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Go Math Grade 5 Answer Key Chapter 1 Place Value, Multiplication, and Expressions
It’s really difficult to find Solutions for all the Problems in Go Math Grade 5 Chapter 1 all in one place. Now, you will no longer have such difficulties. We are providing Go Math Grade 5 Answer Key Chapter 1 Place Value, Multiplication, and Expressions. Check out Step by Step Solutions provided for various lessons and the topics in it. Practice using the 3rd Grade Go Math Answer Key Ch 1 Place Value, Multiplication, and Expressions and score better grades in the exam.
Lesson 1: Investigate • Place Value and Patterns
Lesson 2: Place Value of Whole Numbers
Lesson 3: Algebra • Properties
Lesson 4: Algebra • Powers of 10 and Exponents
- Powers of 10 and Exponents – Page No. 18
- Powers of 10 and Exponents Lesson Check – Page No. 19
- UNLOCK the Problem – Page No. 20
Lesson 5: Algebra • Multiplication Patterns
- Multiplication Patterns – Page No. 22
- Multiplication Patterns Lesson Check – Page No. 23
- Multiplication Patterns Lesson Check 1 – Page No. 24
Mid-Chapter Checkpoint
Lesson 6: Multiply by 1-Digit Numbers
Lesson 7: Multiply by Multi-Digit Numbers
- Multiply by Multi-Digit Numbers – Page No. 33
- Multiply by Multi-Digit Numbers Lesson Check – Page No. 34
Lesson 8: Relate Multiplication to Division
- Relate Multiplication to Division – Page No. 37
- Relate Multiplication to Division Lesson Check – Page No. 38
Lesson 9: Problem Solving • Multiplication and Division
Lesson 10: Algebra • Numerical Expressions
Lesson 11: Algebra • Evaluate Numerical Expressions
- Evaluate Numerical Expressions – Page No. 49
- Evaluate Numerical Expressions Lesson Check – Page No. 50
Lesson 12: Algebra • Grouping Symbols
Review/Test
- Review/Test – Page No. 55
- Review/Test – Page No. 56
- Review/Test – Page No. 57
- Review/Test – Page No. 58
Place Value and Patterns – Share and Show – Page No. 7
Complete the sentence.
Question 1.
500 is 10 times as much as ______
Answer:
50
Explanation:
Let the unknown number is S.
500 = 10S
S = 500/10 = 50.
500 is 10 times as much as 50.
Question 2.
20,000 is \(\frac{1}{10}\) of ______
Answer:
2,00,000
Explanation:
Let the unknown number is S.
20,000 = \(\frac{1}{10}\) S
S = 20,000 X 10 = 2,00,000
Use place-value patterns to complete the table
Question 5.
| Numbers | 10 times as much as | \(\frac{1}{10}\) of |
| 10 | ______ | ______ |
| 3,000 | ______ | ______ |
| 800 | ______ | ______ |
| 50 | ______ | ______ |
Answer:
| Numbers | 10 times as much as | \(\frac{1}{10}\) of |
| 10 | ___1___ | ___100___ |
| 3,000 | ___300___ | ___30,000___ |
| 800 | ___80___ | ___8,000___ |
| 50 | ___5___ | ___500___ |
Explanation:
1. 10 is 10 times as much as ______
Let the unknown number is S.
10 = 10S
S = 10/10 = 1.
10 is 10 times as much as 1.
10 is \(\frac{1}{10}\) of ______
Let the unknown number is S.
10 = \(\frac{1}{10}\) S
S = 10 X 10 = 100.
2. 3,000 is 10 times as much as ______
Let the unknown number is S.
3,000 = 10S
S = 3,000/10 = 300.
3,000 is 10 times as much as 300.
3,000 is \(\frac{1}{10}\) of ______
Let the unknown number is S.
3,000 = \(\frac{1}{10}\) S
S = 3,000 X 10 = 30,000.
3. 800 is 10 times as much as ______
Let the unknown number is S.
800 = 10S
S = 800/10 = 80.
800 is 10 times as much as 80.
800 is \(\frac{1}{10}\) of ______
Let the unknown number is S.
800 = \(\frac{1}{10}\) S
S = 800 X 10 = 8,000.
4. 50 is 10 times as much as ______
Let the unknown number is S.
50 = 10S
S = 50/10 = 5.
50 is 10 times as much as 5.
50 is \(\frac{1}{10}\) of ______
Let the unknown number is S.
50 = \(\frac{1}{10}\) S
S = 50 X 10 = 500.
Question 6.
| Numbers | 10 times as much as | \(\frac{1}{10}\) of |
| 400 | ______ | ______ |
| 90 | ______ | ______ |
| 6,000 | ______ | ______ |
| 200 | ______ | ______ |
Answer:
| Numbers | 10 times as much as | \(\frac{1}{10}\) of |
| 400 | __40____ | ___4,000___ |
| 90 | ___9___ | ___900___ |
| 6,000 | __600____ | __60,000____ |
| 200 | ___20___ | ___2,000___ |
Explanation:
1. 400 is 10 times as much as ______
Let the unknown number is S.
400 = 10S
S = 400/10 = 40.
400 is 10 times as much as 40.
400 is \(\frac{1}{10}\) of ______
Let the unknown number is S.
400 = \(\frac{1}{10}\) S
S = 400 X 10 = 4,000.
2. 90 is 10 times as much as ______
Let the unknown number is S.
90 = 10S
S = 90/10 = 9.
90 is 10 times as much as 9.
90 is \(\frac{1}{10}\) of ______
Let the unknown number is S.
90 = \(\frac{1}{10}\) S
S = 90 X 10 = 900.
3. 6,000 is 10 times as much as ______
Let the unknown number is S.
6,000 = 10S
S = 6,000/10 = 600.
6,000 is 10 times as much as 600.
6,000 is \(\frac{1}{10}\) of ______
Let the unknown number is S.
6,000 = \(\frac{1}{10}\) S
S = 6,000 X 10 = 60,000.
4. 200 is 10 times as much as ______
Let the unknown number is S.
200 = 10S
S = 200/10 = 20.
200 is 10 times as much as 20.
200 is \(\frac{1}{10}\) of ______
Let the unknown number is S.
200 = \(\frac{1}{10}\) S
S = 200 X 10 = 2,000.
Complete the sentence with 100 or 1,000.
Question 13.
200 is ______ times as much as 2
Answer:
200 is 100 times as much as 2
Explanation:
Let the unknown number be S.
200 = 2S
S = 200/2 = 100
Question 16.
600 is ______ times as much as 6
Answer:
600 is 100 times as much as 6
Explanation:
Let the unknown number be S.
600 = 6S
S = 600/6= 100
Question 17.
50,000 is ______ times as much as 500
Answer:
50,000 is 100_ times as much as 500
Explanation:
Let the unknown number be S.
50,000 = 500S
S = 50,000/500= 100
Question 18.
30,000 is ______ times as much as 30
Answer:
30,000 is 1,000 times as much as 30
Explanation:
Let the unknown number be S.
30,000 = 30S
S = 30,000/30 = 1,000
Place Value and Patterns – Problem Solving – Page No. 8
Sense or Nonsense?
Question 20.
Mark and Robyn used base-ten blocks to show that 300 is 100 times as much as 3. Whose model makes sense? Whose model is nonsense? Explain your reasoning.
Type below:
__________
Answer:
Robyn’s model makes sense. Because the given data 300 is 100 times as much as 3. It clearly states that there are 100 model-blocks and one model blocks should take to solve the problem.
Question 20.
Explain how you would help Mark understand why he should have used small cubes instead of longs.
Type below:
__________
Answer:
Mark’s drew 100 model-blocks and 10 model-blocks which. To get 300 is 100 times as much as 3, he needs to do 300/3 = 100 model blocks.
Place Value of Whole Numbers – Share and Show – Page No. 11
Complete the place-value chart to find the value of each digit.
Question 1.
Type below:
__________
Answer:
7,333,820
Explanation:
7 x 1,000,000 = 7,000,000
3 x 100,000 = 300,000
3 x 1,000 = 3000
8 x 100 = 800
2 x 10 = 20
Write the value of the underlined digit.
Question 2.
1,574,833
__________
Answer:
4,000
Explanation:
(1 x 1,000,000) + (5 x 1,00,000) + (7 x 10,000) + (4 x 1,000) + (8 x 100) + (3 x 10) + (3 x 1)
4 x 1,000 = 4 thousands = 4,000
Question 5.
301,256,878
__________
Answer:
3,00,000,000
Explanation:
(3 x 1,00,000,000) + (0 x 10,000,000) + (1 x 1,000,000) + (2 x 1,00,000) + (5 x 10,000) + (6 x 1,000) + (8 x 100) + (7 x 10) + (8 x 1)
3 x 1,00,000,000 = 3 hundred- millions = 3,00,000,000
Write the number in two other forms.
Question 6.
(8 × 100,000) + (4 × 1,000) + (6 × 1) =
__________
Answer:
80,4006
Eight Hundred Four Thousand Six
Explanation:
(8 × 100,000) + (4 × 1,000) + (6 × 1) = 800,000 + 4,000 + 6 = 80,4006
On Your Own
Write the value of the underlined digit.
Question 8.
849,567,043
__________
Answer:
40,000,000
Explanation:
(8 x 1,00,000,000) + (4 x 10,000,000) + (9 x 1,000,000) + (5 x 1,00,000) + (6 x 10,000) + (7 x 1,000) + (0 x 100) + (4 x 10) + (3 x 1)
4 x 10,000,000 = 4 ten- millions = 40,000,000
Question 9.
9,422,850
__________
Answer:
4,00,000
Explanation:
(9 x 1,000,000) + (4 x 1,00,000) + (2 x 10,000) + (2 x 1,000) + (8 x 100) + (5 x 10) + (0 x 1)
4 x 1,00,000 = 4 Hundred Thousand = 4,00,000
Question 10.
96,283
__________
Answer:
90,000
Explanation:
(9 x 10,000) + (6 x 1,000) + (2 x 100) + (8 x 10) + (3 x 1)
9 x 10,000 = 9 ten-thousands = 90,000
Question 12.
791,350
__________
Answer:
300
Explanation:
(7 x 1,00,000) + (9 x 10,000) + (1 x 1,000) + (3 x 100) + (5 x 10) + (0 x 1)
3 x 100 = 3 hundred = 300
Question 13.
27,911,534
__________
Answer:
7,000,000
Explanation:
(2 x 10,000,000) + (7 x 1,000,000) + (9 x 1,00,000) + (1 x 10,000) + (1 x 1,000) + (5 x 100) + (3 x 10) + (4 x 1)
7 x 1,000,000 = Seven Million = 7,000,000
Question 14.
