zMath Intervention Math  - Unit 11: Divide Fractions
Some of the questions in this unit may be answered by recording an audio file. If you chose to record the answer, click on the "Add Recording" button and follow the on-screen instructions closely. Once you have completed and attached the recording, enter the word “COMPLETE” in the text box. (Note: If your computer does not have a built-in microphone, a microphone or microphone/headset combination is needed to record audio.)

For problems in this unit that require fraction entries, enter the fractions and mixed numbers as shown in the example below.

Reciprocals

1) A fraction times its reciprocal equals _______ .

2) What is the reciprocal of 7/9?

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3) Briefly describe how to find the reciprocal of a mixed number.

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4) What is the reciprocal of 7 5/8?

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Division of Fractions

5) What is the quotient?

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6) What is the quotient?

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7) What is the quotient if 32 is divided by 4/9?

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8) Divide 7/8 by 7/16.

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9) Divide 56 by 8/9.

10) What fraction is halfway between 3/16 and 7/8?

11) Rachel is having a new roof installed on her house. She needs several rows of rectangular-shaped shingles to complete each side. If each shingle is 5/6 feet long and her roof measures 70 feet long, how many shingles will she need for just one row?

12) What is the quotient?

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13) What is the quotient?

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14) What is the quotient?

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15) What is the quotient?

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16) What is the quotient of 6 1/2 is divided by 1/2?

17) A 12-foot board may be cut into pieces that are 3/4-foot long. How many pieces may be cut from the board?

Fractions to Decimals and Vice Versa

18) What is the decimal for 3/5?

19) What is the decimal for 9/10?

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20) What is the decimal for 3/4?

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21) What is the decimal for 5/8?

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22) What is the decimal for 11/18? Round the answer to the nearest hundredth.

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For the next four problems, change each decimal to a fraction. Show both the decimal fraction and the simplified fraction. For example: 0.15 = 15/100 which simplifies to 3/20.

23) What are the decimal fraction and the simplified fraction for 0.8?

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24) What are the decimal fraction and the simplified fraction for 0.25?

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25) What are the decimal fraction and the simplified fraction for 0.06?

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26) What are the mixed decimal fraction and the simplified mixed fraction for 9.875?

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27) The length of Nail A is 3/8 inch. The length of Nail B is 0.625 inch. Which nail is longer or are they both the same length? (Hint: Express the length of Nail A as a decimal, and then compare the two lengths.)

28) Are the two numbers equal? Explain why or why not. (The bar above the six represents “repeating sixes”.)

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29) Are the two numbers equal? Explain why or why not.

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Unit Pricing and Comparative Shopping

For the next four problems, find the unit price for each offer, and determine which is the better buy or if the prices are the same.

30) Apples: 3 lb for $3.98 or 5 lb for $4.98?

31) Red raspberry Jam: 48 oz for $7.98 or 12 oz for $1.98?

32) Bag of chips: 7.5 oz bag for $0.99 or 24 oz bag for $3.99?

33) One quart of milk for $1.09 or one gallon for $3.59 (Hint: There are four quarts in one gallon.)

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