas to finish the book?
______

Answer: 6 pages

Explanation:

Lucas has 36 pages of a book left to read
If he reads 6 pages a day, how many days will it take Lucas to finish the book
Let the number of days Lucas take to finish the book = a
a × 6 = 36
a = 36/6 = 6 days
Thus Lucas take 6 days to finish the book

Question 18.
Juan has $24 to spend at the bookstore. If books cost $6 each, how many books can he buy?
______

Answer: 4 books

Explanation:

Juan has $24 to spend at the bookstore
Each book costs $6
Number of books he can buy = x
x × 6 = 24
x = 24/6
x = 4
Therefore Juan can buy 4 books.

Divide by 6 – Page No. 400

Lesson Check

Question 1.
Ella earned $54 last week babysitting. She earns $6 an hour. How many hours did Ella babysit last week?
Options:
a. 6 hours
b. 7 hours
c. 8 hours
d. 9 hours

Answer: 9 hours

Explanation:

Ella earned $54 last week babysitting
She earns $6 an hour
To find:
How many hours did Ella babysit last week
Divide Ella earned last week by she earns for an hour
= $54 ÷ $6 = 9 hours
Thus Ella babysits last week for 9 hours.

Question 2.
What is the unknown factor and quotient?
Options:
6 × □ = 42 42 ÷ 6 = □
Options:
a. 6
b. 7
c. 8
d. 9

Answer: 7

Explanation:

□ be the unknown factor
6 × □ = 42
□  = 42/6 = 7
The factors of 6 and 42 is 7
Use a related multiplication fact here
42 ÷ 6 = □
□ = 7
42 ÷ 6 = 7
So, the correct answer is  option B.

Spiral Review

Question 3.
Coach Clarke has 48 students in his P.E. class. He places the students in teams of 6 for an activity. How many teams can Coach Clarke make?
Options:
a. 7
b. 8
c. 9
d. 54

Answer: 8

Explanation:

Coach Clarke has 48 students in his P.E. class
He places the students in teams of 6 for an activity
Number of teams can Coach Clarke make = x
Divide Number of students by the number of students in each team
48 ÷ 6 = 8
Thus Coach Clarke can make 8 teams.

Question 4.
Each month for 7 months, Eva reads 3 books. How many more books does she need to read before she has read 30 books?
Options:
a. 7
b. 9
c. 27
d. 33

Answer: 9

Explanation:

Eva reads 3 books per month
For 7 months = 3 × 7 = 21
We need to find how many more books does she need to read before she has read 30 books
Subtract the number of books she read for 7 months from a number of books
= 30 – 21 = 9 books
So, the answer is option B.

Question 5.
Each cow has 4 legs. How many legs will 5 cows have?
Options:
a. 9
b. 16
c. 20
d. 24

Answer: 20

Explanation:

Each cow has 4 legs
Number of legs will 5 cows have = x
x = 5 × 4 = 20 legs
Thus 5 cows will have 20 legs.

Question 6.
Find the product.
3 × 9
Options:
a. 36
b. 27
c. 18
d. 12

Answer: 27

Explanation:

We find the product of 3 and 9 by simply calculating 9 times 3 which equals 27.
You can also find the answer by checking the multiplication table.
Thus the answer is option B.

Mid -Chapter Checkpoint – Page No. 401

Concepts and Skills

Question 1.
Explain how to find 20 ÷ 4 by making an array.
Type below:
__________

Answer: 5

■ ■ ■ ■ ■
■ ■ ■ ■ ■
■ ■ ■ ■ ■
■ ■ ■ ■ ■

Explanation:

Total number of tiles = 20
Make a row of 5 tiles
Continue to make as many rows of 5 tiles as you can
We get 5 tiles in each row
So, the division equation is 20 ÷ 4 = 5

Question 2.
Explain how to find 30 ÷ 6 by making equal groups.
Type below:
__________

Answer: 5

By seeing the picture we can see that there are 6 groups of 5 each.

Find the unknown factor and quotient.

Question 3.
10 × _____ = 50
_____ = 50 ÷ 10

Answer: 5, 5

Explanation:

Let the unknown factor be y
10 × y = 50
y = 50/10 = 5
In order to find the quotient, we need to check whether the dividend the product in the related multiplication fact or not.
If both are related then the unknown factor is the quotient
That means 5 is the quotient.

Question 4.
2 × _____ = 16
_____ = 16 ÷ 2

Answer: 8, 8

Explanation:

Let the unknown factor be p
2 × p = 16
p = 16/2 = 8
To find the quotient we need to check whether the dividend the product in the related multiplication fact or not.
If both are related then the unknown factor is the quotient.
Therefore, 16 ÷ 2 = 8

Question 5.
2 × _____ = 20
_____ = 20 ÷ 2

Answer: 10, 10

Explanation:

Let the unknown factor be p
2 × p = 20
p = 20/2 = 10
To find the quotient we need to check whether the dividend the product in the related multiplication fact or not.
If both are related then the unknown factor is the quotient.
20 ÷ 2 = 10
Therefore, the unknown factor and quotient are 10.

Question 6.
5 × _____ = 20
_____ = 20 ÷ 5

Answer: 4, 4

Let the unknown factor be y
5 × y = 20
y = 20/5 = 4
In order to find the quotient, we have to check whether the dividend the product in the related multiplication fact or not.
If both are related then the unknown factor is the quotient.
20 ÷ 5 = 4
That means 4 is the quotient.

Find the quotient.

Question 7.
_____ = 6 ÷ 6

Answer: 1

Explanation:

6/6 = 1
The number which is divided by the same number will be always 1. Thus the quotient is 1.

Question 8.
21 ÷ 3 = _____

Answer: 7

Explanation:

3 divides 21 seven times.
Thus the quotient of 21 ÷ 3 is 7.

Question 9.
_____ = 0 ÷ 3

Answer: 0

Explanation:

0 divided by any number will be 0. Thus the quotient is 0.

Question 10.
36 ÷ 4 = _____

Answer: 9

Explanation:

4 divides 36 nine times.
So, the quotient is 9.

Question 11.
5)\(\bar { 3 5 }\)
_____

Answer: 7

Explanation:

35 ÷ 5

5 divides 35 seven times. Thus the quotient is 7.

Question 12.
4)\(\bar { 2 4 }\)
_____

Answer: 6

Explanation:

24 ÷ 4 = _

4 divides 24 six times. So, the quotient is 6.

Question 13.
6)\(\bar { 5 4 }\)
_____

Answer: 9

Explanation:

54 ÷ 6 = x
Let x represents the unknown number.
6 divides 56 nine times.
Thus the quotient is 9.

