Rational Numbers as Decimals

Topic 1 Review

Vocabulary Review

Use page 6 in your workbook to help you with the following questions.

Multiple Choice

A decimal that ends is a(n) _.

• additive inverse

• complex fraction

• terminating decimal

• repeating decimal

Multiple Choice

Two numbers that have a sum of 0 are _.

• additive inverses

• complex fractions

• terminating decimals

• repeating decimals

Multiple Choice

A _ is a fraction $$\frac{a}{b}$$ where a and/or b are fractions and b is not equal to 0.

• additive inverse

• complex fraction

• terminating decimal

• repeating decimal

Lesson 1-1 Review

Quick Review

Integers are the counting numbers, their opposties, and 0. Opposite integers are the same distance from 0 in opposite directions. Opposite quantities combine to make 0.

The descent of her climb is represented by -3. She has to climb 3 miles to return to her starting point.

A climber descends 3 miles into a canyon. What integer represents the descent of her climb? How far does she have to climb to return to her starting point?

Example

Fill in the Blank

On a cold winter morning, the temperature was -4 degrees Fahrenheit. By noon, the temperature increased 4 degrees. What was the temperature at noon

Fill in the Blank

Audrey deposits $27 in her account. Then she makes two withdrawals, one for $15 and one for $12. What is the total change to the balance of Audrey's account?

Lesson 1-2 Review

Quick Review

All rational numbers have an equivalent decimal form. The decimal equivalent will be either a terminating decimal or a repeating decimal. A terminating decimal ends in repeating zeros. A repeating decimal has a never-ending pattern of the same digits.

Example

Multiple Select

Which fractions have a decimal equivalent that is a repeating decimal. If possible, select all that apply.

• $$\frac{13}{65}$$

• $$\frac{141}{47}$$

• $$\frac{11}{12}$$

• $$\frac{19}{3}$$

Fill in the Blank

Greg bought $$19\frac{11}{16}$$ gallons of gas. What decimal should the meter on the gas pump read?

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Fill in the Blank

$$\frac{9}{11}=$$

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Fill in the Blank

$$\frac{4}{5}=$$

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Fill in the Blank

$$-\frac{17}{5}=$$

-

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Fill in the Blank

$$\frac{5}{9}=$$

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Lesson 1-3

Quick Review

To add integers with the same sign, add the absolute value of each integer. The sign of the sum will be the same as the sign of the addends. To add integers with different signs, find the difference of the absolute value of each integer. The sign of the sum will be the same as the sign of the greater addend.

Example

Fill in the Blank

Jonah's cell phone came with 64 GB of membory. He has used 15 GB. He then uses 5 MB of memory to record photos and videos from a trip. Use the addition expression $$64+\left(-15\right)+\left(-5\right)$$ to find how much memory is left on his phone

Multiple Choice

Stella walks down a flight of stairs to the basement. Then she walks back up the stairs and up another flight of stairs to the second floor of her house. Each flight of stairs represents a change of 12 feet in height. How far is Stella above the ground?

• 0 ft

• -12 ft

• 12 ft

• 24 ft

Find the sum for each of the following

Multiple Choice

$$64+\left(-15\right)=$$

• 49

• -49

• 79

• -79

Multiple Choice

$$-121+\left(-34\right)=$$

• 155

• -155

• -87

• 87

Multiple Choice

$$-86+92=$$

• 178

• -178

• -6

• 6

Multiple Choice

$$109+\left(-162\right)=$$

• -271

• 271

• -53

• 53

Lesson 1-4 Review

Quick Review

To subtract integers, use the additive inverse to write an equivalent addition expression. Then follow the rules for addition. When the signs are the same, find the sum of the absolute values. When the signs are different, find the difference. Use the sign of the number with the greater absolute value.

Example

Fill in the Blank

The temperature is 1 degree Fahrenheit at dusk. It is 8 degrees colder at dawn. What is the temperature at dawn?

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Fill in the Blank

Kyle and Nadim are on the same space on a board game they are playing. Kyle moves back 2 spaces in one turn and moves back 3 more spaces in his second turn. Nadim has remained in the same place. What integer represents Kyle's location relative to Nadim's location on the game board?

-

Find the difference for each of the following

Multiple Choice

$$82-\left(-14\right)=$$

• 96

• -96

• 68

• -68

Multiple Choice

$$-18-\left(-55\right)=$$

• -73

• 73

• 37

• -37

Multiple Choice

$$-17-44=$$

• -27

• 27

• -61

• 61

Multiple Choice

$$70-\left(-101\right)=$$

• 171

• -171

• -31

• 31

Lesson 1-5 Review

Quick Review

Positive and negative rational numbers and decimals can be added and subtracted following the same rules as adding and subtracting integers.

Example

Fill in the Blank

Doug digs a hold that is 1.7 feet below ground level. He plants a bush that is $$3\frac{2}{10}$$ feet tall from the bottom of the root to the top branch. How much of the bush is above the ground?