105,980,774
__________
Answer:
80,000
Explanation:
(1 x 1,00,000,000) + (0 x 10,000,000) + (5 x 1,000,000) + (9 x 1,00,000) + (8 x 10,000) + (0 x 1,000) + (7 x 100) + (7 x 10) + (4 x 1)
8 x 10,000 = 8 ten-thousand = 80,000
Question 15.
8,265,178
__________
Answer:
5,000
Explanation:
(8 x 1,000,000) + (2 x 1,00,000) + (6 x 10,000) + (5 x 1,000) + (1 x 100) + (7 x 10) + (8 x 1)
5 x 1,000 = 5 one-thousand = 5,000
Write the number in two other forms.
Question 16.
345,000
Type below:
__________
Answer:
Three Hundred Forty-Five Thousand
(3 x 1,00,000) + (4 x 10,000) + (5 x 1,000) + (0 x 100) + (0 x 10) + (0 x 1)
Question 17.
119,000,003
Type below:
__________
Answer:
One Hundred Nineteen Million Three
(1 x 100,000,000) + (1 x 10,000,000) + (9 x 1,000,000) + (0 x 1,00,000) + (0 x 10,000) + (0 x 1,000) + (0 x 100) + (0 x 10) + (3 x 1)
Place Value of Whole Numbers – Problem Solving – Page No. 12
Use the table for 18–19.
Question 18.
Which planet is about 10 times as far as Earth is from the Sun?
__________
Answer:
Saturn
Explanation:
Saturn = 1,427,000/10 = 142,700 which is 10 times as far as Earth
Question 19.
Which planet is about \(\frac{1}{10}\) of the distance Uranus is from the Sun?
__________
Answer:
Mars
Explanation:
Mars = 227,900
\(\frac{1}{10}\) x 2,871,000 = 287,100
Which planet is about \(\frac{1}{10}\) of the distance Uranus is from the Sun
Question 22.
Test Prep In the number 869,653,214, which describes how the digit 6 in the ten-millions place compares to the digit 6 in the hundred-thousands place?
Options:
A. 10 times as much as
B. 100 times as much as
C. 1,000 times as much as
D.\(\frac{1}{10}\) of
Answer:
B. 100 times as much as
Explanation:
869,653,214
(8 x 100,000,000) + (6 x 10,000,000) + (9 x 1,000,000) + (6 x 1,00,000) + (5 x 10,000) + (3 x 1,000) + (2 x 100) + (1 x 10) + (4 x 1)
6 x 10,000,000 = 60,000,000
6 x 1,00,000 = 6,00,000
60,000,000/6,00,000 = 100
Properties – Share and Show – Page No. 15
Use properties to find 4 × 23 × 25.
Question 1.
23 × × 25 ________ Property of Multiplication
23 × ( × ) ________ Property of Multiplication
23 ×
__________
____
Answer:
23 x 4 x 25; Commutative Property of Multiplication
23 x (4 x 25); Associative Property of Multiplication
23 x 100
2,300
Use properties to find the sum or product.
Question 2.
89 + 27 + 11 = ____
Answer:
89 + (27 + 11); Associative Property of Addition
89 + 38
127
Question 3.
9 × 52 = ____
Answer:
468
Explanation:
9 x 52
Write 52 = (50 + 2)
9 x (50 + 2)
(9 x 50) + (9 x 2); Distributive Property of Multiplication
450 + 18
468
Question 4.
107 + 0 + 39 + 13 = ____
Answer:
107 + 0 + 39 + 13
(107 + 0) + (39 + 13); Associative Property of Addition
107 + 0 = 107; Identity Property of Addition
107 + 52 = 159
Complete the equation, and tell which property you used.
Question 6.
Describe how you can use properties to solve problems more easily.
Type below:
__________
Answer:
Using Properties of Addition and Properties of Multiplication, we can solve problems more easily. Simplifying problems is easy with the properties.
On Your Own
Practice: Copy and Solve Use properties to find the sum or product.
Question 7.
3 × 78 = ____
Answer:
234, Associative Property of Multiplication
Explanation:
Write 78 as 6 x 13
3 x 6 x 13
(3 x 6) x 13; Associative Property of Multiplication
18 x 13 = 234
Question 8.
4 × 60 × 5 = ____
Answer:
1,200; Associative Property of Multiplication
Explanation:
4 x 60 x 5
4 x (60 x 5); Associative Property of Multiplication
4 x 300 = 1,200
Question 9.
21 + 25 + 39 + 5 = ____
Answer:
90; Associative Property of Addition
Explanation:
(21 + 25) + (39 + 5); Associative Property of Addition
46 + 44 = 90
Complete the equation, and tell which property you used.
Question 10.
11 + (19 + 6) = (11 + ____) + 6
Answer:
11 + (19 + 6) = (11 + 19) + 6; Associative Property of Addition
Question 11.
25 + 14 = ____ + 25
Answer:
25 + 14 = 14 + 25; Commutative Property of Addition
Question 12.
Show how you can use the Distributive Property to rewrite and find (32 × 6) + (32 × 4).
____
Answer:
(32 × 6) + (32 × 4) = 32 x (6 + 4); Distributive Property
Properties – Problem Solving – Page No. 16
Question 14.
Jacob is designing an aquarium for a doctor’s office. He plans to buy 6 red blond guppies, 1 blue neon guppy, and 1 yellow guppy. The table shows the price list for the guppies. How much will the guppies for the aquarium cost?
$ ____
Answer:
$162
Explanation:
Jacob is designing an aquarium for a doctor’s office. He plans to buy 6 red blond guppies, 1 blue neon guppy, and 1 yellow guppy.
(6 x $22) + (1 x $11) + (1 x $19) = $132 + $11 + $19 = $162
Question 15.
Sylvia bought 8 tickets to a concert. Each ticket costs $18. To find the total cost in dollars, she added the product 8 × 10 to the product 8 × 8, for a total of 144. Which property did Sylvia use?
i. Distributive Property
ii. Associative Property
Answer:
i. Distributive Property
Explanation:
Sylvia bought 8 tickets to a concert. Each ticket costs $18.
To find the total cost in dollars = 8 x $18
Using Distributive Property
(8 × 10) + (8 × 8) = 8 x (10 + 8) = 144.
Question 17.
Test Prep Canoes rent for $29 per day. Which expression can be used to find the cost in dollars of renting 6 canoes for a day?
Options:
A. (6 + 20) + (6 + 9)
B. (6 × 20) + (6 × 9)
C. (6 + 20) × (6 + 9)
D. (6 × 20) × (6 × 9)
Answer:
B. (6 × 20) + (6 × 9)
Explanation:
Canoes rent for $29 per day. For renting 6 canoes for a day, 6 x $29
6 x $(20 + 9) = (6 x 20) + (6 x 9)
Powers of 10 and Exponents – Share and Show – Page No. 18
Write in exponent form and word form.
Question 1.
10 × 10
Exponent form:
Word form:
Type below:
__________
Answer:
Exponent form: 102
Word form: the second power of ten
Explanation:
10 × 10
Base = 10;
Exponent = 2;
Exponent Form: 102
Word Form: the second power of ten
Find the value.
Question 3.
102 = ____
Answer:
100
Explanation:
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
Powers of 10 and Exponents – On Your Own – Page No. 19
Write in exponent form and word form.
Question 6.
10 × 10 × 10
exponent form:
word form:
Type below:
__________
Answer:
Exponent form: 103
Word form: the third power of ten
Explanation:
10 × 10 × 10
Base = 10;
Exponent = 3;
Exponent Form: 103
Word Form: the third power of ten
Find the value.
Question 8.
104 = ____
Answer:
10,000
Explanation:
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
104 = 10 x 10 x 10 x 10 = 10,000;
Question 10.
6 × 104 = ____
Answer:
60,000
Explanation:
6 × 104
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
104 = 10 x 10 x 10 x 10 = 10,000;
6 x 10,000 = 60,000
Complete the pattern.
Question 12.
9 × 100 = _______ = 9
9 × 101 = _______ = 90
9 × 102 = _______ = 900
9 × 103 = _______ = 9,000
9 × 104 = _______ = 90,000
Answer:
9 × 100 = 9 x 1 = 9
9 × 101 = 9 x 10 = 90
9 × 102 = 9 x 10 x 10 = 900
9 × 103 = 9 x 10 x 10 x 10= 9,000
9 × 104 = 9 x 10 x 10 x 10 x 10 = 90,000
Explanation:
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
104 = 10 x 10 x 10 x 10 = 10,000;
Question 13.
12 × 100 = 12 × 1 = _______
12 × 101 = 12 × 10 = _______
12 × 102 = 12 × 10 × 10 = _______
12 × 103 = 12 × 10 × 10 × 10 _______
12 × 104 = 12 × 10 × 10 × 10 × 10 _______
Answer:
12 × 100 = 12 × 1 = 12
12 × 101 = 12 × 10 = 120
12 × 102 = 12 × 10 × 10 = 1,200
12 × 103 = 12 × 10 × 10 × 10 = 12,000
12 × 104 = 12 × 10 × 10 × 10 × 10 = 120,000
Explanation:
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
104 = 10 x 10 x 10 x 10 = 10,000;
Question 15.
Explain how to write 50,000 using exponents.
Type below:
__________
Answer:
5 x 104
Explanation:
5 x 10,000
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
104 = 10 x 10 x 10 x 10 = 10,000;
10,000 = 10 x 10 x 10 x 10 = 104
5 x 104
Powers of 10 and Exponents – UNLOCK the Problem – Page No. 20
Question 16.
Lake Superior is the largest of the Great Lakes. It covers a surface area of about 30,000 square miles. How can you show the estimated area of Lake Superior as a whole number multiplied by a power of ten?
a. What are you asked to find?
Options:
A. 3 × 102 sq mi
B. 3 × 103 sq mi
C. 3 × 104 sq mi
D. 3 × 105 sq mi
Answer:
C. 3 × 104 sq mi
Explanation:
Lake Superior is the largest of the Great Lakes. It covers a surface area of about 30,000 square miles.
3 x 10,000
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
104 = 10 x 10 x 10 x 10 = 10,000;
10,000 = 10 x 10 x 10 x 10 = 104
3 x 104
Question 16.
b. How can you use a pattern to find the answer?
Type below:
__________
Answer:
3 x 10,000
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
104 = 10 x 10 x 10 x 10 = 10,000;
10,000 = 10 x 10 x 10 x 10 = 104
3 x 104
Question 16.
c. Write a pattern using the whole number 3 and powers of ten.