Question 14.
3)\(\bar { 9 }\)
_____

Answer: 3

Explanation:

9 ÷ 3 = 3
3 divides 9 three times.
So, the quotient is 3 and the remainder is 0.

Mid -Chapter Checkpoint – Page No. 402

Question 15.
Carter has 18 new books. He plans to read 3 of them each week. How many weeks will it take Carter to read all of his new books?
_____ weeks

Answer: 6 weeks

Explanation:

Given,
Carter has 18 new books
He plans to read 3 of them each week.
Number of weeks will it take Carter to read all of his new books = x
To find x we need to divide the number of new books by number of books he planned to read each week
That means 18 ÷ 3 = 6 weeks

Question 16.
Gabriella made 5 waffles for breakfast. She has 25 strawberries and 15 blueberries to put on top of the waffles. She will put an equal number of berries on each waffle. How many berries will Gabriella put on each waffle?
_____ berries

Answer: 8 berries

Explanation:

Gabriella made 5 waffles for breakfast
She has 25 strawberries and 15 blueberries to put on top of the waffles
Total number of berries = 25 + 15 = 40
Number of strawberries she puts on each waffle = 25 ÷ 5 = 5
Number of blueberries she puts on each waffle = 15 ÷ 5 = 3
Total number of berries she puts on each waffle = 5 + 3 = 8 berries

Question 17.
There are 60 people at the fair waiting in line for a ride. Each car in the ride can hold 10 people. Write an equation that could be used to find the number of cars needed to hold all 60 people.
Type below:
____________

Answer: 60 ÷ 10 = 6

Explanation:

Given that, There are 60 people at the fair waiting in line for a ride.
Each car in the ride can hold 10 people
To write the equation we need to divide the number of people by Each car in the ride can hold 10 people
= 60 ÷ 10 = 6
Therefore, 6 cars are needed to hold all 60 people.

Question 18.
Alyssa has 4 cupcakes. She gives 2 cupcakes to each of her cousins. How many cousins does Alyssa have?
_____ cousins

Answer: 2

Explanation:

Alyssa has 4 cupcakes
She gives 2 cupcakes to each of her cousins
Divide the number of cupcakes by number of cupcakes she gave for each of her cousins
= 4 ÷ 2 = 2 cousins

Divide by 7 – Page No. 407

Find the unknown factor and quotient.

Question 1.

Answer: 6, 6

Explanation:

Let the unknown factor be x.
7 × x  = 42
x = 42/7 = 6
Now to find the quotient first check whether the dividend the product are related multiplication and division facts are not.
If both are related facts then the unknown factor is the quotient.
42 ÷ 7 = 6

Question 2.
7 × _____ = 35 35 ÷ 7 = _____

Answer: 5, 5

Explanation:

7 × y = 35
y = 35/7 = 5
Thus the unknown factor is 5.
Now check whether the dividend the product is related to the multiplication and division facts is not. If both are related facts then the unknown factor is the quotient.
35 ÷ 7 = 5

Question 3.
7 × _____ = 7 7 ÷ 7 = _____

Answer: 1, 1

Explanation:

The number divided by the Same number will be 1. So, the quotient and the unknown factor is 1.

Question 4.
5 × _____ = 20 20 ÷ 5 = _____

Answer: 4, 4

Explanation:

Let a be the unknown factor.
5 × a = 20
a = 20/5 = 4.
Check whether the dividend the product are related to the multiplication and division facts are not. If both are same  then the quotient is equal to the unknown factor I.e., 4

Find the quotient.

Question 5.
7)\(\bar { 2 1 }\)
_____

Answer: 3

Explanation:

21 ÷ 7 = _
7 divides 21 three times.
So, the quotient is 3.

Question 6.
7)\(\bar { 1 4 }\)
_____

Answer: 2

Explanation:

14 divides 7 two times. Thus the quotient is 2.

Question 7.
6)\(\bar { 4 8 }\)
_____

Answer: 8

Explanation:

48 ÷ 6 = x
6 divides 48 8 times. Thus the unknown number or quotient of 48 and 6 is 8.

Question 8.
7)\(\bar { 6 3 }\)
_____

Answer: 9

Explanation:

63 ÷ 7 = _
7 divides 63 nine times. So, the quotient is 9.

Question 9.
_____ = 35 ÷ 7

Answer: 5

Explanation:

7 divides 35 five times. Thus the quotient of 35 and 7 is 5.

Question 10.
0 ÷ 7 = _____

Answer: 0

Explanation:

0 divided by any number is always 0. So the quotient is 0.

Question 11.
_____ = 56 ÷ 7

Answer: 8

Explanation:

7 divides 56 eight times. Thus the quotient of 56 and 7 is 8.

Question 12.
32 ÷ 8 = _____

Answer: 4

Explanation:

8 divides 32 four times. Thus the quotient of 32 and 8 is 4.

Find the unknown number.

Question 13.
56 ÷ 7 = e
e = _____

Answer: 8

Explanation:

56 ÷ 7 = e
e = 56 ÷ 7
= 56/7
e = 8
Thus the unknown value of e is 8.

Question 14.
k = 32 ÷ 4
k = _____

Answer: 8

Explanation:

k = 32 ÷ 4
k = 32/4 = 8
The unknown number k is 8.

Question 15.
g = 49 ÷ 7
g = _____

Answer: 7

Explanation:

Given, g = 49 ÷ 7
7 divides 49 seven times.
g = 49/7 = 7
Therefore g = 7.

Question 16.
28 ÷ 7 = s
s = _____

Answer: 4

Explanation:

s = 28 ÷ 7
s = 28/7 = 4
Thus the unknown value s  is 4.

Problem Solving

Question 17.
Twenty-eight players sign up for basketball. The coach puts 7 players on each team. How many teams are there?
_____

Answer: 4 teams

Explanation:

Total number of players = 28
The coach puts 7 players on each team.
To find the number of teams divide total number of players by number of players in each team.
= 28 ÷ 7 = 4
Therefore total number of teams = 4

Question 18.
Roberto read 42 books over 7 months. He read the same number of books each month. How many books did Roberto read each month?
_____

Answer: 6 books

Explanation:

Roberto read 42 books for 7 months.
Number of books he read per month = 42 ÷ 7 = 6 books.
Therefore he reads 6 books per month.

Divide by 7 – Page No. 408

Lesson Check

Question 1.
Elliot earned $49 last month walking his neighbor’s dog. He earns $7 each time he walks the dog. How many times did Elliot walk his neighbor’s dog last month?
Options:
a. 6
b. 7
c. 8
d. 9

Answer: 7

Explanation:

Elliot earned $49 last month walking his neighbor’s dog.
He earns $7 each time he walks the dog
Divide Elliot earned $49 last month by he earned each time
49 ÷ 7 = 7
Thus the correct answer is option B.

