TG • Grade 5 • Unit 2 • Lesson 11 • Answer Key   1

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Subtract Fractions (SG pp. 100–103) Questions 1–20

1. Answers will vary.2. Explanations will vary.3. 3–8 will be left. Strategies may vary. Students

can trade each fourth (yellow) for 2 eighths(blue). 6–8 – 3–8 = 3–8 .

4. Yes; 3–8 is a little less than 1–2 .5.* A possible response: Keenya’s single-color

method is like finding common denominatorslike Julia does. You end up having the samekind of pieces to subtract or the samedenominator to subtract.

Answer Key • Lesson 11: Subtract Fractions

Subtract Fractions

Mr. Moreno’s Aquarium

It is Jacob’s and Keenya’s turn to feed the tropical fish in Mr. Moreno’s classroomaquarium. Jacob sees that the can of fish food is 3�4 full. Every week, the fish eat3�8 of a can of fish food. Mr. Moreno asks Jacob to estimate how much fish foodwill be left at the end of the week.

“Will the can of fish food be more than half full or less than half full at the end ofthe week?” asked Mr. Moreno.

1. Estimate the amount of fish food that will be left. How would you answer Mr. Moreno’s question? Explain your reasoning.

Jacob decides to estimate this way:

2. Do you agree with Jacob’s estimate? Explain why or why not.

3. Find an exact answer to the problem using fraction circle pieces. Show howyou solved the problem.

is the same as , then must bem , the answer must be less than .

2 frr

Jacob

Since I know is the same as , then must bemore than . So if I subtract more than from , the answer must be less than .

2—81—4

3—81—41—41—23—44 , the ans , the ans4

3 , the ans—4e than . 41 — 8w is the sam is the sam8

2 is the sam—

r mwe , the ans3 So i 1rmo is the sam2oe I knSinc

2ss than . .21 .—

4s , then m m41 m—

.1et be lsur me than frrt mocaf I subtrra So i

m1e aw is the sam4an fr fr41 fr—

8 m m83 m—

mo fr1t besu m3

100 SG • Grade 5 • Unit 2 • Lesson 11

Subtract Fractions

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Student Guide - Page 100

Keenya solves the problem this way:

4. Does Jacob’s estimate agree with Keenya’s exact answer? Explain how youknow.

5. How is Keenya’s method similar to Julia’s method?

B

B

B

B

To solve – , I show both fractions using circle pieces like this.

3 – 4 3 – 8

3–43–8

3–8

3 – 8

I take one piece away from the first fraction for every piece in the second fraction.

I so I can rename it as

e

Then I replace the yellow pieces with blue pieces so all the pieces are thesame size and color. Now the pieces look like this:

I have three pieces left in the first fraction, so my answer is of a can. I write the number sentence like this:

3 �

=�

Y

Y

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B B

Y

B

B

Y Y

Y

B

B

B 4 , – e , , 4 3

ns uiotcafrth w boI sho

, – 4 vo solTTo sol

8 , – – , , 8 3

g sinns uth

, – 8

Y

ikok los lecthe pieoold ce ane sizsam

e thers aecl the pielaue pieth blis wecpiee the ycaplehen I rT

B

B

B

B

:ise thikw o N.rro

e thes so ecue pie

w olele the y

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ns uiotcafr

B

B

B

B

B

e iks lecg sinns u

B

B

B

B

I wran.is of a c3 cee piee thrvI ha8 i of a c– of a c8 i of a c3 i of a c

B

B

B

B

B

enctr senmbeue the nti I wrcat frsirt in the ffes le

n.iotcafry piereve

m the fofrne okaI t

: ise thike lenc

rwey ans, so mniotc

d noce in the secy pier on f foiotcat frsirm the f

y wae ace pien

8 8

B

BB� =

this way:

8–3

8–3

4–3

3 � ?————4 � ??—8 I find a fraction equivalent

to so I can rename it as eighths. It is easier for me to subtract fractions with like denominators.

T

of a can. I write the number sentence like this:

3–4

3–4

Julia solves � this way:

=

6–83–8

3–8=�

=

3 � 2————–4 � 26—8=

Julia

3–88�Julia solves 3

44 –Julia solves 3

? ?�3 8–33 this way:

8

—–—— = 8—6

2�4 –———— 2�3

=

� = 8–3

8–3

8–6

8—?