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Fill in the Blank

Penelope has a birdhouse that is $$4\frac{9}{10}$$ feet above the roof of her garage. She has a second birdhouse that is 5.36 feet below the roof of her garage. What is the distance between the birdhouses?

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Find the sum or difference for each of the following problems.

Fill in the Blank

$$-2.63+3\frac{1}{4}=$$

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Fill in the Blank

$$-4\frac{1}{2}-\left(-1.07\right)=$$

-

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Fill in the Blank

$$0.74+\left(-\frac{3}{5}\right)=$$

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Fill in the Blank

$$-\frac{1}{8}-0.356=$$

-

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Lesson 1-6

Quick Review

Multiply integers the same way you multiply whole numbers. If the signs of the factors are the same, the product is positive. If the signs of the factors are different, the product is negative.

Multiply integers the same way you multiply whole numbers. If the signs of the factors are the same, the product is positive. If the sign of the factors are different, the product is negative.

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Lesson 1-6 Review

Fill in the Blank

Marisa buys 4 books at $13 per book. What integer represents the total change in the amount of money Marisa has?

-

Multiple Select

Which expressions have a product of -18? If possible, select all that apply

• $$-2\cdot-9$$

• $$-6\cdot3$$

• $$-3\cdot6$$

• $$-9\cdot2$$

Fill in the Blank

$$-7\cdot-14=$$

Fill in the Blank

$$9\cdot-20=$$

-

Fill in the Blank

$$-11\cdot-16=$$

Fill in the Blank

$$-15\cdot12=$$

-

The same rules for multiplying integers apply to multiplying rational numbers. If the signs of the factors are the same, the product will be positive. If the signs of the factors are different, the product will be negative.

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Lesson 1-7 Review

Fill in the Blank

Jason spends $2.35 to buy lunch at school. If he buys a lunch on 9 days, what number represents the total change in the amount of money Jason has?

-

$

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Fill in the Blank

$$-2\frac{2}{3}\cdot-4\frac{3}{7}=$$

Write your answer as an improper frraction.

/

Fill in the Blank

$$-3\frac{4}{9}\cdot5\frac{2}{5}=$$

Write your answer as an improper fraction.

-

/

Fill in the Blank

$$6\frac{2}{3}\cdot-4\frac{1}{5}=$$

-

Divide integers the same way you divide whole numbers. The quotient is positive if the signs of the dividend and divisor are the same. The quotient is negative if the signs of the dividend and divisor are different.

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Lesson 1-8 Review

Multiple Select

Which expressions have a quotient of -4? If possible, select all that apply.

• $$\frac{-24}{6}$$

• $$-36\div-9$$

• $$-72\div18$$

• $$\frac{84}{-21}$$

Fill in the Blank

Whitney rolls a ball down a ramp that is 18 feet long. If the ball rolls down 2 feet each second, what integer represents the amount of time, in seconds, the ball takes to reach the end of the ramp?

Fill in the Blank

$$\frac{81}{-9}=$$

-

Fill in the Blank

$$-123\div-4=$$

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Fill in the Blank

$$-\frac{94}{4}=$$

-

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Fill in the Blank

$$65\div\left(-5\right)=$$

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The same rules for dividing integers apply to dividing all rational numbers. The quotient is positive when the numbers being divided have the same signs. The quotient is negative when the numbers being divided have different signs. Complex fractions have a fraction in the numerator, the denominator, or both. To divide a fraction, rewrite as multiplication by its multiplicative inverse, or reciprocal.

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Lesson 1-9 Review

Fill in the Blank

$$\frac{8}{9}\div-1\frac{4}{15}=$$

Use "/" to write your answer as a fraction.

-

/

Fill in the Blank

$$-3.6\div2\frac{1}{7}=$$

Write your answer as an improper fraction.

-

/

Fill in the Blank

A boat drops an anchor 17.5 feet to the bottom of a lake. If the anchor falls at a rate of 0.07 feet each second, how long will it take the anchor to reach the bottom of the lake?

Lesson 1-10 Review

Quick Review

You can use rational numbers to solve problems in the same way that you use whole numbers. Be sure to make sense of the problem you are solving to help you choose the correct operations and determine which values will be positive and which will be negative.

Example

Fill in the Blank

In 5 rounds of a game, Jill scored -3, 8, 9, -7, and 13. What integer represents her average score for the 5 rounds?

Fill in the Blank

Peter signed up for a program that costs $10.50 per month to stream movies to his computer. He decided to cancel his service after $$\frac{5}{6}$$ month. He only has to pay for the amount of time he used the service. What number represents the total change in the amount of money Peter has after paying for the service?

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$

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Fill in the Blank

Maggie spent $4.05 on cheese and fruit at the farmer's market. She bought $$\frac{1}{8}$$ pound of apples, $$\frac{1}{4}$$ pound of pears, and 1.25 pounds of bananas. If fruit cost $0.80 per pound, how much did Maggie spend on cheese?

$

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