This handy Spectrum Math Grade 7 Answer Key Chapter 1 Pretest provides detailed answers for the workbook questions
Spectrum Math Grade 7 Chapter 1 Pretest Answers Key
Check What You Know
Adding and Subtracting Rational Numbers
Evaluate each expression.
Question 1.
a. opposite of 45 ______
Answer: -45
opposite of 45 is -45
-45 and 45 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.
b. opposite of -9 ______
Answer: 9
opposite of -9 is 9
-9 and 9 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.
c. opposite of -10 ______
Answer: 10
opposite of -10 is 10
-10 and 10 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.
Question 2.
a. opposite of 21 ______
Answer: -21
opposite of 21 is -21
-21 and 21 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.
b. opposite of 6 ______
Answer: -6
opposite of 6 is -6
-6 and 6 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.
c. opposite of -10 ______
Answer: 10
opposite of -10 is 10
-10 and 10 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.
Question 3.
a. opposite of 52 ______
Answer: -52
opposite of 52 is -52
-52 and 52 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.
b. opposite of -89 ______
Answer: 89
opposite of -89 is 89
-89 and 89 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.
c. opposite of 18 ______
Answer: -18
opposite of 18 is -18
-18 and 18 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.
Question 4.
a. |7| ______
Answer: 7
|7| = 7
-7 and 7 are absolute value because they are the same distance from zero on opposite sides of the number line.
The absolute value of a number is a number that is the same distance from zero on a number line. The distance is always a positive quantity (or zero). Absolute value is shown by vertical bars on each side of the number.
b. |-34| ______
Answer: 34
|-34| = 34
-34 and 34 are absolute value because they are the same distance from zero on opposite sides of the number line.
The absolute value of a number is a number that is the same distance from zero on a number line. The distance is always a positive quantity (or zero). Absolute value is shown by vertical bars on each side of the number.
c. |58| ______
Answer: 58
|58| = 58
-58 and 58 are absolute value because they are the same distance from zero on opposite sides of the number line.
The absolute value of a number is a number that is the same distance from zero on a number line. The distance is always a positive quantity (or zero). Absolute value is shown by vertical bars on each side of the number.
Question 5.
a. -|35| ______
Answer: -35
-|35| = -35
-35 and 35 are absolute value because they are the same distance from zero on opposite sides of the number line.
The absolute value of a number is a number that is the same distance from zero on a number line. The distance is always a positive quantity (or zero). Absolute value is shown by vertical bars on each side of the number.
b. -|-56| ______
Answer: -56
-|-56| = -56
-56 and 56 are absolute value because they are the same distance from zero on opposite sides of the number line.
The absolute value of a number is a number that is the same distance from zero on a number line. The distance is always a positive quantity (or zero). Absolute value is shown by vertical bars on each side of the number.
c. |-39| ______
Answer: 39
|-39| = 39
-39 and 39 are absolute value because they are the same distance from zero on opposite sides of the number line.
The absolute value of a number is a number that is the same distance from zero on a number line. The distance is always a positive quantity (or zero). Absolute value is shown by vertical bars on each side of the number.
Identify the property of addition described as commutative, associative, or identity.
Question 6.
The sum of any number and zero is the original number. ___________
Answer: identity property
The sum of any number and zero is the original number. = identity property
An identity in mathematics is a number, n, that results in the same number, n, when other numbers are added to it. The identity of the additive is always zero. This brings us to the identity property of addition, which simply states that when you add zero to any number, it equals the number itself.
Question 7.
When two numbers are added, the sum is the same regardless of the order of addends. ___________
Answer: commutative property
When two numbers are added, the sum is the same regardless of the order of addends = commutative property
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.
Question 8.
When three or more numbers are added, the sum is the same regardless of how the addends are grouped. _________
Answer: associative property
When three or more are grouped numbers are added, the sum is the same regardless of how the addends are grouped = associative property
The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.