Question 2.
Which is the unknown factor and quotient?
Options:
7 × □ = 63 63 ÷ 7 = □
Options:
a. 6
b. 7
c. 8
d. 9

Answer: 9

Explanation:

7 × □ = 63
□  = 63/7 = 9
Thus the correct answer is option D.

Spiral Review

Question 3.
Maria puts 6 strawberries in each smoothie she makes. She makes 3 smoothies. Altogether, how many strawberries does Maria use in the smoothies?
Options:
a. 9
b. 12
c. 18
d. 24

Answer: 18

Explanation:

Maria puts 6 strawberries in each smoothie she makes
She makes 3 smoothies
For each smoothie, she puts 6 strawberries
For 3 smoothie she puts y strawberries
y = 6 × 3 = 18
Therefore the correct answer is option C.

Question 4.
Kaitlyn makes 4 bracelets. She uses 8 beads for each bracelet. How many beads does she use in all?
Options:
a. 12
b. 16
c. 32
d. 40

Answer: 32

Explanation:

Kaitlyn makes 4 bracelets
She uses 8 beads for each bracelet
Multiply number of bracelets with number of beads for each bracelet
8 × 4 = 32

Question 5.
What is the unknown factor?
2 × 5 = 5 × □
Options:
a. 10
b. 5
c. 2
d. 1

Answer: 2

Explanation:
2 × 5 = 5 × □
According to the commutative property of multiplication a × b = b × a
So, 2 × 5 = 5 × 2
Thus the correct answer is option C.

Question 6.
Which division equation is related to the following multiplication equation?
3 × 4 = 12
Options:
a. 12 ÷ 4 = 3
b. 8 ÷ 2 = 4
c. 12 ÷ 2 = 6
d. 10 ÷ 5 = 2

Answer: 12 ÷ 4 = 3

Explanation:
The related multiplication and division fact of 3 × 4 = 12 is 12 ÷ 4 = 3.

Divide by 8 – Page No. 413

Find the unknown factor and quotient.

Question 1.

Answer: 4, 4

Explanation:

Let x be the unknown factor.
8 × x = 32
x = 32/8 = 4
So the unknown factor = 4
Now check whether the dividend the product is related to the multiplication and division facts is not.
If both are related facts then the unknown factor is the quotient.
32 ÷ 8 = 4
So, 4 is the quotient.

Question 2.
3 × ______ = 27 27 ÷ 3 = ______

Answer: 9, 9

Explanation:

Let y be the unknown factor.
3 × y = 27
y = 27/3 = 9
y = 9
Now check whether the dividend the product is related to the multiplication and division facts is not.
If both are related facts then the unknown factor is the quotient.
27 ÷ 3 = 9
Thus the quotient is 9.

Question 3.
8 × ______ = 8 8 ÷ 8 = ______

Answer: 1, 1

Explanation:

8 × x = 8
x = 8/8 = 1
The number divided by the same number is always 1. Thus the quotient of 8 ÷ 8 = 1.

Question 4.
8 × ______ = 72 72 ÷ 8 = ______

Answer: 9, 9

Explanation:

8 × x = 72
x = 72/8 = 9
Check if the dividend the product is related to the multiplication and division facts.
If both are related facts then the unknown factor is the quotient.
72 ÷ 8 = 9
Thus the quotient is 9.

Find the quotient.

Question 5.
______ = 24 ÷ 8

Answer: 3

Explanation:

24 ÷ 8
8 divides 24 three times. So, the quotient of 24 ÷ 8 is 3.

Question 6.
40 ÷ 8 = ______

Answer: 5

Explanation:

40 ÷ 8 = 5 because 8 divides 40 five times.
Thus the quotient is 5.

Question 7.
______ = 56 ÷ 8

Answer: 7

Explanation:

56 ÷ 8
8 divides 56 seven times. So, the quotient of 56 and 8 is 7.

Question 8.
14 ÷ 2 = ______

Answer: 7

Explanation:

7 divides 14 two times. thus the quotient of 14 ÷ 2 = 7.

Question 9.
8)\(\bar { 6 4 }\)
______

Answer: 8

Explanation:

64 ÷ 8 = 8
8 divides 64 eight times. So, the quotient of 64 ÷ 8 = 8.

Question 10.
7)\(\bar { 2 8 }\)
______

Answer: 4

Explanation:

28 ÷ 7
7 divides 28 four times.
28/7 = 4
Thus the quotient is 4.

Question 11.
8)\(\bar { 1 6 }\)
______

Answer: 2

Explanation:

16 ÷ 8 = x
x = 16/8 = 2
8 divides 16 two times. Thus the quotient is 2.

Question 12.
8)\(\bar { 4 8 }\)
______

Answer: 6

Explanation:

48 ÷ 8 = y
y = 48/8 = 6
8 divides 48 six times. So, the quotients is 6.

Find the unknown number.

Question 13.
16 ÷ p = 8
p = ______

Answer: 2

Explanation:

p is the unknown number
16 ÷ p = 8
Make p as the subject.
We get p = 16/8 = 2.
p = 2

Question 14.
25 ÷ □ = 5
□ = ______

Answer: 5

Explanation:

□ is the unknown number
25 ÷ □ = 5
□ = 25/5 = 5
Therefore the value □ is 5.

Question 15.
24 ÷ a = 3
a = ______

Answer: 8

Explanation:

a is the unknown number
24 ÷ a = 3
a = 24 ÷ 3 = 8
So, the value of a is 8.

Question 16.
k ÷ 10 = 8
k = ______

Answer: 80

Explanation:

K is the unknown number
k ÷ 10 = 8
k = 8 × 10
k = 80

Problem Solving

Question 17.
Sixty-four students are going on a field trip. There is 1 adult for every 8 students. How many adults are there?
______

Answer: 8 adults

Explanation:

Total number of students going for trip = 64
There are 1 adult for every 8 students
Total number of adults = x
x × 8 = 64 × 1
x = 64/8 = 8
Therefore there are 8 adults for every 8 students.

Question 18.
Mr. Chen spends $32 for tickets to a play. If the tickets cost $8 each, how many tickets does Mr. Chen buy?
______

Answer: 4 tickets

Explanation:

Mr. Chen spends $32 for tickets to a play.
The tickets cost $8 each.
To find the number of tickets that Mr. Chen buys we need to divide the total cost of tickets by the cost of each ticket.
= 32/8 = 4
Thus the cost of each ticket is $4.

