; Sample answer: of the bucket will be filled with one faucet ... or subtract. Write in simplest...

Add or subtract. Write in simplest form.

SOLUTION: Rename using the LCD, 24.

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SOLUTION: Students should use the Commutative and Associative Properties of Addition to find the sum.

ANSWER:

Justify Conclusions Choose an operation to solve the problem. Explain your reasoning. Write in simplest form.

10. Mrs. Escalante was riding a bicycle on a bike path. After riding of a mile, she discovered that she still needed to

travel of a mile to reach the end of the path. How long is the bike path?

SOLUTION: Because Mrs. Escalante is trying to find the total length of the path, use addition.

Add mile and mile. Rename using the LCD, 12.

So, the bike path is miles long.

ANSWER:

Addition; Sample answer: To find the bike path's length, add and ;

11. Four students were scheduled to give book reports in 1 hour. After the first report, hour remained. The next two

reports took hour and hour. What fraction of the hour remained?

SOLUTION:

Begin with hour and subtract the time spent on the next two reports. The result is the amount of time remaining.

Rename using the LCD, 12.

So, hour remained for the final report.

ANSWER:

Subtraction; Sample answer: To find how much time remained, subtract from ; h

12. One hundred sixty cell phone owners were surveyed.

a. What fraction of owners prefers using their cell phone for text messaging or playing games? Explain. b. What fraction of owners prefers using their phone to take pictures or text message?

SOLUTION: a. Add the fractions that represent cell phone owners who use their phones for text messaging or playing games.

So, of cell phone owners use their phones for text messaging or taking pictures.

b. Add the fractions that represent cell phone owners who use their phones for taking pictures or text messaging.

ANSWER:

a. ; Add and .

b. ; Add and .

13. Pepita and Francisco each spend an equal amount of time on homework. The table shows the fraction of time they spend on each subject.

Complete the table by determining the missing fraction for each student.

SOLUTION: For each student, add the given amounts and subtract the result from 1, which represents the entire time spent on homework. Pepita: Rename using the LCD, 6.

So, Pepita spent of the time on math.

Francisco: Rename using the LCD, 8.

So, Francisco spent of the time on English.

ANSWER:

14. Chellise saves of her allowance and spends of her allowance at the mall. What fraction of her allowance

remains? Explain.

SOLUTION: To find the remaining fraction of her allowance, add the amounts Chellise saves and spends, and subtract that amount from 1, which represents the whole amount of her allowance. Rename using the LCD, 15.

So, of Chellise’s allowance remains.

ANSWER:

15. Persevere with Problems Fractions whose numerators are 1, such as or , are called unit fractions.

Describe a method you can use to add two unit fractions mentally.

SOLUTION: Students should generalize the process for adding unlike fractions.

Sample answer: Let and represent the unit fractions, where a and b are not zero. Multiply the first numerator

by b and the second numerator by a. Write the product over the denominator ab. Write in simplest form.

ANSWER:

16. Use a Counterexample Provide a counterexample to the following statement.

The sum of three fractions with odd numerators is never .

SOLUTION:

Students should show three fractions with odd numerators that have a sum of .

Sample answer:

ANSWER:

Sample answer:

17. Reason Inductively Suppose a bucket is placed under two faucets. If one faucet is turned on alone, the bucket willbe filled in 6 minutes. If the other faucet is turned on alone, the bucket will be filled in 4 minutes. What fraction of thebucket will be filled in 1 minute if both faucets are turned on at the same time? Explain.

SOLUTION:

; Sample answer: of the bucket will be filled with one faucet, while another of the bucket will be filled by the other faucet. Add these fractions to find the sum.

ANSWER:

; Sample answer: of the bucket will be filled with one faucet, while another of the bucket will be filled by the other faucet. Add these fractions to find the sum

ANSWER:

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Choose an operation to solve the problem. Explain your reasoning. Then solve the problem. Write in simplest form.

24. Ebony is building a shelf to hold the two boxes shown. What is the least width she should make the shelf?

SOLUTION: Because Ebony is trying to find the total amount of space needed to hold the boxes, use addition.

Add foot and foot. Rename using the LCD, 20.

So, Ebony should make the shelf at least feet wide.

ANSWER:

Addition; Sample answer: To find the smallest width to make the shelf, add and ;

25. Makayla bought pound of ham and pound of turkey. How much more turkey did she buy?

SOLUTION: Because Makayla is finding how much more turkey, use subtraction.

Subtract pound from pound. Rename using the LCD, 8.

So, Makayla bought pound more turkey than ham.

ANSWER:

Subtraction; Sample answer: To find how much more turkey Makayla bought, subtract from ; lb

26. Persevere with Problems Find the sum of and .

SOLUTION:

Evaluate and . Then find their sum.

ANSWER:

27. Find the Error Theresa is finding . Find her mistake and correct it. Explain your answer.

SOLUTION:

Theresa did not rename the fractions using the LCD, 20.

ANSWER:

Theresa did not rename the fractions using the LCD.

28. The table gives the number of hours Orlando spent at football practice.

Select the appropriate numbers below to complete the model to find the number of hours Orlando spent practicing onTuesday and Friday.

How many more hours did he practice on Friday than on Thursday?

SOLUTION: Insert the appropriate numbers related to the days into the model, and then add the fractions together using the LCD of 12.

So, Orlando practiced hours practicing on Tuesday and Friday.

To determine how many more hours he practiced on Friday than Thursday, subtract from using the LCD of 6.

So, Orlando practiced more hours on Friday than Thursday.

ANSWER:

29. Brett has of his weekly allowance left to spend. He has budgeted of his allowance to save for a new video

game and of his income for savings. Determine if each statement is true or false.

a. Brett will have of his income left if he only buys the video game.

b. Brett will have of his income left if he only puts money into savings.

c. Brett will have of his income left after buying the video game and putting money into savings.

SOLUTION:

Subtract the appropriate fraction(s) from and determine if the statement is true. a. Subtract the fraction of video game from the fraction of the monthly income Brett has left. Rename using the LCD, 24.

Brett has of his monthly income left after buying the video game, so the statement is false.

b. Subtract the fraction of savings from the fraction of the monthly income Brett has left. Rename using the LCD, 6.

Brett has of his monthly income left after putting money into savings, so the statement is true.

c. Add the fraction of savings and video games together using the LCD of 24, the subtract it from also using the LCD of 24.

Brett has of his monthly income left after putting money into savings and buying the video game, so the statement is true.

ANSWER:

Write each improper fraction as a mixed number.

SOLUTION:

Write as the sum of and .

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eSolutions Manual - Powered by Cognero Page 1

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; Sample answer: of the bucket will be filled with one faucet ... or subtract. Write in simplest...

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