?�4 ———— ?�3

4o so I c so I c43 so I c–

inamoe denikth liwat frracao subtrrae tm

sie It is ea.thsheigenam ran so I c3tn equiiotcad a frainI f

.srotinans iotcar or f sie

s t ae ienamt enlavn equi

ailuJ

Subtract Fractions SG • Grade 5 • Unit 2 • Lesson 11 101

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Student Guide - Page 101

*Answers and/or discussion are included in the lesson.

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2 TG • Grade 5 • Unit 2 • Lesson 11 • Answer Key

6. Answers and explanations will vary. Possibleresponse: Jacob’s estimate is about right. 7–8 is alittle more than 3–4 , so taking away 1–4 is a littlemore than 1–2 .

7. 5–8 tank has drained.8. 7–8 – 1–4 = 5–8 or 7–8 – 2–8 = 5–8 .9. Answers will vary. Possible response: I

estimated 1–2 tank and 5–8 is a little more than 4–8which is equal to 1–2 . My estimate was close.

10. Estimates will vary. Estimates should be just alittle less than 2–3 since 1–12 is a small amount.

11. No; 1–9 is a small amount and is not close to 2–3 .12. Jacob subtracted the numerators and

denominators separately.13.* 7–12 tank of water was added.

2–3 � 1–12 � 7–12 or 8–12 � 1–12 � 7–1214. Between 0 and 1–2 ; 1–4 mile15. Closest to 1–2 ; 7–8 � 1–2 � 3–8 or 7–8 � 4–8 � 3–8 cup16. Closest to 0; 1–6 of her allowance; 1–3 � 1–2 � 5–6 and

6–6 � 5–6 � 1–617. Closest to 0; 1–5 mile; 4–10 � 1–5 � 1–5 mile18. 3–8 of a tank; 5–8 � 1–4 � 3–819. Number sentences will vary. One sentence is

given for each.A. 5–10 ; 8–10 � 3–10 � 5–10 B. 3–8 ; 7–8 � 4–8 � 3–8C. 1–5 ; 3–5 � 2–5 � 1–5 D. 1–12; 8–12 � 7–12 � 1–12E. 3–10 ; 8–10 � 5–10 � 3–10 F. 7–10 ; 10–10 � 3–10 � 7–10G. 1–12; 4–12 � 3–12 � 1–12 H. 8–12; 9–12 � 1–12 � 8–12

20. Problems chosen will vary. Sample solution for19G: Solve 1–3 � 1–4 with circle pieces:

Solve 1–3 � 1–4 using a multiplication strategy:1–3 � 4–4 � 4–121–4 � 3–3 � 3–124–12 � 3–12 � 1–12

BK

BK

BK

BK

Before cleaning the aquarium, Jacob drains all the water. The aquarium was 7�8 fullwhen he started draining it. A little later he sees that it is 1�4 full. Jacob estimatesthat about 1�2 of the tank has drained out so far.

6. Make an estimate of your own. Is Jacob’s estimate too high or too low?Explain your reasoning.

7. Find the exact amount of water that has drained out of the fish tank bysolving the problem with fraction circle pieces.

8. Write a number sentence for your solution to Question 7.

9. Does your estimate in Question 6 agree with your answer in Question 7?Explain.

After cleaning the aquarium, Jacob refills it with a small hose from the sink. Whenhe first checks the tank, it is 1�12 full. Two minutes later, it is

2�3 full.

10. Estimate how much water was added to the tank during the two minutes.Show the location of your estimate by marking an “X” on a number line likethe one shown below.

Jacob decides to solve the problem without using circle pieces.

11. Is Jacob’s answer reasonable? Why or why not?

12. If his answer is not reasonable, what mistake did Jacob make?

13. Use circle pieces to find an exact answer to the problem. Include a numbersentence.

0 11–2

Jacob

So the answer is of the tank was added.1—9

2—31—9

1—12 = =– 2–1————12–3

102 SG • Grade 5 • Unit 2 • Lesson 11

Subtract Fractions

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Check-In: Questions 14–20Solve the subtraction problems in Questions 14–19 using fraction circlepieces or another strategy. For each problem, first estimate whether theanswer is closest to 0, 1–2, or 1.