Divide by 8 – Page No. 413

Lesson Check

Question 1.
Mrs. Wilke spends $72 on pies for the school fair. Each pie costs $8. How many pies does Mrs. Wilke buy for the school fair?
Options:
a. 6
b. 7
c. 8
d. 9

Answer: 9

Explanation:

Mrs. Wilke spends $72 on pies for the school fair
Each pie costs $8.
To know how many pies does Mrs. Wilke buy for the school fair
We have to divide 72 ÷ 8 = 9
Thus Mrs. Wilke buys 9 pies for the school fair.

Question 2.
Find the unknown factor and quotient.
8 × □ = 40
40 ÷ □ = 8
Options:
a. 4
b. 5
c. 6
d. 7

Answer: 5

Explanation:

8 × □ = 40
□ = 40/8 = 5
So, the answer is option B.

Spiral Review

Question 3.
Find the product.
(3 × 2) × 5
Options:
a. 6
b. 10
c. 20
d. 30

Answer: 30

Explanation:
(3 × 2) × 5
6 × 5 = 30
Thus the answer is option D.

Question 4.
Which of the following has the same product as 4 × 9?
Options:
a. 3 × 8
b. 9 × 4
c. 5 × 6
d. 7 × 2

Answer: 9 × 4

Explanation:
Among all the 4 options 9 × 4 is the same product as 4 × 9
So, the correct answer is option B.

Question 5.
Find the unknown factor.
8 × □ = 32
Options:
a. 4
b. 5
c. 6
d. 32

Answer: 4

Explanation:

8 × □ = 32
□ = 32/8 = 4
Thus the correct answer is option A.

Question 6.
Which multiplication sentence represents the array?

Options:
a. 1 × 8 = 8
b. 4 + 4 = 8
c. 2 × 4 = 8
d. 4 × 3 = 12

Answer: 2 × 4 = 8

Explanation:

There are 2 rows and each row contains 4 arrays
The sentence that represents the array is 2 × 4 = 8
So, the correct answer is option C.

Divide by 9 – Page No. 419

Find the quotient.

Question 1.

Answer: 4

Explanation:

Factors of 9 are 3, 3
First, divide by 3
36 ÷ 3 = 12
Next divide by 3
12 ÷ 3 = 4
So, the quotient is 4.

Question 2.
30 ÷ 6 = _______

Answer: 5

Explanation:

Factors of 6 are 3, 2
So, first divide by 3
30 ÷ 3 = 30/3 = 10
Next divide by 2
10 ÷ 2 = 5
So, 30 ÷ 6 = 5

Question 3.
_______ = 81 ÷ 9

Answer: 9

Explanation:

Factors of 9 are 3, 3
So, first divide by 3
81 ÷ 3 = 27
Next divide by 3
27 ÷ 3 = 9
The quotient is 9.

Question 4.
27 ÷ 9 = _______

Answer: 3

Explanation:

Factors of 9 are 3, 3
So, first divide by 3
27 ÷ 3 = 9
Next divide by 3
9 ÷ 3 = 3
The quotient is 3.

Question 5.
9 ÷ 9 = _______

Answer: 1

Explanation:

Factors of 9 are 3, 3
So, first divide by 3
9 ÷ 3 = 3
Next divide by 3
3 ÷ 3 = 1
Thus the quotient is 1.

Question 6.
_______ = 63 ÷ 7

Answer: 9

Explanation:

7 divides 63 nine times. Thus the quotient of 63 ÷ 7 is 9.

Question 7.
36 ÷ 6 = _______

Answer: 6

Explanation:

The Factors of 6 are 3, 2
So, first divide 36 by 3
36 ÷ 3 = 12
Next divide 12 by 2
12 ÷ 2 = 6
Thus the quotient of 36 ÷ 6 = 6

Question 8.
_______ = 90 ÷ 9

Answer: 10

Explanation:

Factors of 9 are 3, 3
So, first divide by 3
90 ÷ 3 = 30
Next divide 30 by 3
30 ÷ 3 = 10
So, the quotient is 10.

Question 9.
9)\(\bar { 6 3 }\)
_______

Answer: 7

Explanation:

Factors of 9 are 3, 3
So, first, divide by 3
63 ÷ 3 = 21
Next divide 21 by 3
21 ÷ 3 = 7

Question 10.
9)\(\bar { 1 8 }\)
_______

Answer: 2

Explanation:

Factors of 9 are 3, 3
So, first, divide by 3
18 ÷ 3 = 6
Again divide 6 by 3
6 ÷ 3 = 2

Question 11.
7)\(\bar { 4 9 }\)
_______

Answer: 7

Explanation:

7 divides 49 seven times.
49 ÷ 7 = 7
So, the quotient is 7.

Question 12.
9)\(\bar { 4 5 }\)
_______

Answer: 5

Explanation:

Factors of 9 are 3, 3
So, first, divide by 3
45 ÷ 3 = 15
Next divide 15 by 3
15 ÷ 3 = 5
So, 5 is the quotient.

Find the unknown number.

Question 13.
48 ÷ 8 = g
g = _______

Answer: 6

Explanation:

g is the unknown number
g = 48 ÷ 8
g = 48/8 = 6
Thus g = 6.

Question 14.
s = 72 ÷ 9
s = _______

Answer: 8

Explanation:

s is the unknown number
s = 72 ÷ 9
9 divides 72 eight times.
s = 72/9 = 8
s = 8.

Question 15.
m = 0 ÷ 9
m = _______

Answer: 0

Explanation:

m is the unknown number.
0 divided by any number is 0.
m = 0 ÷ 9 = 0
So. m = 0

Question 16.
54 ÷ 9 = n
n = _______

Answer: 6

Explanation:

n is the unknown number.
54 ÷ 9 = n
9 divides 54 six times.
n = 54/9 = 6
n = 6

Problem Solving

Question 17.
A crate of oranges has trays inside that hold 9 oranges each. There are 72 oranges in the crate. If all trays are filled, how many trays are there?
_______

Answer: 8 trays

Explanation:

A crate of oranges has trays inside that hold 9 oranges each.
Each tray holds 9 oranges.
There are 72 oranges in the crate.
To find the number of trays divide the total number of oranges by number of oranges in one tray.
= 72 ÷ 9 = 8
Therefore there are 8 trays.

Question 18.
Van has 45 new baseball cards. He puts them in a binder that holds 9 cards on each page. How many pages does he fill?
_______

Answer: 5 pages

Explanation:

Given that Van has 45 new baseball cards.
He puts them in a binder that holds 9 cards on each page.
Number of pages he filled = x
x × 9 = 45
x = 45/9 = 5 pages.
Therefore Van has filled 5 pages.