3 × 101 = 3 × 10 =
3 × 102 = =
3 × 103 = =
3 × 104 = =
Type below:
__________
Answer:
3 × 101 = 3 × 10 =
3 × 102 = 3 x 10 x 10 = 300
3 × 103 = 3 x 10 x 10 x 10 = 3,000
3 × 104 = 3 x 10 x 10 x 10 x 10 = 30,000
Question 16.
d. Fill in the correct answer choice above.
Type below:
__________
Answer:
3 × 104 = 3 x 10 x 10 x 10 x 10 = 30,000
Question 17.
The Earth’s diameter through the equator is about 8,000 miles. What is the Earth’s estimated diameter written as a whole number multiplied by a power of ten?
Options:
A. 8 × 101 miles
B. 8 × 102 miles
C. 8 × 103 miles
D. 8 × 104 miles
Answer:
C. 8 × 103 miles
Explanation:
The Earth’s diameter through the equator is about 8,000 miles.
8 x 1,000
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
1,000 = 10 x 10 x 10
8 x 1,000 = 8 x 103
Question 18.
The Earth’s circumference around the equator is about 25 × 103 miles. What is the Earth’s estimated circumference written as a whole number?
Options:
A. 250,000 miles
B. 25,000 miles
C. 2,500 miles
D. 250 miles
Answer:
B. 25,000 miles
Explanation:
The Earth’s circumference around the equator is about 25 × 103 miles.
25 × 103 miles;
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
25 x 1,000 = 25,000 miles
Multiplication Patterns – Share and Show – Page No. 22
Use mental math and a pattern to find the product.
Question 1.
What basic fact can you use to help you find 30×4,000?
30 × 4,000 = ____
Answer:
3 x 4 = 12
Explanation:
30 × 4,000
The basic fact is 3 x 4 = 12
Use mental math to complete the pattern.
Question 2.
1 × 1 = 1
1 × 101 = _______
1 × 102 = _______
1 × 103 = _______
Answer:
1 × 1 = 1
1 × 101 = 10
1 × 102 = 100
1 × 103 = 1,000
Explanation:
1 × 1 = 1
1 × 101 = 1 x 10 = 10
1 × 102 = 1 x 10 x 10 = 100
1 × 103 = 1 x 10 x 10 x 10 = 1,000
Question 3.
7 × 8 = 56
(7 × 8) × 101 = _______
(7 × 8) × 102 = _______
(7 × 8) × 106 = _______
Answer:
7 × 8 = 56
(7 × 8) × 101 = 560
(7 × 8) × 102 = 5,600
(7 × 8) × 106 = 56,000,000
Explanation:
7 × 8 = 56
(7 × 8) × 101 = 56 x 10 = 560
(7 × 8) × 102 = 56 x 10 x 10 = 5,600
(7 × 8) × 106 = 56 x 10 x 10 x 10 x 10 x 10 x 10 = 56,000,000
Question 4.
6 × 5 = _______
6 × 5 × _______ = 300
6 × 5 × _______ = 3000
6 × 5 × _______ = 30,000
Answer:
6 × 5 = 30
6 × 5 × 101 = 300
6 × 5 × 103 = 3000
6 × 5 × 104 = 30,000
Explanation:
6 × 5 = 30
6 × 5 × 10 = 300
6 × 5 × 10 x 10 x 10 = 3000
6 × 5 × 10 x 10 x 10 x 10 = 30,000
On Your Own
Use mental math to complete the pattern.
Question 6.
3 × 7 = 21
(3 × 7) × 101 = _______
(3 × 7) × 102 = _______
(3 × 7) × 103 = _______
Answer:
3 × 7 = 21
(3 × 7) × 101 = 210
(3 × 7) × 102 = 2,100
(3 × 7) × 103 = 21,000
Explanation:
3 × 7 = 21
(3 × 7) × 101 = 21 x 10 = 210
(3 × 7) × 102 = 21 x 10 x 10 = 2,100
(3 × 7) × 103 = 21 x 10 x 10 x 10 = 21,000
Question 7.
5 × 4 = _______
(5 × 4) × _______ = 200
(5 × 4) × _______ = 2,000
(5 × 4) × _______ = 20,000
Answer:
5 × 4 = 20
(5 × 4) × 101 = 200
(5 × 4) × 102 = 2,000
(5 × 4) × 103 = 20,000
Explanation:
5 × 4 = 20
(5 × 4) × 10 = 200
(5 × 4) × 10 x 10 = 2,000
(5 × 4) × 10 x 10 x 10 = 20,000
Question 8.
5 × 7 = _______
(5 × 7) × _______ = 350
(5 × 7) × _______ = 3,500
(5 × 7) × _______ = 35,000
Answer:
5 × 7 = 35
(5 × 7) × 101 = 350
(5 × 7) × 102 = 3,500
(5 × 7) × 103 = 35,000
Explanation:
5 × 7 = 35
(5 × 7) × 10 = 350
(5 × 7) × 10 x 10 = 3,500
(5 × 7) × 10 x 10 x 10 = 35,000
Question 10.
6 × 7 = 42
(6 × 7) × 101 = _______
(6 × 7) × 102 = _______
(6 × 7) × 103 = _______
Answer:
6 × 7 = 42
(6 × 7) × 101 = 420
(6 × 7) × 102 = 4,200
(6 × 7) × 103 = 42,000
Explanation:
6 × 7 = 42
(6 × 7) × 101 = 42 x 10 = 420
(6 × 7) × 102 = 42 x 10 x 10 = 4,200
(6 × 7) × 103 = 42 x 10 x 10 x 10 = 42,000
Use mental math and a pattern to find the product.
Question 11.
(6 × 6) × 101 = ____
Answer:
(6 × 6) × 101 = 360
Explanation:
6 x 6 =36
(6 × 6) × 101 = 36 x 10 = 360
Question 14.
(4 × 3) × 102 = ____
Answer:
1,200
Explanation:
(4 × 3) = 12
(4 × 3) × 101 = 12 x 10 = 120
(4 × 3) × 102 = 12 x 10 x 10 = 1,200
Question 15.
(2 × 5) × 103 = ____
Answer:
10,000
Explanation:
(2 × 5) = 10
(2 × 5) × 101 = 10 x 10 = 100
(2 × 5) × 102 = 10 x 10 x 10 = 1,000
(2 × 5) × 103 = 10 x 10 x 10 x 10 = 10,000
Question 16.
(2 × 8) × 102 = ____
Answer:
1,600
Explanation:
(2 × 8) = 16
(2 × 8) × 101 = 16 x 10 = 160
(2 × 8) × 102 = 16 x 10 x 10 = 1,600
Question 17.
(6 × 5) × 103 = ____
Answer:
30,000
Explanation:
(6 × 5) = 30
(6 × 5) × 101 = 30 x 10 = 300
(6 × 5) × 102 = 30 x 10 x 10 = 3,000
(6 × 5) × 103 = 30 x 10 x 10 x 10 = 30,000
Multiplication Patterns – Share and Show – Page No. 23
Use mental math to complete the table.
Question 20.
1 roll = 50 dimes ; Think:50 dimes per roll × 20 rolls =(5 × 2) × (10 × 10)
Type below:
__________
Answer:
Explanation:
1 roll = 50 dimes ;
Think:50 dimes per roll × 20 rolls =(5 × 2) × (10 × 10) = 10 x 102
50 dimes per roll × 30 rolls = (5 x 3) x (10 × 10) = 15 x 102
50 dimes per roll × 40 rolls = (5 x 4) x (20 × 10) = 20 x 102
50 dimes per roll × 50 rolls = (5 x 5) x (10 × 10) = 25 x 102
50 dimes per roll × 60 rolls = (5 x 6) x (10 × 10) = 30 x 102
50 dimes per roll × 70 rolls = (5 x 7) x (10 × 10) = 35 x 102
50 dimes per roll × 80 rolls = (5 x 8) x (10 × 10) = 40 x 102
50 dimes per roll × 90 rolls = (5 x 9) x (10 × 10) = 45 x 102
50 dimes per roll × 100 rolls = (5 x 10) x (10 × 10) = 50 x 102
Question 21.
1 roll = 40 quarters ; Think:40 quarters per roll × 20 rolls =(4 × 2) × (10 × 10)
Type below:
__________
Answer:
Explanation:
1 roll = 40 quarters ;
Think:40 quarters per roll × 20 rolls =(4 × 2) × (10 × 10) = 8 x 102
40 quarters per roll × 30 rolls =(4 × 3) × (10 × 10) = 12 x 102
40 quarters per roll × 40 rolls =(4 × 4) × (10 × 10) = 16 x 102
40 quarters per roll × 50 rolls =(4 × 5) × (10 × 10) = 20 x 102
40 quarters per roll × 60 rolls =(4 × 6) × (10 × 10) = 24 x 102
40 quarters per roll × 70 rolls =(4 × 7) × (10 × 10) = 28 x 102
40 quarters per roll × 80 rolls =(4 × 8) × (10 × 10) = 32 x 102
40 quarters per roll × 90 rolls =(4 × 9) × (10 × 10) = 36 x 102
40 quarters per roll × 100 rolls =(4 × 10) × (10 × 10) = 40 x 102
Question 22.
Type below:
__________
Answer:
Explanation:
80 x 800 = 64 x 103
80 x 6 = (8 x 6) x 10 = 48 x 101
80 x 70 = (8 x 7) x (10 x 10) = 56 x 102
80 x 9,000 = (8 x 9) x (10 x 10 x 10 x 10) = 64 x 104
Question 23.
Type below:
__________
Answer:
Explanation:
Given that
90 x 9,000 = (9 x 9) x 10 x 10 x 10 x 10 = 81 x 104
90 x 6 = (9 x 6) x 10 = 54 x 101
90 x 70 = (9 x 7) x (10 x 10) = 63 x 102
90 x 800 = (9 x 8) x (10 x 10 x 10) = 72 x 103
Problem Solving
Use the table for 24–26.
Question 24.
What if you magnified the image of a cluster fly by 9 × 103 ? What would the length appear to be?
____ mm
Answer:
9,000 mm
Explanation:
9 × 103 = 9 x 10 x 10 x 10 = 9,000
Question 26.
John wants to magnify the image of a fire ant and a crab spider so they appear to be the same length. How many times their actual sizes would he need to magnify each image?
Fire ant by _______ times
Crab spider by ______ times
Answer:
Fire ant by 5 times
Crab spider by 4 times
Explanation:
Given that Fire ant = 4 mm
crab spider = 5 mm
So, to make them have the same lengths, multiply fire ant by 5 mm and multiply Crab spider by 4 mm
Multiplication Patterns – Share and Show – Page No. 24
Question 27.