Question 9.
a. 7 + (1 + 9) = (7 + 1) + 9
___________
Answer: associative property
7 + (1 + 9) = (7 + 1) + 9 = associative property
When three or more are grouped numbers are added, the sum is the same regardless of how the addends are grouped = associative property
The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.
b. 3 + 0 = 3
_________
Answer: identity property
3 + 0 = 3 = identity property
The sum of any number and zero is the original number. = identity property
An identity in mathematics is a number, n, that results in the same number, n, when other numbers are added to it. The identity of the additive is always zero. This brings us to the identity property of addition, which simply states that when you add zero to any number, it equals the number itself.
Question 10.
a. 9 + 5 = 5 + 9
_________
Answer: commutative property
9 + 5 = 5 + 9 = commutative property
When two numbers are added, the sum is the same regardless of the order of addends = commutative property
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.
b. 8 + 10 = 10 + 8
_________
Answer: commutative property
8 + 10 = 10 + 8 = commutative property
When two numbers are added, the sum is the same regardless of the order of addends = commutative property
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.
Question 11.
a. 6 + (-6) = 0
_________
Answer: commutative property
6 + (-6) = 0 = commutative property
When two numbers are added, the sum is the same regardless of the order of addends = commutative property
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.
b. (6 + 3) + 7 = 6 + (3 + 7)
____________
Answer: associative property
(6 + 3) + 7 = 6 + (3 + 7)= associative property
When three or more are grouped numbers are added, the sum is the same regardless of how the addends are grouped = associative property
The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.
Question 12.
a. 15 + 0 = 15
_____________
Answer: identity property
15 + 0 = 15 = identity property
The sum of any number and zero is the original number. = identity property
An identity in mathematics is a number, n, that results in the same number, n, when other numbers are added to it. The identity of the additive is always zero. This brings us to the identity property of addition, which simply states that when you add zero to any number, it equals the number itself.
b. 13 + 2 = 2 + 13
Answer: commutative property
13 + 2 = 2 + 13 = commutative property
When two numbers are added, the sum is the same regardless of the order of addends = commutative property
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.
Add or subtract. Write fractions in simplest form.
Question 13.
a.
Answer: 4\(\frac{11}{12}\)
2\(\frac{1}{4}\) + 2\(\frac{2}{3}\)
Partition the fractions and whole numbers to add them separately.
= (2 + 2) + \(\frac{1}{4}\) + \(\frac{2}{3}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 4 + [\(\frac{1}{4}\) x \(\frac{3}{3}\)] + [\(\frac{2}{3}\) x \(\frac{4}{4}\)]
= 4 + \(\frac{3}{12}\) + \(\frac{8}{12}\)
= 4 + \(\frac{3 + 8}{12}\)
After simplification,
= 4 + \(\frac{11}{12}\)
Therefore, the result is given by,
= 4\(\frac{11}{12}\)
b.
Answer: 5\(\frac{9}{14}\)
3\(\frac{1}{2}\) + 2\(\frac{1}{7}\)
Partition the fractions and whole numbers to add them separately.
= (3 + 2) + \(\frac{1}{2}\) + \(\frac{1}{7}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 5 + [\(\frac{1}{2}\) x \(\frac{7}{7}\)] + [\(\frac{1}{7}\) x \(\frac{2}{2}\)]
= 5 + \(\frac{7}{14}\) + \(\frac{2}{14}\)
= 5 + \(\frac{7 + 2}{14}\)
After simplification,
= 5 + \(\frac{9}{14}\)
Therefore, the result is given by,
= 5\(\frac{9}{14}\)
c.
Answer: 6\(\frac{19}{24}\)
2\(\frac{1}{8}\) + 4\(\frac{2}{3}\)
Partition the fractions and whole numbers to add them separately.
= (2 + 4) + \(\frac{1}{8}\) + \(\frac{2}{3}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 6 + [\(\frac{1}{8}\) x \(\frac{3}{3}\)] + [\(\frac{2}{3}\) x \(\frac{8}{8}\)]
= 6 + \(\frac{3}{24}\) + \(\frac{16}{24}\)
= 6 + \(\frac{3 + 16}{24}\)
After simplification,
= 6 + \(\frac{19}{24}\)
Therefore, the result is given by,
= 6\(\frac{19}{24}\)
d.