Divide by 9 – Page No. 420

Lesson Check

Question 1.
Darci sets up a room for a banquet. She has 54 chairs. She places 9 chairs at each table. How many tables have 9 chairs?
Options:
a. 5
b. 6
c. 7
d. 8

Answer: 6

Explanation:

Darci sets up a room for a banquet. She has 54 chairs.
She places 9 chairs at each table.
Divide the number of chairs by the number of chairs at each table
54 ÷ 9 = 6
Thus 6 tables have 9 chairs

Question 2.
Mr. Robinson sets 36 glasses on a table. He puts the same number of glasses in each of 9 rows. How many glasses does he put in each row?
Options:
a. 4
b. 5
c. 6
d. 7

Answer: 4

Explanation:

Mr. Robinson sets 36 glasses on a table.
He puts the same number of glasses in each of 9 rows.
Number of glasses in each row = x
x = 36 ÷ 9 |
x = 4
So, the correct answer is option A.

Spiral Review

Question 3.
Each month for 9 months, Jordan buys 2 sports books. How many more sports books does he need to buy before he has bought 25 sports books?
Options:
a. 6
b. 7
c. 8
d. 9

Answer: 7

Explanation:

Question 4.
Find the product.
8
× 7
——
Options:
a. 49
b. 56
c. 63
d. 64

Answer: 56

Explanation:

Add 8 7 times = 8 + 8 + 8 + 8 + 8 + 8 + 8 = 56
Thus the product of 8 and 7 is 56
So, the correct answer is option B.

Question 5.
Adriana made 30 pet collars to bring to the pet fair. She wants to display 3 pet collars on each hook. How many hooks will Adriana need to display all 30 pet collars?
Options:
a. 32
b. 12
c. 10
d. 9

Answer: 10

Explanation:

Adriana made 30 pet collars to bring to the pet fair.
She wants to display 3 pet collars on each hook
Divide No. of pet collars by number in each hook
30 ÷ 3 = 10
So, the correct answer is option C.

Question 6.
Carla packs 4 boxes of books. Each box has 9 books. How many books does Carla pack?
Options:
a. 36
b. 27
c. 13
d. 5

Answer: 36

Explanation:

Carla packs 4 boxes of books
Each box has 9 books
Total number of books = x
x = 4 × 9 = 36
Thus Carla packs 36 books

Problem Solving Two-Step Problems – Page No. 425

Solve the problem.

Question 1.
Jack has 3 boxes of pencils with the same number of pencils in each box. His mother gives him 4 more pencils. Now Jack has 28 pencils. How many pencils are in each box?

Answer: 8 pencils

Explanation:

Jack has 3 boxes of pencils with the same number of pencils in each box
His mother gives him 4 more pencils
Now Jack has 28 pencils
To find the number of pencils in each box subtract that 4 pencils from total pencils
= 28 – 4 = 24
Now, there are 24 pencils
To know the number of pencils in each box divide number of pencils by number of boxes
= 24 ÷ 3 = 8 pencils
There are 8 pencils in each box.

Question 2.
The art teacher has 48 paintbrushes. She puts 8 paintbrushes on each table in her classroom. How many tables are in her classroom?
Type below:
__________

Answer: 6 tables

Explanation:

Given,
The art teacher has 48 paintbrushes
She puts 8 paintbrushes on each table in her classroom
Number of tables in her classroom = y
Divide the total number of paintbrushes by number of paintbrushes on each table
= 48 ÷ 8 = 6 tables
Thus there are 6 tables in her classroom

Question 3.
Ricardo has 2 cases of video games with the same number of games in each case. He gives 4 games to his brother. Ricardo has 10 games left. How many video games were in each case?
Type below:
__________

Answer: 7 video games

Explanation:

Ricardo has 2 cases of video games with the same number of games in each case
He gives 4 games to his brother
Ricardo has 10 games left
To find the number of video games in each case first add the number of video games
10 + 4 = 14
Now Divide number of video games by number of cases
= 14 ÷ 2 = 7 video games
There are 7 video games in each case

Question 4.
Patty has $20 to spend on gifts for her friends. Her mother gives her $5 more. If each gift costs $5, how many gifts can she buy?
Type below:
__________

Answer: 5 gifts

Explanation:

Patty has $20 to spend on gifts for her friends
Her mother gives her $5 more.
If each gift costs $5 then the number of gifts she buys = x
Add $20 + $5 = $25
Divide the total amount by each gift cost
25 ÷ 5 = 5
Thus Patty buys 5 gifts for her friends.

Question 5.
Joe has a collection of 35 DVD movies. He received 8 of them as gifts. Joe bought the rest of his movies over 3 years. If he bought the same number of movies each year, how many movies did Joe buy last year?
Type below:
__________

Answer: 9 movies

Explanation:

Joe has a collection of 35 DVD movies
He received 8 of them as gifts.
Joe bought the rest of his movies over 3 years
Subtract gifted DVDs from total collection = 35 – 8 = 27
Now, to know movies did Joe buy last year
divide 27 ÷ 3 = 9 movies
Thus Joe bought 9 movies last year.

Question 6.
Liz has a 24-inch-long ribbon. She cuts nine 2-inch pieces from her original ribbon. How much of the original ribbon is left?
Type below:
__________

Answer: 6 inches

Explanation:

Liz has a 24-inch-long ribbon
She cuts nine 2-inch pieces from her original ribbon
= 9 × 2 inches = 18 inches
Subtract 18 from 24 inches
= 24 – 18
= 6 inches
The original ribbon left is 6 inches.

Two-Step Problems – Page No. 426

Lesson Check

Question 1.
Gavin saved $16 to buy packs of baseball cards. His father gives him $4 more. If each pack of cards costs $5, how many packs can Gavin buy?
Options:
a. 3
b. 4
c. 5
d. 6

Answer: 4

Explanation:

Gavin saved $16 to buy packs of baseball cards
His father gives him $4 more
= $16 + $4 = $20
Each pack of cards costs $5
Divide 20 ÷ 5 = 4
Gavin can buy 4 packs of baseball cards.

Question 2.
Chelsea buys 8 packs of markers. Each pack contains the same number of markers. Chelsea gives 10 markers to her brother. Then, she has 54 markers left. How many markers were in each pack?
Options:
a. 6
b. 7
c. 8
d. 9

Answer: 8

Explanation:

Chelsea buys 8 packs of markers
Chelsea gives 10 markers to her brother.
She has 54 markers left.
Total number of markers = 54 + 10 = 64 markers
Divide total number of markers by number of packs
= 64 ÷ 8 =8
There are 8 markers in each pack.
So, the correct answer is option C.