What does the product of any whole-number factor multiplied by 100 always have? Explain.
Type below:
__________
Answer:
The product of any whole number factor multiplied by 100 has two digits which are 0 in ones and tens places.
Example: 2 x 100 = 200
Question 28.
Test Prep How many zeros are in the product (5 × 4) × 104?
Options:
A. 3
B. 4
C. 5
D. 6
Answer:
C. 5
Explanation:
(5 × 4) × 104 = 20 x 104 = 2 x 105
5 zeroes
Use patterns and mental math to solve.
Question 31.
Lymphocytes and eosinophils are types of white blood cells. A blood sample has about 10 times as many lymphocytes as eosinophils. If there are 2 × 102 eosinophils in the sample, about how many lymphocytes are there?
______ lymphocytes
Answer:
2 × 103 lymphocytes
Explanation:
Lymphocytes and eosinophils are types of white blood cells. A blood sample has about 10 times as many lymphocytes as eosinophils.
There are 2 × 102 eosinophils in the sample
Then, Lymphocytes = 10 x 2 × 102 eosinophils = 2 × 103
Question 32.
An average person has 6 × 102 times as many red bloods cells as white blood cells. A small sample of blood has 7 × 103 white blood cells. About how many red blood cells are in the sample?
______ red blood cells
Answer:
42 x 105 red blood cells
Explanation:
Let the red blood cells = S
S = 7 × 103 x 6 × 102
S = 42 x 105
Mid-Chapter Checkpoint – Vocabulary – Page No. 25
Choose the best term for the box.
Question 1.
A group of three digits separated by commas in a multidigit number is a __
________
Answer:
Period
Question 2.
An __ is the number that tells how many times a base is used as a factor
________
Answer:
exponent
Concepts and Skills
Complete the sentence.
Question 3.
7 is \(\frac{1}{10}\) of ______
Answer:
70
Explanation:
Let the unknown number is S.
7 = \(\frac{1}{10}\) S
S = 7 X 10 = 70
Question 4.
800 is 10 times as much as ______
Answer:
80
Explanation:
Let the unknown number is S.
800 = 10S
S = 800/10 = 80.
Write the value of the underlined digit.
Question 5.
6,581,678
________
Answer:
80,000
Explanation:
(6 x 1,000,000) + (5 x 1,00,000) + (8 x 10,000) + (1 x 1,000) + (6 x 100) + (7 x 10) + (8 x 1)
8 x 10,000 = 80,000
Question 6.
25,634
________
Answer:
600
Explanation:
(2 x 10,000) + (5 x 1,000) + (6 x 100) + (3 x 10) + (4 x 1)
6 x 100 = 600
Question 7.
34,634,803
________
Answer:
4,000,000
Explanation:
(3 x 10,000,000) + (4 x 1,000,000) + (6 x 1,00,000) + (3 x 10,000) + (4 x 1,000) + (8 x 100) + (0 x 10) + (3 x 1)
4 x 1,000,000 = 4,000,000
Question 8.
2,764,835
________
Answer:
700,000
Explanation:
(2 x 1,000,000) + (7 x 1,00,000) + (6 x 10,000) + (4 x 1,000) + (8 x 100) + (3 x 10) + (5 x 1)
7 x 1,00,000 = 700,000
Complete the equation, and tell which property you used.
Question 9.
8 × (14 + 7) = ________ + (8 × 7)
Answer:
8 × (14 + 7) = (8 x 14) + (8 × 7);
Distributive Property of Multiplication
Explanation:
8 × (14 + 7)
(8 x 14) + (8 × 7); Distributive Property of Multiplication
Question 10.
7 + (8 + 12) = ________ + 12
Answer:
7 + (8 + 12) = (7 + 8) + 12
Associative Property of Addition
Find the value.
Question 11.
103 = ______
Answer:
1,000
Explanation:
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
Question 12.
6 × 102 = ______
Answer:
600
Explanation:
6 × 102
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
6 x 100 = 600
Question 13.
4 × 104 = ______
Answer:
40,000
Explanation:
4 × 104
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
104 = 10 x 10 x 10 x 10 = 10,000;
4 x 10,000 = 40,000
Use mental math and a pattern to find the product.
Question 14.
70 × 300 = ______
Answer:
21,000
Explanation:
70 × 300 = (7 x 3) x (10 x 10 x 10) = 21 x 1,000 = 21,000
Question 15.
(3 × 4) × 103 = ______
Answer:
12,000
Explanation:
(3 × 4) × 103
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
12 x 1,000 = 12,000
Mid-Chapter Checkpoint – Page No. 26
Fill in the bubble completely to show your answer.
Question 16.
DVDs are on sale for $24 each. Which expression can be used to find the cost in dollars of buying 4 DVDs?
Options:
A. (4 + 20) + (4 + 4)
B. (4 × 20) + (4 × 4)
C (4 + 20) × (4 + 4)
D. (4 × 20) × (4 × 4)
Answer:
B. (4 × 20) + (4 × 4)
Explanation:
24 can be written as 25 – 1
4 x 24 = 4 x (20 + 4) = (4 x 20) + (4 x 4)
Question 17.
The Muffin Shop chain of bakeries sold 745,305 muffins last year. Which choice shows that number in expanded form?
Options:
A. (7 × 100,000) + (45 × 10,000) + (3 × 100) + (5 × 10)
B. (7 × 100,000) + (4 × 10,000) + (5 × 1,000) + (5 × 10)
C. (7 × 100,000) + (4 × 10,000) + (5 × 1,000) + (3 × 100) + (5 × 1)
D. (7 × 100,000) + (4 × 10,000) + (3 × 100) + (5 × 1)
Answer:
C. (7 × 100,000) + (4 × 10,000) + (5 × 1,000) + (3 × 100) + (5 × 1)
Explanation:
First, we can write 745,305 as:
700,000 + 40, 000 + 5,000 + 300 + 5
(7 x 100,000) + (4 x 10,000) + (5 x 1,000) + (3 x 100) + 5
Question 18.
The soccer field at Mario’s school has an area of 6,000 square meters. How can Mario show the area as a whole number multiplied by a power of ten?
Options:
A. 6 × 104 sq m
B. 6 × 103 sq m
C. 6 × 102 sq m
D. 6 × 101 sq m
Answer:
B. 6 × 103 sq m
Explanation:
6,000 square meters = 6 x 1,000 = 6 x 10 x 10 x 10 = 6 × 103 sq m
Question 19.
Ms. Alonzo ordered 4,000 markers for her store. Only \(\frac{1}{10}\) of them arrived. How many markers did she receive?
Options:
A. 4
B. 40
C. 400
D. 1,400
Answer:
C. 400
Explanation:
Ms. Alonzo ordered 4,000 markers for her store. Only \(\frac{1}{10}\) of them arrived.
4,000 x \(\frac{1}{10}\) = 400
Question 20.
Mark wrote the highest score he made on his new video game as the product of 70 × 6,000. What was his score?
Options:
A. 420
B. 4,200
C. 42,000
D. 420,000
Answer:
D. 420,000
Explanation:
Mark wrote the highest score he made on his new video game as the product of 70 × 6,000.
(7 x 6) x (10 x 10 x 10 x 10) = 42 x 10,000 = 420,000
Multiply by 1-digit numbers – Share and Show – Page No. 29
Complete to find the product.
Question 1.
6 × 796 Estimate: 6 × ___ = ___
______
Answer:
4,776
Explanation:
Estimate. Then find the product.
Question 2.
Estimate: ___
6 0 8
× 8
———-
Estimate: ________
Product: 608 × 8 = ________
Answer:
Estimate: 6,000
Product: 608 × 8 = 4,864
Explanation:
Estimate: 608 is close to 600; 8 is close to 10
600 x 10 = 6,000
608 x 8
Multiply the ones; 8 x 8 = 64. 4 ones and 6 tens. Write the ones and the
regrouped tens.
Multiply the tens; 0 x 8 = 0 + 6 = 6
Multiply the hundreds; 6 x 8 = 48.
So, 4,864 is the product of 608 × 8
Product: 4,864
Question 4.
Estimate:
1,925
× 7
———–
Estimate: ________
Product: 1,925 × 7 = ________
Answer:
Estimate: 10,000
Product: 1,925 × 7 = 13,475
Explanation:
Estimate: 1,925 is close to 2000; 7 is close to 5
2,000 x 5 = 10,000
1,925 × 7
Multiply the ones; 7 x 5 = 35. 5 ones and 3 tens. Write the ones and the
regrouped tens.
Multiply the tens; 7 x 2 = 14; 14 + 3 = 17; 7 tens and 1 hundreds. Write the tens and regrouped hundreds.
Multiply the hundreds; 7 x 9 = 63; 63 + 1 = 64. 4 hundred and 6 thousand Write the hundreds and regrouped thousands.
Multiply the thousands; 7 x 1 = 7; 7 + 6 = 13
So, 13,475 is the product of 1,925 × 7
Product: 13,475
On Your Own
Estimate. Then find the product.
Question 5.
Estimate:__
7 9 4
× 3
———-
Estimate: ________
Product:794 × 3 = ________
Answer:
Estimate: 800
Product:794 × 3 = 2,382
Explanation:
Estimate: 794 is close to 800 and 3 is close to 1
800 x 1 = 800
794 x 3 = (700 + 90 + 4) x 3 = (700 x 3) + (90 x 3) + (4 x 3) = 2100 + 270 + 12 = 2,382
Question 7.
Estimate:
3,102
× 5
———–
Estimate: ________
Product: 3,102 × 5 = ________
Answer:
Estimate: 15,500
Product: 3,102 × 5 = 15,510
Explanation:
Estimate: 3,102 is close to 3,100 and 5 is close to 5
3,100 x 5 = 15,500
3,102 x 5 = (3,000 + 100 + 0 + 2) x 5 = (3000 x 5) + (100 x 5) + 0 + (2 x 5) = 15,000 + 500 + 0 + 10 = 15,510
Algebra Solve for the unknown number.
Question 8.
3 9 6
× 6
———
2, 3 6
396 × 6 = 23 ______ 6
Answer:
7
Explanation:
396 x 6 = (300 + 90 + 6) x 6 = (300 x 6) + (90 x 6) + (6 x 6) = 1800 + 540 + 36 = 2376. So, the unknown number is 7
Question 9.
5,1 2
× 8
——–
16
Type below:
__________
Answer:
5127 x 8 = 41,016.
Unknown numbers = 7 and 410
Explanation:
5,127 x 8 = (5000 + 100 + 20 + 7) x 8 = (5000 x 8) + (100 x 8) + (20 x 8) + (7 x 8) = 40000 + 800 + 160 + 56 = 41,016
Question 10.