14. Jackie is running a 3�4 -mile race. How much farther does she have to go aftershe has run 1�2 of a mile?

15. Ming is making cookies. Ming poured 7�8 of a cup of sugar into a measuringcup. The recipe for cookie dough calls for 1�2 of a cup of sugar. How muchsugar should Ming take out of the measuring cup?

16. Shannon spent 1�3 of her allowance on a CD and 1�2 of her allowance on amovie. What fraction of her allowance does she have left?

17. Jerome lives 4�10 of a mile from school. Lee Yah lives1�5 of a mile from school.

How much farther from school does Jerome live than Lee Yah?

18. Mr. Moreno always fills up the gas tank in his car when there is 1�4 tank left. The gasgauge of his car is shown. How much ofthe tank of gas does Mr. Moreno have touse before filling it up again? Hint: Thinkof a number line.

19. Solve each of the following subtraction problems. Write a number sentenceto show how you solved each problem.

A. 4�5 � 3�10 B. 7�8 � 1�2 C. 3�5 � 2�5 D. 2�3 � 7�12

E. 4�5 � 1�2 F. 1� 3�10 G. 1�3 � 1�4 H. 3�4 � 1�12

20. Choose one problem from Question 19. Show or tell how to solve it withcircle pieces and then with a multiplication strategy.

E F

Subtract Fractions SG • Grade 5 • Unit 2 • Lesson 11 103

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Student Guide - Page 103

Answer Key • Lesson 11: Subtract Fractions

*Answers and/or discussion are included in the lesson.

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ySubtract Fractions (SG p. 104) HomeworkQuestions 1–8

1. A. closest to 1–2 ; 6–12B. closest to 0; 1–12C. closest to 1; 5–6D. closest to 1; 9–10E. closest to 0; 1–8F. closest to 0; 0G. closest to 1–2 ; 5–12H. closest to 1–2 ; 3–5I. closest to 0; 2–10

2. 1� 3–5 � 2–5 box of popcorn3. 3–4 � 1–8 � 5–8 mile4. Miguel’s eraser is longer; 10–12 � 7–12 � 3–12 inch

longer5. Ming’s ride is shorter; 2–3 � 1–2 � 1–6

or 4–6 – 3–6 � 1–6 shorter6. 7–8 � 1–4 � 5–8 pound7. 1–2 � 1–8 � 5–8 ; 8–8 � 5–8 � 3–8 of the collection8. 4–5 – 4–10 � 4–10 ; 4–10 of the bag

TG • Grade 5 • Unit 2 • Lesson 11 • Answer Key   3

Answer Key • Lesson 11: Subtract Fractions

1. For each problem, estimate whether the difference is closest to 0, 1�2 , or 1.Then solve the subtraction problems using the Fraction Circle Pieces pagein the Student Guide Reference section or another strategy.

A. 5�6 � 4�12 B. 2�3 � 7�12 C. 2�2 � 1�6

D. 5�5 � 1�10 E. 1�4 � 1�8 F. 6�8 � 3�4

G. 2�4 � 1�12 H. 1� 2�5 I. 2�5 � 2�10

Mr. Moreno’s students wrote the following word problems about their class.Solve each problem. Include number sentences.

2. Jacob ate 3�5 of a box of carmel popcorn. How much of the box of popcorn is left?

3. Keenya is going on a 3�4 -mile walk through thepark. She already walked 1�8 mile. How muchfarther does Keenya need to walk?

4. Julia’s purple eraser is 7�12 of an inch long.Miguel’s red eraser is 5�6 of an inch long.Whose eraser is longer? How much longer?

5. Ming rides his bike 3�6 of a block to school and Mark rides his bike 2�3 of a block toschool. Who rides a shorter distance to school? How much shorter is thatstudent’s ride?

6. Fern made 7�8 of a pound of fudge. Her little sister ate1�4 of a pound. How

much fudge is left for Fern?

7. Sam shared his baseball card collection with his friends. Josh took 1�2 andMichael took 1�8 of the cards. What fraction of the collection was left forSam?

8. Kathy had 4�5 of a bag of sticky sour candies. She tripped and spilled4�10 of the

bag of candies. What fraction of the bag did not spill?

104 SG • Grade 5 • Unit 2 • Lesson 11

Subtract Fractions

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Student Guide - Page 104