Spiral Review

Question 3.
Each foot has 5 toes. How many toes will 6 feet have?
Options:
a. 11
b. 25
c. 30
d. 35

Answer: 30

Explanation:

Each foot has 5 toes
Number of toes will 6 feet have = x
x × 1 = 5 × 6
x = 30 toes
Thus the correct answer is option C.

Question 4.
Each month for 5 months, Sophie makes 2 quilts. How many more quilts does she need to make before she has made 16 quilts?
Options:
a. 3
b. 6
c. 7
d. 8

Answer: 6

Explanation:

Sophie makes 2 quilts each month
Number of quilts for 5 months = x
x = 5 × 2 = 10
She has made 16 quilts
Subtract the number of quilts for 5 months from a number of quilts
= 16 – 10 = 6 quilts
So, the answer is option B.

Question 5.
Meredith practices the piano for 3 hours each week. How many hours will she practice in 8 weeks?
Options:
a. 18 hours
b. 21 hours
c. 24 hours
d. 27 hours

Answer: 24 hours

Explanation:

Meredith practices the piano for 3 hours each week
Number of hours she practice in 8 weeks = y
y = 8 × 3
y = 24 hours
So, the answer is option C.

Question 6.
Find the unknown factor.
9 × □ = 36
Options:
a. 3
b. 4
c. 6
d. 8

Answer: 4

Explanation:

□ is the unknown factor
9 × □ = 36
□ = 36/9
□ = 4
Thus the correct answer is option B.

Order of Operations – Page No. 431

Write correct if the operations are listed in the correct order.
If not correct, write the correct order of operations.

Question 1.
45 – 3 × 5 subtract, multiply

Answer: multiply, subtract

Explanation:

Step 1:

First, multiply from left to right

Step 2:
Then subtract from left to right

3 × 5 = 15
45 – 15 = 30

Question 2.
3 × 4 ÷ 2 divide, multiply
__________

Answer: multiply, divide

Explanation:

Step 1:

First, divide from left to right

Step 2:
Then divide from left to right
4 ÷ 2 = 2
3 × 2 = 6
3 × 4 ÷ 2 = 6

Question 3.
5 + 12 ÷ 2 divide, add
__________

Answer: correct

Explanation:

Step 1:

First, divide from left to right

Step 2:
Then add from left to right
12 ÷ 2 = 6, 5 + 6 = 11

Question 4.
7 × 10 + 3 add, multiply
__________

Answer: multiply, add

Explanation:

Step 1:

First, multiply from left to right

Step 2:
Then add from left to right

Follow the order of operations to find the unknown number.

Question 5.
6 + 4 × 3 = n
n = _______

Answer: 18

Explanation:

Step 1:

First, multiply from left to right

Step 2:
Then add from left to right

n = 6 + 4 × 3
n = 6 + 12 = 18

Question 6.
8 − 3 + 2 = k
k = _______

Answer: 7

Explanation:

Step 1:

First, add from left to right

Step 2:
Then subtract from left to right
k = 8 − 3 + 2
k = 8 – 1 = 7

Question 7.
24 ÷ 3 + 5 = p
p = _______

Answer: 13

Explanation:

Step 1:

First, divide from left to right

Step 2:
Then add from left to right
24 ÷ 3 + 5
8 + 5 = 13
p = 13

Question 8.
12 − 2 × 5 = r
r = _______

Answer: 2

Explanation:

Step 1:

First, multiply from left to right

Step 2:
Then subtract from left to right
r = 12 − 2 × 5
r = 12 – 10 = 2

Question 9.
7 × 8 − 6 = j
j = _______

Answer: 50

Explanation:

Step 1:

First, multiply from left to right

Step 2:
Then subtract from left to right
j = 7 × 8 − 6
j = 56 – 6 = 50

Question 10.
4 + 3 × 9 = w
w = _______

Answer: 31

Explanation:

Step 1:

First, multiply from left to right

Step 2:
Then add from left to right
w = 4 + 3 × 9
w = 4 + 27
w = 31

Problem Solving

Question 11.
Shelley bought 3 kites for $6 each. She gave the clerk $20. How much change should Shelley get?
_______

Answer: $2

Explanation:

Shelley bought 3 kites for $6 each
She gave the clerk $20
Each kite = $6
Three kites = 3 × $6 = $18
$20 – $18 = $2
Thus Shelley gets $2 change

Question 12.
Tim has 5 apples and 3 bags with 8 apples in each bag. How many apples does Tim have in all?
_______

Answer: 29 apples

Explanation:

Tim has 5 apples
There are 3 bags
Each bag has 8 apples
Number of apples in 3 bags = 8 × 3 = 24 apples
Now to find the total number of apples that Tim have
Add 24 apples and extra 5 apples
We get 24 + 5 = 29 apples

Order of Operations – Page No. 432

Lesson Check

Question 1.
Natalie is making doll costumes. Each costume has 4 buttons that cost 3¢ each and a zipper that costs 7¢. How much does she spend on buttons and a zipper for each costume?
Options:
a. 19¢
b. 33¢
c. 40¢
d. 49¢

Answer: 19¢

Explanation:

Natalie is making doll costumes. Each costume has 4 buttons that cost 3¢ each and a zipper that costs 7¢.
Each button cost 3¢
Cost of 4 buttons = 4 × 3 = 12¢
Add cost of 4 buttons and zipper that costs 7¢
12¢ + 7¢ = 19¢

Question 2.
Leonardo’s mother gave him 5 bags with 6 flower bulbs in each bag to plant. He has planted all except 3 bulbs. How many flower bulbs has Leonardo planted?
Options:
a. 12
b. 15
c. 27
d. 33

Answer: 27

Explanation:

Leonardo’s mother gave him 5 bags with 6 flower bulbs in each bag to plant
Each bag has 6 flower bulbs
5 bags have x flower bulbs
x = 5 × 6 = 30 flower bulbs
He has planted all except 3 bulbs
Subtract 3 bulbs from 30 flower bulbs
30 – 3 = 27 flower bulbs
Thus the correct answer is option C.

Spiral Review

Question 3.
Each story in Will’s apartment building is 9 feet tall. There are 10 stories in the building. How tall is the apartment building?
Options:
a. 90 feet
b. 80 feet
c. 19 feet
d. 9 feet

Answer: 90 feet

Explanation:

Each story in Will’s apartment building is 9 feet tall
There are 10 stories in the building
= 10 × 9 = 90 feet
Thus the correct answer is option A.

Question 4.
Which of the following describes a pattern in the table?

Options:
a. Add 3.
b. Multiply by 2.
c. Subtract 3.
d. Multiply by 4

Answer: Multiply by 4

Explanation:

The above pattern shows that the number of tables is multiplied by 4.
So, the correct answer is option D.