Answer: 3\(\frac{53}{35}\)
1\(\frac{5}{7}\) + 2\(\frac{4}{5}\)
Partition the fractions and whole numbers to add them separately.
= (1 + 2) + \(\frac{5}{7}\) + \(\frac{4}{5}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 3 + [\(\frac{5}{7}\) x \(\frac{5}{5}\)] + [\(\frac{4}{5}\) x \(\frac{7}{7}\)]
= 3 + \(\frac{25}{35}\) + \(\frac{28}{35}\)
= 3 + \(\frac{25 + 28}{35}\)
After simplification,
= 3 + \(\frac{53}{35}\)
Therefore, the result is given by,
= 3\(\frac{53}{35}\)
Question 14.
a.
Answer: 4\(\frac{1}{12}\)
6\(\frac{1}{3}\) – 2\(\frac{1}{4}\)
Partition the fractions and whole numbers to subtract them separately.
= (6 – 2) + \(\frac{1}{3}\) – \(\frac{1}{4}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 4 + [\(\frac{1}{3}\) x \(\frac{4}{4}\)] – [\(\frac{1}{4}\) x \(\frac{3}{3}\)]
= 4 + \(\frac{4}{12}\) – \(\frac{3}{12}\)
= 4 + \(\frac{4 – 3}{12}\)
After simplification,
=4 + \(\frac{1}{12}\)
Therefore, the result is given by,
= 4\(\frac{1}{12}\)
b.
Answer: \(\frac{1}{8}\)
\(\frac{3}{8}\) – \(\frac{1}{4}\)
Partition the fractions and whole numbers to subtract them separately.
= \(\frac{3}{8}\) – \(\frac{1}{4}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{3}{8}\) x \(\frac{4}{4}\)] – [\(\frac{1}{4}\) x \(\frac{8}{8}\)]
= \(\frac{12}{32}\) – \(\frac{8}{32}\)
= \(\frac{12 – 8}{32}\)
After simplification,
= \(\frac{4}{32}\)
Therefore, the result is given by,
= \(\frac{1}{8}\)
c.
Answer: 2\(\frac{1}{2}\)
5\(\frac{3}{10}\) – 2\(\frac{4}{5}\)
Partition the fractions and whole numbers to subtract them separately.
= (5 – 2) + \(\frac{3}{10}\) – \(\frac{4}{5}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 3 + [\(\frac{3}{10}\) x \(\frac{5}{5}\)] – [\(\frac{4}{5}\) x \(\frac{10}{10}\)]
= 3 + \(\frac{15}{50}\) – \(\frac{40}{50}\)
= 2 + \(\frac{65}{50}\) – \(\frac{40}{50}\)
= 2 + \(\frac{65 – 40}{50}\)
After simplification,
=2 + \(\frac{25}{50}\)
=2 + \(\frac{1}{2}\)
Therefore, the result is given by,
=2\(\frac{1}{2}\)
d.
Answer: 2\(\frac{3}{7}\)
3\(\frac{4}{7}\) – 1\(\frac{1}{2}\)
Partition the fractions and whole numbers to subtract them separately.
= (3 – 1) + \(\frac{4}{7}\) – \(\frac{1}{2}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 2 + [\(\frac{4}{7}\) x \(\frac{2}{2}\)] – [\(\frac{1}{2}\) x \(\frac{7}{7}\)]
= 2 + \(\frac{8}{14}\) – \(\frac{2}{14}\)
= 2 + \(\frac{8 – 2}{14}\)
After simplification,
=2 + \(\frac{6}{14}\)
=2 + \(\frac{3}{7}\)
Therefore, the result is given by,
= 2\(\frac{3}{7}\)
Question 15.
a.
-3 + 2 = _____
Answer: -1
-3 + 2 = – 3 – (-2) = -1
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.
b.
3 + (-2) = ____
Answer: 1
3 + (-2) = 3 – 2 = 1
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.
c.
7 + (-4) = _____
Answer: 3
7 + (-4) = 7 – 4 = 3
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.
Question 16.
a.
-8 + (-3) = ____
Answer: -11
-8 + (-3) = -8 – 3 = -11
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.
b.