8, 5 6
× 7
———
60,03
Type below:
__________
Answer:
8,576 x 7 = 60,032
Explanation:
8,576 x 7 = (8000 + 500 + 70 + 6) x 7 = (8000 x 7) + (500 x 7) + (70 x 7) + (6 x 7) = 56000 + 3500 + 490 + 42 = 60,032
Practice: Copy and Solve Estimate. Then find the product.
Question 11.
116 × 3 = _______
Estimate: _______
Answer:
Estimate: 300
116 × 3 = 348
Explanation:
Estimate: 116 is close to 100;
100 x 3 = 300
116 x 3
6 x 3 =18; add ones and regroup tens
3 x 1 = 3; 3 + 1 = 4
3 x 1 = 3
So, 348 is the product
Question 12.
338 × 4 = _______
Estimate: _______
Answer:
338 × 4 = 1,352
Estimate: 1,200
Explanation:
Estimate: 338 is close to 300;
300 x 4 = 1,200
338 × 4
8 x 4 =32; add ones and regroup tens
3 x 4 = 12; 12 + 3 = 15; add tens and regroup hundreds
3 x 4 = 12; 12 + 1 = 13
So, 1352 is the product
Question 13.
6 × 219 = _______
Estimate: _______
Answer:
6 × 219 = 1,314
Estimate: 1200
Explanation:
Estimate: 219 is close to 200
200 x 6 = 1200
6 × 219
6 x 9 = 54; add ones and regroup tens
6 x 1 = 6; 6 + 5 = 11; add tens and regroup hundreds
6 x 2 = 12; 12 + 1 = 13
So, 1,314
Question 14.
7 × 456 = _______
Estimate: _______
Answer:
7 × 456 = 3192
Estimate: 3500
Explanation:
Estimate: 456 is close to 500
500 x 7 = 3500
7 x 456
7 x 6 = 42; add ones and regroup tens
7 x 5 = 35; 35 + 4 = 39; add tens and regroup hundreds
7 x 4 = 28; 28 + 3 = 31
So, 3192
Question 15.
5 × 1,012 = _______
Estimate: _______
Answer:
5 × 1,012 = 5,060
Estimate: 5,000
Explanation:
Estimate: 1,012 is close to 1,000
1,000 x 5 = 5,000
5 × 1,012
5 x 2 = 10; add ones and regroup tens
5 x 1 = 5; 5 + 1 = 6; add tens and regroup hundreds
5 x 0 = 0
5 x 1 = 5
So, 5,060
Question 16.
2,921 × 3 = _______
Estimate: _______
Answer:
2,921 × 3 = 8,763
Estimate: 9,000
Explanation:
Estimate: 2,921 is close to 3,000
3,000 x 3 = 9,000
2,921 × 3
3 x 1 = 3;
3 x 2 = 6;
3 x 9 = 27; add hundreds and regroup thousands
3 x 2 = 6; 6 + 2 = 8
So, 8,763
Question 18.
9 × 3,033 = _______
Estimate: _______
Answer:
Explanation:
Estimate: 3,033 is close to 3,000
3,000 x 9 = 27,000
9 × 3,033
9 x 3 = 27; add ones and regroup tens
9 x 3 = 27; 27 + = 11; add tens and regroup hundreds
6 x 2 = 12; 12 + 1 = 13
So, 1,314
Multiply by 1-digit numbers – Problem Solving – Page No. 30
What’s the Error?
Question 19.
The Plattsville Glee Club is sending 8 of its members to a singing contest in Cincinnati, Ohio. The cost will be $588 per person. How much will it cost for the entire group of 8 students to attend? Both Brian and Jermaine solve the problem. Brian says the answer is $40,074. Jermaine’s answer is $4,604.
Estimate the cost. A reasonable estimate is _
$ ______
Answer:
$4,800
Explanation:
The Plattsville Glee Club is sending 8 of its members to a singing contest in Cincinnati, Ohio. The cost will be $588 per person.
So, for entire group 8 x $588 = $4,704
Jermaine’s answer is correct. Because the $4,604 is close to $4,704
588 is close to 600. So, 600 x 8 = $4,800
Question 19.
Although Jermaine’s answer seems reasonable, neither Brian nor Jermaine solved the problem correctly. Find the errors in Brian’s and Jermaine’s work.
Then, solve the problem correctly.
What error did Brian make? Explain.
Type below:
__________
Answer:
When Brian multiplied the tens, he wrote the total number of tens in the product instead of regrouping, so the place values of his product are incorrect.
Question 19.
What error did Jermaine make? Explain.
Type below:
__________
Answer:
Jermaine regrouped the wrong amount of hundreds. He regrouped the tens as 6 hundred instead of 7 hundred.
$588 x 8 = $4,704
Question 19.
How could you predict that Jermaine’s answer might be incorrect using your estimate?
Type below:
__________
Answer:
I used 600 × 8 to estimate the product; 588 is 12 less than 600. Since 12 × 8 = 96, and 4,604 is almost 200 less than the estimate of 4,800, the answer is probably too low.
Multiply by 2-digit numbers – Share and Show – Page No. 33
Complete to find the product
Question 1.
Type below:
__________
Answer:
2,752
Explanation:
64 x 3 = 192
64 x 40 = 2,560
2,560 + 192 = 2,752
Question 2.
Type below:
__________
Answer:
21,698
Explanation:
571 x 8 = 4,568
571 x 30 = 17,130
17,130 + 4,568 = 21,698
Estimate. Then find the product.
Question 3.
Estimate:____
2 4
× 1 5
———-
Estimate: ________
Product: ________
Answer:
Estimate: 300
Product: 360
Explanation:
2 4 x 15
Estimate: 20 x 15 = 300
24 x 5 = 120
24 x 10 = 240
Product:: 240 + 120 = 360
On Your Own
Estimate. Then find the product.
Question 6.
Estimate:____
2 8
× 2 2
———-
Estimate: ________
Product: ________
Answer:
Estimate: 600
Product: 616
Explanation:
28 x 22
Estimate: 30 x 20 = 600
28 x 2 = 56
28 x 20 = 560
Product:: 56 + 560 = 616
Question 7.
Estimate:____
9 3
× 7 6
———-
Estimate: ________
Product: ________
Answer:
Estimate: 7200
Product: 7,068
Explanation:
93 x 76
Estimate: 90 x 80 = 7200
93 x 6 = 558
93 x 70 = 6,510
Product:: 558 + 6,510 = 7,068
Question 8.
Estimate:____
2 9 5
× 5 1
———-
Estimate: ________
Product: ________
Answer:
Estimate: 15,000
Product: 15,045
Explanation:
295 x 51
Estimate: 300 x 50 = 15,000
295 x 1 = 295
295 x 50 = 14,750
Product:: 295 + 14,750 = 15,045
Practice: Copy and Solve Estimate. Then find the product.
Question 9.
Estimate: ________
54 × 31 = ________
Answer:
Estimate: 1,500
Product: 1,674
Explanation:
54 x 31
Estimate: 50 x 30 = 1,500
54 x 1 = 54
54 x 30 = 1,620
Product:: 54 + 1,620 = 1,674
Question 10.
Estimate: ________
42 × 26 = ________
Answer:
Estimate: 1,200
Product: 1,092
Explanation:
42 x 26
Estimate: 40 x 30 = 1,200
42 x 6 = 252
42 x 20 = 840
Product:: 252 + 840 = 1,092
Question 11.
Estimate: ________
38 × 64 = ________
Answer:
Estimate: 2,400
Product: 2,432
Explanation:
38 × 64
Estimate: 40 x 60 = 2,400
38 x 4 = 152
38 x 60 = 2,280
Product:: 152 + 2,280 = 2,432
Question 12.
Estimate: ________
63 × 16 = ________
Answer:
Estimate: 1,200
Product: 1,008
Explanation:
63 x 16
Estimate: 60 x 20 = 1,200
63 x 6 = 378
63 x 10 = 630
Product:: 378 + 630 = 1,008
Question 13.
Estimate: ________
204 × 41 = ________
Answer:
Estimate: 8,000
Product: 8,364
Explanation:
204 × 41
Estimate: 200 x 40 = 8,000
204 x 1 = 204
204 x 40 = 8,160
Product:: 204 + 8,160 = 8,364
Question 14.
Estimate: ________
534 × 25 = ________
Answer:
Estimate: 15,000
Product: 13,350
Explanation:
534 x 25
Estimate: 500 x 30 = 15,000
534 x 5 = 2,670
534 x 20 = 10,680
Product:: 2,670 + 10,680 = 13,350
Question 15.
Estimate: ________
722 × 39 = ________
Answer:
Estimate: 28,000
Product: 28,158
Explanation:
722 × 39
Estimate: 700 x 40 = 28,000
722 x 9 = 6,498
722 x 30 = 21,660
Product:: 6,498 + 21,660 = 28,158
Question 16.
Estimate: ________
957 × 43 = ________
Answer:
Estimate: 40,000
Product: 44,022
Explanation:
957 × 43
Estimate: 1,000 x 40 = 40,000
957 x 3 = 2,871
957 x 40 = 41,151
Product:: 2,871 + 41,151 = 44,022
Multiply by 2-digit numbers – Problem Solving – Page No. 34
Use the table for 17–20.
Question 17.
How much sleep does a jaguar get in 1 year?
_____ hours
Answer:
4,004 hours
Explanation:
52 weeks x 77 = 4,004 hours
Question 18.
In 1 year, how many more hours of sleep does a giant armadillo get than a platypus?
_____ hours
Answer:
1,508 hours
Explanation:
giant armadillo: 52 x 127 = 6,604
platypus: 52 x 98 = 5,096
6,604 – 5,096 = 1,508
Question 19.
Owl monkeys sleep during the day, waking about 15 minutes after sundown to find food. At midnight, they rest for an hour or two, then continue to feed until sunrise. They live about 27 years. How many hours of sleep does an owl monkey that lives 27 years get in its lifetime?
_____
Answer:
4927.5 days
Explanation:
Given that the time of Owl monkeys sleeps during the day walking about 15 minutes after sundown. Then, at midnight they rest for an hour or two then continue to feed until sunrise. Notice that the above description doesn’t say that they sleep in after sundown. They either eat or rest.
Day time is usually considered from 6 am to 6 pm which is total of 12 hours.
As per the given information, owl monkey sleeps in that period.
Given that owl, monkeys live for 27 years.
So the time for sleeping in their lifetime = 12 hours * 27 years
= (12/24 days) * 27 years
= (1/2 days) * 27 years
= (1/2 days) * (27*365 days)
= (1/2 days) * (9855 days)
= 4927.5 days
Hence final answer is 4927.5 days.