Question 5.
For decorations, Meg cut out 8 groups of 7 snowflakes each. How many snowflakes did Meg cut out in all?
Options:
a. 72
b. 63
c. 58
d. 56

Answer: 56

Explanation:

Meg cut out 8 groups of 7 snowflakes each
Each group has 7 snowflakes
8 groups have x snowflakes
8 × 7 = 56 snowflakes

Question 6.
A small van can hold 6 students. How many small vans are needed to take 36 students on a field trip to the music museum?
Options:
a. 4
b. 6
c. 7
d. 8

Answer: 6

Explanation:

A small van can hold 6 students
Total number of students = 36
Divide the number of students by the number of students in each van
36 ÷ 6 = 6 vans

Review/Test – Page No. 433

Question 1.
Ming divided 35 marbles between 7 different friends. Each friend received the same number of marbles. How many marbles did Ming give to each friend?
35 ÷ 7 = a
7 × a = 35
Options:
a. 4
b. 5
c. 6
d. 7

Answer: 5

Explanation:

Given,
Ming divided 35 marbles between 7 different friends.
Each friend received the same number of marbles
Let the number of marbles that each friend get = a
a × 7 = 35
a = 35/7 = 5
Now check whether the dividend and the product are related facts or not.
If both are same then the quotient and the unknown factor are 5
So, the correct answer is option B.

Question 2.
Mrs. Conner has 16 shoes.

Select one number from each column to show the division equation represented by the picture.
16 ÷ \(\frac{?}{(\text { divisor })}=\frac{?}{(\text { quotient })}\)

Type below:
____________

Answer:

16 ÷ 1 = 16
1 is the divisor and 16 is the quotient

16 ÷ 2 = 8
2 is the divisor and 8 is the quotient.

16 ÷ 4 = 4
4 is the divisor and 4 is the quotient.

16 ÷ 16 = 1
16 is the divisor and 1 is the quotient.

Question 3.
Twenty boys are going camping. They brought 5 tents. An equal number of boys sleep in each tent. How many boys will sleep in each tent?

______ boys

Answer: 4 boys

Explanation:

Given,
Twenty boys are going camping.
They brought 5 tents. An equal number of boys sleep in each tent.
Let the number of boys in each camp = x
x × 5 = 20
x = 20/5
x = 4
Therefore there are 4 boys in each tent.

Review/Test – Page No. 434

Question 4.
Circle a number for the unknown factor and quotient that makes the equation true.
4 × = 28 = 28 ÷ 4
______                                ______

Answer: 7, 7

Explanation:

4 × = 28  = 28 ÷ 4

Question 5.
Mrs. Walters has 30 markers. She gives each student 10 markers. How many students received the markers?

Write a division equation to represent the repeated subtraction.
______ ÷ ______ = ______

Answer: 30 ÷ 10 = 3

Explanation:

Step 1:

Start with 30

Step 2:

Subtract with 10 until you reach 0.

Step 3:

Count the number of times you subtract 10.

You subtracted 10 three times.
So, there are 3 groups of students receive 10 markers.

Question 6.
Complete the chart to show the quotients.

Type below:
____________

Answer:

÷	27	36	45	54
9	3	4	5	6

Explanation:

Divide 27 ÷ 9 = 3
Divide 36 ÷ 9 = 4
Divide 45 ÷ 9 = 5
Divide 54 ÷ 9 = 6

Question 7.
For numbers 7a–7e, select True or False for each equation.
a. 12 ÷ 6 = 2
i. True
ii. False

Answer: True

Explanation:

6 divides 12 by 2 times. So, the quotient is 2.
Thus the above equation is true.

Question 7.
b. 24 ÷ 6 = 3
i. True
ii. False

Answer: False

Explanation:

6 divides 24 four times. So, the quotient is 4.
The above equation is False.

Question 7.
c. 30 ÷ 6 = 6
i. True
ii. False

Answer: False

Explanation:

6 divides 30 five times. The quotient is 5.
The above equation is false.

Question 7.
d. 42 ÷ 6 = 7
i. True
ii. False

Answer: True

Explanation:

6 divides 42 seven times. The quotient is 7
The given equation is True.

Question 7.
d. 48 ÷ 6 = 8
i. True
ii. False

Answer: True

Explanation:

6 divides 48 eight times. So, the quotient is 8.
The above equation is true.

Review/Test – Page No. 435

Question 8.
Alicia says that 6 ÷ 2 + 5 is the same as 5 + 6 ÷ 2. Is Alicia correct or incorrect? Explain.
____________

Answer: Alicia is correct because both the answer of equations are same

6 ÷ 2 + 5 = 3 + 5 = 8
5 + 6 ÷ 2 = 5 + 3 = 8

Question 9.
Keith arranged 40 toy cars in 8 equal rows. How many toy cars are in each row?
______ toy cars

Answer:  5 toy cars

Explanation:

Keith arranged 40 toy cars in 8 equal rows
To know the number of cars in each row
Divide the total number of toy cars by number of equal rows
= 40 ÷ 8 = 40/8 = 5
Thus there are 5 toy cars in each row

Question 10.
Bella made $21 selling bracelets. She wants to know how many bracelets she sold. Bella used this number line.

Write the division equation that the number line represents.
______ ÷ ______ = ______

Answer: 21 ÷ 3 = 7

Explanation:

Step 1:

The count starts at 0.

Step 2:

Jump by 3 until you reach point 21

Step 3:

Count the number of jumps till you reach 21

Step 4:

Number of jumps = 7
So, the answer is 21 ÷ 3 = 7

Question 11.
Each picnic table seats 6 people. How many picnic tables are needed to seat 24 people? Explain the strategy you used to solve the problem.
______ picnic tables

Answer: 4 picnic tables

Explanation:

Given,
Each picnic table seats 6 people
Number of picnic tables are needed to seat 24 people = x
To find the x we have to divide no. of people by number if seats for each picnic table
x = 24 ÷ 6
x = 24/6 = 4
Therefore 4 picnic tables are needed to seat 24 people

Review/Test – Page No. 436

Question 12.
Finn bought 2 packs of stickers. Each pack had the same number of stickers. A friend gave him 4 more stickers. Now he has 24 stickers in all. How many stickers were in each pack? Explain how you solved the problem.
______ stickers

Answer: 14 stickers

Explanation:

Finn bought 2 packs of stickers
A friend gave him 4 more stickers
Now he has 24 stickers in all
Add 24 and 4
24 + 4 = 28 stickers
Divide the number of stickers by number of packs of stickers
= 28 ÷ 2 = 14 stickers
Therefore there are 14 stickers in each pack

Question 13.
Ana used 49 strawberries to make 7 strawberry smoothies. She used the same number of strawberries in each smoothie. How many strawberries did Ana use in each smoothie?
______ strawberries