-7 + 6 = ____
Answer: -1
-7 + 6 = -7 – (-6) = -1
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.
c.
-4 + (-9) = _____
Answer: -13
-4 + (-9) = -4 – 9 = -13
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.
Question 17.
a.
6 – 12 = ____
Answer: -6
6 – 12 = 6 + (-12) = -6
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.
b.
3 – (-4) = ____
Answer: 7
3 – (-4) = 3 + 4 = 7
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.
c.
-2 – 4 = ____
Answer: -6
-2 – 4 = – 2 + (- 4 )= -6
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.
Solve each problem.
Question 18.
One box of cups weighs 4\(\frac{2}{3}\) ounces. Another box weighs 5\(\frac{3}{8}\) ounces. What is the total weight of the two boxes?
The total weights is _______ ounces.
Answer: 10\(\frac{1}{24}\)
The weight of one box of cups = 4\(\frac{2}{3}\) ounces
The weight of second box of cups = 5\(\frac{3}{8}\) ounces
Therefore, the total weight of the cups = weight of first box + weight of second box
= 4\(\frac{2}{3}\) + 5\(\frac{3}{8}\)
4\(\frac{2}{3}\) + 5\(\frac{3}{8}\)
Partition the fractions and whole numbers to add them separately.
= (4 + 5) + \(\frac{2}{3}\) + \(\frac{3}{8}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 9 + [\(\frac{2}{3}\) x \(\frac{8}{8}\)] + [\(\frac{3}{8}\) x \(\frac{3}{3}\)]
= 9 + \(\frac{16}{24}\) + \(\frac{9}{24}\)
= 9 + \(\frac{16 + 9 }{24}\)
After simplification,
=9 + \(\frac{25}{24}\)
= 9 + 1\(\frac{1}{24}\)
Therefore, the result is given by,
= 10\(\frac{1}{24}\)
Therefore The total weights is 10\(\frac{1}{24}\) ounces.
Question 19.
Luggage on a certain airline is limited to 2 pieces per person. Together, the 2 pieces can weigh no more than 58\(\frac{1}{2}\) pounds. If a passenger has one piece of luggage that weighs 32\(\frac{1}{3}\) pounds, what is the most the second piece can weigh?
The second piece can weigh ____ pounds.
Answer: 26\(\frac{5}{6}\)
Number of persons limited for the luggage on a certain airline = 2
Together, the 2 pieces can weigh = 58\(\frac{1}{2}\) pounds
passenger has one piece of luggage that weighs = 32\(\frac{1}{3}\) pounds
second piece weigh = total weight – one piece
= 58\(\frac{1}{2}\) – 32\(\frac{1}{3}\)
58\(\frac{1}{2}\) – 32\(\frac{1}{3}\)
Partition the fractions and whole numbers to add them separately.
= (58 – 32) + \(\frac{1}{2}\) – \(\frac{1}{3}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 26 + [\(\frac{1}{2}\) x \(\frac{3}{3}\)] – [\(\frac{1}{3}\) x \(\frac{2}{2}\)]
= 26 + \(\frac{3}{6}\) – \(\frac{2}{6}\)
= 26 + \(\frac{3 + 2 }{6}\)
After simplification,
=25 + \(\frac{5}{6}\)
Therefore, the result is given by,
= 26\(\frac{5}{6}\)
Therefore, the second piece can weigh 26\(\frac{5}{6}\) pounds.
Question 20.
Mavis spends 1\(\frac{1}{4}\) hours on the bus every weekday (Monday through Friday). How many hours is she on the bus each week?
She is on the bus ____ hours each week.
Answer: 6\(\frac{1}{4}\)
Mavis spends 1\(\frac{1}{4}\) hours on the bus every weekday (Monday through Friday)
Number of hours is she on the bus each week = 5 x [1\(\frac{1}{4}\)] (As there are 5 days when we count from monday to friday)
By simplification,
5 x [1\(\frac{1}{4}\)] = 5\(\frac{5}{4}\) = 5 + 1\(\frac{1}{4}\) = 6\(\frac{1}{4}\)
Therefore, the result is 6\(\frac{1}{4}\)