Question 20.
Three-toed sloths move very slowly, using as little energy as possible. They sleep, eat, and even give birth upside down. A baby sloth may cling to its mother for as much as 36 weeks after being born. How much of that time is the sloth asleep?
_____ hours
Answer:
3,636 hours
Explanation:
101 x 36 = 3,636
Question 21.
Test Prep A sloth’s maximum speed on the ground is 15 feet in 1 minute. Even though it would be unlikely for a sloth to stay in motion for more than a few moments, how far would a sloth travel in 45 minutes at that speed?
Options:
A. 60 feet
B. 270 feet
C. 675 feet
D. 6,750 feet
Answer:
C. 675 feet
Explanation:
sloth’s maximum speed on the ground is 15 feet in 1 minute. For 45 minutes, 45 x 15 = 675 feet
Relate Multiplication to Division – Share and Show – Page No. 37
Question 1.
Brad has 72 toy cars that he puts into 4 equal groups. How many cars does Brad have in each group? Use the array to show your answer.
4 × = 72 72 ÷ 4 =
4 × ________ = 72
72 ÷ 4 = ________
Answer:
Explanation:
Brad has 18 toy cars in each group.
Because 72÷4 =18
4 × 18 = 72
4 x (9 + 9) = (4 x 9) + (4 x 9)
Use multiplication and the Distributive Property to find the quotient.
Question 2.
108 ÷ 6 = _____
Answer:
18
Explanation:
108 ÷ 6
6 x 18 = 6 x (9 + 9) = (6 x 9) + (6 x 9) = 54 + 54 = 108
(36 + 72) ÷ 6 = (36 ÷ 6) + (72÷ 6) = 6 + 12 = 18
On Your Own
Use multiplication and the Distributive Property to find the quotient.
Question 5.
60 ÷ 4 = _____
Answer:
15
Explanation:
60 ÷ 4
(20 + 40) ÷ 4 = (20 ÷ 4) + (40 ÷ 4) = 5 + 10 = 15
4 x 15 = 4 x (7+ 8) = (4 x 7) + (4 x 8) = 28 + 32 = 60
Question 6.
144 ÷ 6 = _____
Answer:
24
Explanation:
144 ÷ 6
(72 + 72) ÷ 6 = (72 ÷ 6) + (72 ÷ 6) = 12 + 12 = 24
6 x 24 = 6 x ( 12 + 12) = (6 x 12) + (6 x 12) = 72 + 72 = 144
Question 7.
252 ÷ 9 = _____
Answer:
28
Explanation:
252 ÷ 9
(126 + 126) ÷ 9 = (126 ÷ 9) + (126 ÷ 9) = 14 + 14 = 28
6 x 28 = 6 x ( 14 + 14) = (6 x 14) + (6 x 14) = 126 + 126 = 252
Find each quotient. Then compare. Write <, > or =.
Question 8.
51 ÷ 3 _____ 68 ÷ 4
Answer:
51 ÷ 3 = 68 ÷ 4
Explanation:
51 ÷ 3 = 17
68 ÷ 4 = 17
17 = 17.
Question 9.
252 ÷ 6 _____ 135 ÷ 3
Answer:
252 ÷ 6 < 135 ÷ 3
Explanation:
252 ÷ 6 = 42
135 ÷ 3 = 45
42 < 45
Question 10.
110 ÷ 5 _____ 133 ÷ 7
Answer:
110 ÷ 5 > 133 ÷ 7
Explanation:
110 ÷ 5 = 22
133 ÷ 7 = 19
22 > 19
Relate Multiplication to Division – Problem Solving – Page No. 38
Use the table to solve 11–13.
Question 11.
A group of 6 friends share a bag of the 45-millimeter bouncy balls equally among them. How many does each friend get?
____ balls
Answer:
7 balls
Explanation:
A group of 6 friends shares a bag of the 45-millimeter bouncy balls equally among them.
45/6 = 7 balls and 3 balls remained
Question 12.
Mr. Henderson has 2 bouncy-ball vending machines. He buys one bag of the 27-millimeter balls and one bag of the 40-millimeter balls. He puts an equal number of each in the 2 machines. How many bouncy balls does he put in each machine?
________ balls of the 27-millimeter .
________ balls of the 40-millimeter .
________ total balls
Answer:
51 balls of the 27-millimeter
29 balls of the 40-millimeter
80 total balls
Explanation:
There’s 51 27 mm, 29 40 mm
Question 13.
Lindsey buys a bag of each size of bouncy ball. She wants to put the same number of each size of bouncy ball into 5 party-favor bags. How many of each size of bouncy ball will she put in a bag?
________ balls of the 27-millimeter
________ balls of the 40-millimeter
________ balls of the 45-millimeter
Answer:
34 balls of the 27-millimeter
12 balls of the 40-millimeter
34 balls of the 45-millimeter
Explanation:
There’s 34 27 mm, 12 40 mm, and 34 45 mm bouncy balls
Question 15.
Test Prep Which of the following can be used to find 150 ÷ 6?
Options:
A. (6 × 20) + (6 × 5)
B. (6 × 10) + (6 × 5)
C. (2 × 75) + (2 × 3)
D. (6 × 15) + (6 × 5)
Answer:
A. (6 × 20) + (6 × 5)
Explanation:
150 ÷ 6 = 25
25 x 6 = 150
6 x 25 = 6 x (20 + 5) = (6 × 20) + (6 × 5)
Problem Solving Multiplication and Division – Share and Show – Page No. 41
Question 1.
To make concrete mix, Monica pours 34 pounds of cement, 68 pounds of sand, 14 pounds of small pebbles, and 19 pounds of large pebbles into a large wheelbarrow. If she pours the mixture into 9 equalsize bags, how much will each bag weigh?
First, find the total weight of the mixture.
____ pounds
Answer:
135 pounds
Explanation:
34 + 68 + 14 + 19 = 135
Question 1.
Then, divide the total by the number of bags. Break the total into two simpler numbers to make the division easier, if necessary.
Finally, find the quotient and solve the problem.
So, each bag will weigh _ pounds.
____ pounds
Answer:
15 pounds
Explanation:
now, calculate 135/9 = 15 pounds.
Question 2.
What if Monica pours the mixture into 5 equal-size bags? How much will each bag weigh?
____ pounds
Answer:
27 pounds
Explanation:
135/5 = 27
Question 3.
Taylor is building doghouses to sell. Each doghouse requires 3 full sheets of plywood which Taylor cuts into new shapes. The plywood is shipped in bundles of 14 full sheets. How many doghouses can Taylor make from 12 bundles of plywood?
____
Answer:
56 doghouses
Explanation:
Taylor is building doghouses to sell. Each doghouse requires 3 full sheets of plywood which Taylor cuts into new shapes. The plywood is shipped in bundles of 14 full sheets.
(12 x 14)/3 = 168/3 = 56 doghouses
Question 4.
Eileen is planting a garden. She has seeds for 60 tomato plants, 55 sweet corn plants, and 21 cucumber plants. She plants them in 8 rows, with the same number of plants in each row. How many seeds are planted in each row?
____ seeds / row
Answer:
17 seeds
Explanation:
Eileen is planting a garden. She has seeds for 60 tomato plants, 55 sweet corn plants, and 21 cucumber plants. She plants them in 8 rows, with the same number of plants in each row.
60 + 55 + 21 = 136
136/8 = 17
Problem Solving Multiplication and Division – On Your Own – Page No. 42
Question 5.
Starting on day 1 with 1 jumping jack, Keith doubles the number of jumping jacks he does every day. How many jumping jacks will Keith do on day 10?
____ jumping jack
Answer:
512 jumping jacks
Explanation:
She doubled the number so you’re supposed to multiply by 2.
On day 1, 1 jumping pack;
On day 2, 2 jumping packs;
On day 3, 2 x 2 = 4 jumping packs;
On day 4, 2 x 2 x 2 = 8 jumping packs;
On day 5, 2 x 2 x 2 x 2 = 16 jumping packs;
On day 6, 2 x 2 x 2 x 2 x 2 = 32 jumping packs;
On day 7, 2 x 2 x 2 x 2 x 2 x 2 = 64 jumping packs;
On day 8, 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128 jumping packs;
On day 9, 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 jumping packs;
On day 10, 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 512 jumping packs;
512 jumping jacks
Question 6.
Starting in the blue square, in how many different ways can you draw a line that passes through every square without picking up your pencil or crossing a line you’ve already drawn? Show the ways.
____ ways
Answer:
8 ways
Explanation:
8 ways
Question 7.
On April 11, Millie bought a lawn mower with a 50-day guarantee. If the guarantee begins on the date of purchase, what is the first day on which the mower will no longer be guaranteed?
__________
Answer:
May 31
Explanation:
The guarantee begins on April 11. April has 30 days. So, we have 20 days of the guarantee in April.
May has 31 days. So, we have 30 days of the guarantee in May.
Therefore, the last day of the guarantee is May 31.
Question 10.
Test Prep Dee has 112 minutes of recording time. How many 4-minute songs can she record?
Options:
A. 28
B. 27
C. 18
D. 17
Answer:
A. 28
Explanation:
Dee has 112 minutes of recording time. 112/4 = 28
Numerical Expressions – Share and Show – Page No. 45
Circle the expression that matches the words.
Question 1.
Teri had 18 worms. She gave 4 worms to Susie and 3 worms to Jamie.
(18 – 4) + 3 18 – (4 + 3)
__________
Answer:
18 – (4 + 3)
Explanation:
Teri had 18 worms. She gave 4 worms.
18 – 4 = 14.
3 worms to Jamie
14 – 3 = 11.
(18 – 4) + 3 = 14 + 3 = 17 not equal to 11;
18 – (4 + 3) = 18 – 7 = 11 = 11
Question 2.
Rick had $8. He then worked 4 hours for $5 each hour.
$8 + (4 × $5) ($8 + 4) × $5
__________
Answer:
$8 + (4 × $5)
Explanation:
Rick had $8. He then worked 4 hours for $5 each hour = 4 x $5 = $20;
$20 +$8 =$28.
$8 + (4 × $5) = 8 + 20 = $28 = $28.
Write an expression to match the words.
Question 4.
Lynda has 27 fewer fish than Jack. Jack has 80 fish.
Type below:
__________
Answer:
80 – 27 = 53
Explanation:
Lynda has 27 fewer fish than Jack. Jack has 80 fish. 80 – 27 = 53
Write words to match the expression.
Question 5.
34 – 17
Type below:
__________
Answer:
Anna has 17 fewer apples than Jack. Jack has 34 apples.
Explanation:
34 – 17 = 17.