Answer: 7 strawberries

Explanation:

Ana used 49 strawberries to make 7 strawberry smoothies. She used the same number of strawberries in each smoothie
Divide number of strawberries by number of strawberry smoothies
49 ÷ 7 = 7 strawberries

Question 14.
For numbers 14a–14e, use the order of operation to select True or False for each equation.
a. 81 ÷ 9 + 2 = 11
i. True
ii. False

Answer: True

Explanation:

Step 1:

First, divide from left to right
81 ÷ 9 = 9

Step 2:
Then add from left to right
9 + 2 = 11
So, the above statement is true

Question 14.
b. 6 + 4 × 5 = 50
i. True
ii. False

Answer: True

Explanation:

Step 1:

First, add from left to right
6 + 4 = 10

Step 2:
Then multiply from left to right
10 × 5 = 50
Thus the above equation is true

Question 14.
c. 10 + 10 ÷ 2 = 15
i. True
ii. False

Answer: True

Explanation:

Step 1:

First, divide from left to right
10 ÷ 2 = 5

Step 2:
Then add from left to right
10 + 5 = 15
So, the answer is true

Question 14.
d. 12 − 3 × 2 = 6
i. True
ii. False

Answer: True

Explanation:

Step 1:

First, multiply from left to right
3 × 2 = 6

Step 2:
Then subtract from left to right
12 – 6 = 6
Thus the above equation is true

Question 14.
e. 20 ÷ 4 × 5 = 1
i. True
ii. False

Answer: True

Explanation:

Step 1:

First, multiply from left to right
4 × 5 = 20

Step 2:
Then divide from left to right
20 ÷ 20 = 1
Thus the above equation is true.

Question 15.
A flower shop sells daffodils in bunches of 9. It sells 27 daffodils. How many bunches of daffodils does the shop sell?
_______ bunches

Answer: 3 bunches

Explanation:

A flower shop sells daffodils in bunches of 9
It sells 27 daffodils
Divide the number of daffodils by number daffodils in each bunch
= 27 ÷ 9 = 3 bunches

Review/Test – Page No. 437

Question 16.
Aviva started a table showing a division pattern.

Part A
Complete the table.
Compare the quotients when dividing by 10 and when dividing by 5. Describe a pattern you see in the quotients.
Type below:
__________

Answer:

÷	20	30	40	50
10	2	3	4	5
5	4	6	8	10

Divide by 10:

20 ÷ 10 = 2
30 ÷ 10 = 3
40 ÷ 10 = 4
50 ÷ 10 = 5

Divide by 5:

20 ÷ 5 = 4
30 ÷ 5 = 6
40 ÷ 5 = 8
50 ÷ 5 = 10

Question 16.
Part B
Find the quotient, a.
70 ÷ 10 = a
a = _____

How could you use a to find the value of n? Find the value of n.
70 ÷ 5 = n
n = _____
a = _____
n = _____

Answer: n = 14; a = 7

Explanation:

Let a be the unknown factor
70 ÷ 10 = a
a = 70/10
10 divides 70 seven times. So, the quotient a is 7.

n represents the unknown number
70 ÷ 5 = n
n = 70/5 = 14
5 divides 70 fourteen times. The value of n is 14.

Question 17.
Ben needs 2 oranges to make a glass of orange juice. If oranges come in bags of 10, how many glasses of orange juice can he make using one bag of oranges?
_____ glasses

Answer: 5 glasses

Explanation:

Ben needs 2 oranges to make a glass of orange juice.
1 bag contains 10 oranges.
10 ÷ 2 = 5 glasses
Thus 5 glasses of orange juice can be made by one bag of oranges.

Review/Test – Page No. 438

Question 18.
For numbers 18a–18e, select True or False for each equation.
a. 0 ÷ 9 = 0
i. True
ii. False

Answer: True

Explanation:

0 divided by any number will be always 0. So, the quotient is 0.
The above equation is true.

Question 18.
b. 9 ÷ 9 = 1
i. True
ii. False

Answer: True

Explanation:

9 divides 9 one time. Thus the quotient is 1.
The above equation is true.

Question 18.
c. 27 ÷ 9 = 4
i. True
ii. False

Answer: False

Explanation:

9 divides 27 three times. So, the quotient is 3.
Thus the above equation is false.

Question 18.
d. 54 ÷ 9 = 6
i. True
ii. False

Answer: True

Explanation:

9 divides 54 six times. The quotient is 6.
So, the above statement is true.

Question 18.
e. 90 ÷ 9 = 9
i. True
ii. False

Answer: False

Explanation:

9 divides 90 ten times. The quotient is 10.
So, the above statement is false.

Question 19.
Ellen is making gift baskets for four friends. She has 16 prizes she wants to divide equally among the baskets. How many prizes should she put in each basket?
_______ prizes

Answer: 4 prizes

Explanation:

Ellen is making gift baskets for 4 friends.
She has 16 prizes she wants to divide equally among the baskets.
Divide the number of prizes by the number of friends
= 16 ÷ 4 = 4
Thus she should put 4 prizes in each basket.

Question 20.
Emily is buying a pet rabbit. She needs to buy items for her rabbit at the pet store.
Part A
Emily buys a cage and 2 bowls for $54. The cage costs $40. Each bowl costs the same amount. What is the price of 1 bowl? Explain the steps you used to solve
the problem.
$ _______

Answer: $7

Explanation:

Emily buys a cage and 2 bowls for $54.
The cage costs $40.
Subtract the cost of cage from $54
$54 – $40 = $14
The cost of 2 bowls = $14
The cot of 1 bowl = x
x × 2 = 14
x = 14/2 = 7
Therefore the cost of each bowl = $7

Question 20.
Part B
Emily also buys food and toys for her rabbit. She buys a bag of food for $20. She buys 2 toys for $3 each. Write one equation to describe the total amount Emily spends on food and toys. Explain how to use the order of operations to solve the equation.
Type below:
____________

Answer: $26

Explanation:

Rule 1: First perform any calculations inside parentheses.
Rule 2: Next perform all multiplications and divisions, working from left to right.
Rule 3: Lastly, perform all additions and subtractions, working from left to right.
$20 + $3 × 2
$20 + $6 = $26

We wish the knowledge shared regarding the Go Math Answer Key for Grade 3 Chapter 7 Division Facts and Strategies have helped you during your preparation. You will find various approaches to solve problems in our Go Math Grade 3 Answer Key Chapter 7 Division Facts and Strategies Extra Practice. Those who want to arrive at the solutions easily can choose the method of your convenience. Check out the review links provided at the end of the chapter and improvise on the skills.