Anna has 17 fewer apples than Jack. Jack has 34 apples.
Question 6.
6 × (12 – 4)
Type below:
__________
Answer:
Teri had 12 worms. She gave 4 worms to Susie. She sell remaining worms for $6 each.
Explanation:
Teri had 12 worms. She gave 4 worms to Susie. She sell remaining worms for $6 each.
On Your Own
Write an expression to match the words.
Question 7.
José shared 12 party favors equally among 6 friends.
Type below:
__________
Answer:
12/6 = 2
Explanation:
José shared 12 party favors equally among 6 friends. 12/6 = 2
Question 8.
Braden has 14 baseball cards. He finds 5 more baseball cards.
Type below:
__________
Answer:
14 + 5 = 19
Explanation:
Braden has 14 baseball cards. He finds 5 more baseball cards. 14 + 5 = 19
Question 9.
Isabelle bought 12 bottles of water at $2 each.
Type below:
__________
Answer:
12 x $2 = $24
Explanation:
Isabelle bought 12 bottles of water at $2 each. 12 x $2 = $24
Question 10.
Monique had $20. She spent $5 on lunch and $10 at the bookstore.
Type below:
__________
Answer:
20 – (5 + 10)
Explanation:
Monique had $20. She spent $5 on lunch and $10 at the bookstore. 20 – (5 + 10)
Write words to match the expression.
Question 11.
36 ÷ 9
Type below:
__________
Answer:
Anna shared 36 apples to 9 friends.
Question 12.
35 – (16 + 11)
Type below:
__________
Answer:
Monique had 35 balls. She gave 16 to her one frined and 11 to other friend.
Draw a line to match the expression with the words.
Question 13.
Fred catches 25 fish. Then he
releases 10 fish and catches 8 more. • •3 × (15 – 6)
Nick has 25 pens. He gives 10 pens to
one friend and 8 pens to another friend. • •15 – 6
Jan catches 15 fish and lets 6 fish go. • •25 – (10 + 8)
Libby catches 15 fish and lets 6 fish go
for three days in a row. • •(25 – 10) + 8
Type below:
__________
Answer:
Fred catches 25 fish. Then he releases 10 fish and catches 8 more = (25 – 10) + 8
Nick has 25 pens. He gives 10 pens to one friend and 8 pens to another friend = 25 – (10 + 8)
Jan catches 15 fish and lets 6 fish go = 15 – 6
Libby catches 15 fish and lets 6 fish go for three days in a row = 3 × (15 – 6)
Numerical Expressions – Problem Solving – Page No. 46
Use the rule and the table for 14.
Question 14.
Write a numerical expression to represent the total number of lemon tetras that could be in a 20-gallon aquarium.
_____ lemon tetras
Answer:
2 lemon tetras
Explanation:
From the given data, increase each inch of lenth, 1 gallon of water increases.
2 + 3 + 5 + 3 + 5 = 18 inches. So, 18 gallon of water available in aquarium. Add 1 lemon tetra to get the 20 gallon of water. So, in total there are 2 lemon tetra available.
Question 15.
Write a word problem for an expression that is three times as great as (15 + 7). Then write the expression.
Type below:
__________
Answer:
3 x (15 + 7)
Explanation:
Given that that is three times as great as (15 + 7)
Question 16.
What’s the Question? Lu has 3 swordtails in her aquarium. She buys 2 more swordtails.
Type below:
__________
Answer:
3 + 2 = 5
Explanation:
Lu has 3 swordtails in her aquarium. She buys 2 more swordtails. So, 3 + 2 = 5 swordtails
Question 17.
Tammy gives 45 stamps to her 9 friends. She shares them equally among her friends. Write an expression to match the words. How many stamps does each friend get?
_____ stamps
Answer:
45/9 = 5 stamps
Explanation:
Tammy gives 45 stamps to her 9 friends. 45/9 = 5.
Question 18.
Test Prep Josh has 3 fish in each of 5 buckets. Then he releases 4 fish. Which expression matches the words?
Options:
a. (3 × 4) – 5
b. (5 × 4) – 3
c. (5 × 3) – 4
d. (5 – 3) × 4
Answer:
c. (5 × 3) – 4
Explanation:
Josh has 3 fish in each of 5 buckets. 3 x 5.
Then he releases 4 fish. (3 x 5) – 4
Evaluate Numerical Expressions – Share and Show – Page No. 49
Evaluate the numerical expression.
Question 1.
10 + 36 ÷ 9
_____
Answer:
14
Explanation:
10 + 36 ÷ 9 = 10 + (36 ÷ 9) = 10 + 4 = 14
Question 2.
10 + (25 – 10) ÷ 5
_____
Answer:
13
Explanation:
10 + (25 – 10) ÷ 5 = 10 + 15 ÷ 5 = 10 + (15 ÷ 5) = 10 + 3 = 13
Question 3.
9 – (3 × 2) + 8
_____
Answer:
11
Explanation:
9 – (3 × 2) + 8 = 9 – 6 + 8 = 3 + 8 = 11
On Your Own
Evaluate the numerical expression.
Question 6.
36 – (8 + 5)
_____
Answer:
23
Explanation:
36 – (8 + 5) = 36 – 13 = 23
Question 7.
125 – (68 + 7)
_____
Answer:
50
Explanation:
125 – (68 + 7) = 125 – 75 = 50
Question 8.
(4 × 6) – 12
_____
Answer:
12
Explanation:
(4 × 6) – 12 = 24 – 12 = 12
Question 9.
3 × (22 – 2)
_____
Answer:
60
Explanation:
3 × (22 – 2) = 3 x 20 = 60
Question 10.
23 + (16 – 7)
_____
Answer:
32
Explanation:
23 + (16 – 7) = 23 + 9 = 32
Question 11.
(25 – 4) ÷ 3
_____
Answer:
7
Explanation:
(25 – 4) ÷ 3 = 21 ÷ 3 = 7
Rewrite the expression with parentheses to equal the given value.
Question 12.
100 – 30 ÷ 5
value: 14
Type below:
__________
Answer:
(100 – 30) ÷ 5 = 14
Explanation:
100 – 30 ÷ 5 = (100 – 30) ÷ 5 = 70 ÷ 5 = 14
Question 13.
12 + 17 – 3 × 2
value: 23
Type below:
__________
Answer:
23
Explanation:
(12 + 17) – (3 × 2) = 29 – 6 = 23
Question 14.
9 + 5 ÷ 5 + 2
value: 12
Type below:
__________
Answer:
12
Explanation:
9 + (5 ÷ 5) + 2 = 9 + 1 + 2 = 12
Evaluate Numerical Expressions – UNLOCK the Problem – Page No. 50
Question 15.
A movie theater has 4 groups of seats. The largest group of seats, in the middle, has 20 rows, with 20 seats in each row. There are 2 smaller groups of seats on the sides, each with 20 rows and 6 seats in each row. A group of seats in the back has 5 rows, with 30 seats in each row. How many seats are in the movie theater?
a. What do you need to know?
Type below:
__________
Answer:
We have to know the number of seats in each row to calculate the total number of seats.
Question 15.
b. What operation can you use to find the number of seats in the back group of seats? Write the expression.
Type below:
__________
Answer:
A group of seats in the back has 5 rows with 30 seats in each row. So, to calculate the number of seats, we can use multiplication.
Question 15.
c. What operation can you use to find the number of seats in both groups of side seats? Write the expression.
Type below:
__________
Answer:
2 x (20 x 6) = 2 x 120 = 240
Question 15.
d. What operation can you use to find the number of seats in the middle group? Write the expression.
Type below:
__________
Answer:
20 x 20 = (2 x 2) x (10 x 10) = 4 x 100 = 400
Question 15.
e. Write an expression to represent the total number of seats in the theater.
Type below:
__________
Answer:
(20 x 20) + (2 x 20 x 6) + (5 x 30)
Question 15.
f. How many seats are in the theater? Show the steps you use to solve the problem.
_____ seats
Answer:
(20 x 20) + (2 x 20 x 6) + (5 x 30) = 400 + 240 + 150 = 640 + 150 = 790
Question 16.
Test Prep In the wild, an adult giant panda eats about 30 pounds of food each day. Which expression shows how many pounds of food 6 pandas eat in 3 days?
Options:
a. 3 + (30 × 6)
b. 3 × (30 × 6)
c. (30 × 6) ÷ 3
d. (30 × 6) – 3
Answer:
b. 3 × (30 × 6)
Explanation:
1 panda eats 30 pounds of food each day.
for 3 days, 3 x 30 = 90
1 panda eats 90 pounds of food in 3 days.
6 pandas can eat 90 x 6 = 540 pounds.
3 + (180) = 183 not equal to 540 pounds.
3 x (30 x 6) = 3 x (180) = 540
Question 17.
Test Prep Which expression has a value of 6?
Options:
a. (6 ÷ 3) × 4 + 8
b. 27 – 9 ÷ 3 × ( 4 + 1)
c. (18 + 12) × 6 – 4
d. 71 – 5 × (9 + 4)
Answer:
d. 71 – 5 × (9 + 4)
Explanation:
(6 ÷ 3) × 4 + 8 = 2 x 4 + 8 = 8 + 8 = 16
27 – 9 ÷ 3 × ( 4 + 1) = 27 – (9 ÷ 3) × 5 = 27 – 3 x 5 = 27 – 15 = 12
(18 + 12) × 6 – 4 = 180 – 4 = 176
71 – 5 × (9 + 4) = 71 – (5 x 13) = 71 – 65 = 6
Grouping Symbols – Share and Show – Page No. 53
Evaluate the numerical expression.
Question 1.
12 + [(15 – 5) + (9 – 3)]
12 + [10 + ____]
12 +____
____
Answer:
12 + [(15 – 5) + (9 – 3)]
12 + [10 + 6]
12 + 16
28
On Your Own
Evaluate the numerical expression.
Question 4.
4 + [(16 – 4) + (12 – 9)]
____
Answer:
4 + [(16 – 4) + (12 – 9)]
4 + [12 + 3]
4 + 15 = 19
Question 5.
24 – [(10 – 7) + (16 – 9)]
____
Answer:
24 – [(10 – 7) + (16 – 9)]
24 – [3 + 7] = 24 – 10 = 14
Question 6.
16 ÷ [(13 + 7) – (12 + 4)]
____
Answer:
16 ÷ [(13 + 7) – (12 + 4)]
16 ÷ [20 – 16]
16 ÷ 4 = 4
Question 7.
5 × [(7 – 2) + (10 – 8)]
____
Answer:
5 × [(7 – 2) + (10 – 8)]
5 x [5 + 2]
5 x 7 = 35
Question 8.
[(17 + 8) + (29 – 12)] ÷ 6
____
Answer:
[(17 + 8) + (29 – 12)] ÷ 6
[25 + 17] ÷ 6
42 ÷ 6 = 7
Question 9.
[(6 × 7) + (3 × 4)] – 28
____
Answer:
[(6 × 7) + (3 × 4)] – 28
[42 + 12] – 28
54 – 28 = 26
Grouping Symbols – UNLOCK the Problem – Page No. 54
Question 12.
Dan has a flower shop. Each day he displays 24 roses. He gives away 10 and sells the rest. Each day he displays 36 carnations. He gives away 12 and sells the
rest. What expression can you use to find out how many roses and carnations Dan sells in a week?
a. What information are you given?
Type below:
__________
Answer:
Each day, Dan displays 24 roses (gives away 10 and sells the rest), and he displays 36 carnations (gives away 12 and selles the rest).
Question 12.
b. What are you being asked to do?
Type below:
__________
Answer:
We have to find out how many roses and carnations Dan sells in a week.
Question 12.
c. What expression shows how many roses Dan sells in one day?
Type below:
__________
Answer:
24 – 10 = 14 roses
Question 12.
d. What expression shows how many carnations Dan sells in one day?
Type below:
__________
Answer:
36 – 12 = 24 carnation
Question 12.
e. Write an expression to represent the total number of roses and carnations Dan sells in one day.
Type below:
__________
Answer:
(24 – 10) + (36 – 12) = 14 + 24 = 38 roses and carnations
Question 12.
f. Write the expression that shows how many roses and carnations Dan sells in a week.
Type below:
__________
Answer:
7 x ((24 – 10) + (36 – 12)) = 7 x (14 + 24) = 7 x 38 = 266 roses and carnations
Question 13.
Evaluate the expression to find out how many roses and carnations Dan sells in a week.
____ flowers
Answer:
7 x ((24 – 10) + (36 – 12))
7 x (14 + 24)
7 x 38 = 266 roses and carnations
Explanation:
Question 14.
Test Prep Which expression has a value of 4?
Options:
a. [(4 × 5) + (9 + 7)] + 9
b. [(4 × 5) + (9 + 7)] ÷ 9
c. [(4 × 5) – (9 + 7)] × 9
d. [(4 + 5) + (9 + 7)] – 9
Answer:
b. [(4 × 5) + (9 + 7)] ÷ 9
Explanation:
[(4 × 5) + (9 + 7)] + 9 = [20 + 16] + 9 = 36 + 9 = 45
[(4 × 5) + (9 + 7)] ÷ 9 = [20 + 16] ÷ 9 = 36 ÷ 9 = 4
Chapter Review/Test – Vocabulary – Page No. 55
Question 1.
The ____ states that multiplying a sum by a number is the same as multiplying each addend in the sum by the number and then adding the products.
__________
Answer:
Distributive Property
Concepts and Skills
Complete the sentence.
Question 3.
50 is \(\frac{1}{10}\) of _____
Answer:
500
Explanation:
Let the unknown number is S.
50 = \(\frac{1}{10}\) S
S = 50 X 10 = 500
Complete the equation, and tell which property you used.
Question 5.
45 + 16 =__ + 45
Type below:
Type below:
________
Answer:
45 + 16 = 16 + 45; Commutative Property of Addition
Explanation:
45 + 16 = 16 + 45; Commutative Property of Addition
Find the value.
Question 6.
102 = _____
Answer:
100
Explanation:
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
Estimate. Then find the product.
Question 9.
Estimate:
5 7 9
× 6
———-
Estimate: _____ Product: _____
Answer:
Estimate: 3,600
Product: 3,474
Explanation:
Estimate: 579 is close to 600;
600 x 6 = 3,600
579 x 6
6 x 9 =54; add ones and regroup tens
6 x 7 = 42; 42 + 5 = 47; add tens and regroup hundreds
6 x 5 = 30; 30 + 4 = 34
So, 3,474 is the product
Question 10.
Estimate:
7,316
× 6
———-
Estimate: _____ Product: _____
Answer:
Estimate: 42,000
Product: 43,986
Explanation:
Estimate: 7,316 is close to 7,000;
7,000 x 6 = 42,000
7,316 x 6
6 x 6 = 36; add ones and regroup tens
6 x 1 = 6; 6 + 3 = 18; add tens and regroup hundreds
6 x 3 = 18; 18 + 1 = 19; add hundreds and regroup thousads
6 x 7 = 42; 42 + 1 = 43
So, 43,986 is the product
Question 11.
Estimate:
4 3 6
× 3 2
———-
Estimate: _____ Product: _____
Answer:
Estimate: 12,000
Product: 13,952
Explanation:
Estimate: 436 is close to 400; 32 is close to 30
400 x 30 = 12,000
436 x 32;
436 x 2 = 872
436 x 30 = 13,080
13,080 + 872 = 13,952
Use multiplication and the Distributive Property to find the quotient.
Evaluate the numerical expression.
Question 15.
42 − (9 + 6) = _____
Answer:
42 − (9 + 6)
42 – 15
27
Question 16.
15 + (22 − 4) ÷ 6 = _____
Answer:
15 + (22 − 4) ÷ 6
15 + (18 ÷ 6)
15 + 3
18
Question 17.
6 × [(5 × 7) − (7 + 8)] = _____
Answer:
6 × [(5 × 7) − (7 + 8)]
6 x [35 – 15]
6 x [20]
120
Chapter Review/Test – Page No. 56
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Question 18.
Erica’s high score on her new video game is 30,000 points. Maria’s high score is \(\frac{1}{10}\) of Erica’s. How many points did Maria score?
Options:
A. 30
B. 300
C. 3,000
D. 30,000
Answer:
C. 3,000
Explanation:
Erica’s high score on her new video game is 30,000 points. Maria’s high score is \(\frac{1}{10}\) of Erica’s.
30,000 x \(\frac{1}{10}\) = 3,000
Question 19.
Rich makes $35 a week mowing lawns in his neighborhood. Which expression can be used to show how much money he makes in 8 weeks?
Options:
A. (8 × 30) + (8 × 5)
B. (8 × 30) + (8 × 5)
C. (8 + 30) × (8 + 5)
D. (8 × 30) × (8 × 5)
Answer:
B. (8 × 30) + (8 × 5)
Explanation:
Rich makes $35 a week mowing lawns in his neighborhood.
8 x $35 = 8 x (30 + 5) = (8 x 30) + (8 x 5)
Question 20.
Mr. Rodriguez bought a supply of 20 reams of printer paper. Each ream contains 500 sheets of paper. How many sheets of printer paper are there?
Options:
A. 1,000
B. 5,000
C. 10,000
D. 100,000
Answer:
C. 10,000
Explanation:
Mr. Rodriguez bought a supply of 20 reams of printer paper. Each ream contains 500 sheets of paper.
500 x 20 = 10,000
Chapter Review/Test – Page No. 57
Fill in the bubble completely to show your answer.
Question 22.
Megan used the following expression to find the quotient of a division problem.
(4 × 12) + (4 × 6)
What was the division problem and the quotient?
Options:
A. 24 ÷ 4 = 6
B. 48 ÷ 4 = 12
C. 64 ÷ 4 = 16
D. 72 ÷ 4 = 18
Answer:
D. 72 ÷ 4 = 18
Explanation:
Megan used (4 × 12) + (4 × 6)
4 x (12 + 6)
4 x 18 = 72
72 ÷ 4 = 18
Question 23.
It is 1,325 feet from Kinsey’s house to her school. Kinsey walks to school each morning and gets a ride home each afternoon. How many feet does Kinsey walk to school in 5 days?
Options:
A. 6,725 feet
B. 6,625 feet
C. 6,525 feet
D. 5,625 feet
Answer:
B. 6,625 feet
Explanation:
It is 1,325 feet from Kinsey’s house to her school. Kinsey walks to school each morning and gets a ride home each afternoon.
1,325 feet x 5 = 6,625 feet
Question 24.
An adult elephant eats about 300 pounds of food each day. Which expression shows about how many pounds of food a herd of 12 elephants eats in 5 days?
Options:
A. 5 + (300 × 12)
B. 5 × (300 × 12)
C. (300 × 12) ÷ 5
D. (300 × 12) − 5
Answer:
B. 5 × (300 × 12)
Explanation:
An adult elephant eats about 300 pounds of food each day.
(300 x 12)
In 5 days, 5 × (300 × 12)
Question 25.
Carla can type 265 characters a minute on her computer keyboard. At that rate, how many characters can she type in 15 minutes?
Options:
A. 2,975
B. 3,875
C. 3,905
D. 3,975
Answer:
D. 3,975
Explanation:
Carla can type 265 characters a minute on her computer keyboard.
In 15 minutes, 265 x 15 = 3,975
Chapter Review/Test – Page No. 58
Constructed Response
Question 26.
Donavan copied the problem below from the board. He missed one of the numbers needed to show his work. What number is missing in his work? Explain how you found the missing number
17 × 5 = ( ______ +7) × 5
= ( ______ × 5) + (7 × 5)
Answer:
Missing number is 10. Using the Distributive Property, the sum of the two number within the () has to be equal to the other factor 17.
10 + 7 = 17
17 × 5 = ( 10 +7) × 5
= ( 10 × 5) + (7 × 5)
Performance Task
Question 27.
Drew’s weekly allowance is $8.00. His friend Jan’s weekly allowance is $10. Drew spends $3 a week and Jan spends $4 a week.
A. Write two expressions to show how much money each person has at the end of the week. Use parentheses.
Drew has __ .
Jan has __ .
Type below:
__________
Answer:
Drew has ($8 – $3) .
Jan has ($10 – $4).
Question 27.
B. Drew and Jan decide that they want to put their money together to buy a video game. Write an expression that shows how much they can save each week. Explain.
Type below:
__________
Answer:
(8 – 3) + (10 – 4); Add the amount of money Drew and Jan have at the end of the week. This equals the amount they can save a week.
Question 27.
C. The video game Drew and Jan want to buy costs $55. Write an expression to show how many weeks it will take them to save enough to buy the video game. Use parentheses and brackets in your expression. Then evaluate the expression.
_____ weeks
Answer:
55 ÷ [(8 – 3) +(10 – 4)]
55 ÷ [5 + 6]
55 ÷ 11
5
It will take them 5 weeks to save the money from the game.
Conclusion:
You need not look everywhere to seek assistance regarding Go Math Grade 5 Ch 1. Simply access Go Math Grade 5 Answer Key Chapter 1 Place Value, Multiplication, and Expressions and know how to approach while solving different problems on the related concepts.