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TG • Grade 5 • Unit 10 • Lesson 6 • Answer Key 1
Answer Key • Lesson 6: Workshop: Add and Subtract Fractions
Student Guide
Workshop: Add and Subtract Fractions (SG p. 479)Questions 1–5
1. >12. <13. >14. <15. A. 10�14 or 5�7 ; Lee Yah is incorrect.
B. 13�10 ; Roberto is correct.C. 19�12 = 17�12 ; Tanya is correct.
Workshop: Add and Subtract Fractions
Mr. Moreno’s class played a game. He asked the students to estimate the sum ordifference of two fractions and then decide whether the exact answer was greaterthan or less than 1. Students put their thumbs up to indicate “greater than 1” ortheir thumbs down to indicate “less than 1.”
Here are the problems Mr. Moreno presented. Estimate the sums ordifferences. Write “> 1” if the answer is greater than one and “<1” if theanswer is less than one. Do not solve the problems using paper and pencil.
1. 5��12 � 5�6 � 2. 4��10 � 4�8 � 3. 2 7��10 � 12�4 � 4. 17�8 � 14�5 �
5. Mr. Moreno gave the students this problem:
Here are the students’ solutions. Find exact answers and tell whether their solutions are correct or incorrect.
Use the Self-Check Questions and the Workshop Menu in the Find Fraction Sumsand Differences pages in the Student Activity Book to help you choose practicewith adding and subtracting fractions.
Lee Yah
5—1014—524—72—14+ 3—4
5—6+–A. B. C.
Workshop: Add and Subtract Fractions SG • Grade 5 • Unit 10 • Lesson 6 479
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Find two fractions with a sum or a difference between 1 and 2.
Student Guide - Page 479
2 TG • Grade 5 • Unit 10 • Lesson 6 • Answer Key
Copyright © Kendall H
unt Publishing Company
Answer Key • Lesson 6: Workshop: Add and Subtract Fractions
Student Activity Book
Find Fraction Sums and Differences(SAB pp. 409–419)Questions 1–17
1. A. Estimates will vary. Possible response:about 11�2
B. 19�12 = 17�12C. 10 black pieces + 9 black pieces =
19 black pieces or 1 red whole and 7 black pieces
2. A. Estimates will vary. Possible response: alittle more than 2
B. 310�15 � 16�15 = 2 4�15C. Responses will vary. Possible response: I
estimated that the difference would be alittle more than 2, and 2 4�15 is so I amconfident about my answer.
3.
75——100
H.
20 11—8
C.35——100
I.4—5
A.6—71
F.3—41
D.4—91
G.3—4
B.3—25
J.1—20
E.
Find Fraction Sums and DifferencesUse the Fractions on Number Lines Chart, Fraction Chart, Multiplication andDivision Facts and Adding and Subtracting Fractions Menu in the StudentGuide Reference section.
Self-Check: Questions 1–21. A. Estimate the sum: 10��12 � 3�4 .
B. Solve 10��12 � 3�4 using paper and pencil.
C. Check your answer in Question 1B with fraction circle pieces. Show ortell which pieces you use. Is your answer correct?
2. A. Estimate the sum: 3 2�3 �12�5 .
B. Solve 3 2�3 �12�5 using paper and pencil.
C. How do you know if your answer in Question 2B is reasonable?
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Workshop: Add and Subtract Fractions SAB • Grade 5 • Unit 10 • Lesson 6 409
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Student Activity Book - Page 409
Think about your work on Self-Check: Questions 1–2 and your progress withestimating and finding fraction sums and differences. Use the WorkshopMenu to choose practice for estimating and finding fraction sums anddifferences.
Refer to any pages in the Student Guide Reference section as you work.
EstimateFor Questions 3 and 4, use a benchmark fraction number line, picture fractioncircle pieces, think about “friendlier fractions” that are close to the actualfractions, or use other strategies to help you estimate.
3. Label about where each of the following fractions would be on the numberline below. An example is given.
A. 4�5 B. 3�4
C. 1�8 D. 1 3�4
E. 1��20 F. 1 6�7
G. 1 4�9 H. 75��100
I. 35��100 J. 3��25
Can I Do This?
Workshop Menu
Working On It! Getting It! Got It!
I could use someextra help.
I just needsome morepractice.
I’m ready for achallenge.
Estimate fraction sums and differences.
Add and subtract fraction using models and paper and pencil.
Q# 3A–E, 5A–D, 6
Q# 3C–G, 4, 5E–I, 6
Q# 3F–J, 4, 5G–L, 6
Q# 7–8, 11–12, 14,
16–17
Q# 8–10, 13A–E,15–17
Q# 8–10, 13D–H, 15–17
Can I Do This?
sums and Estimate fraction
orking On It!W
orkshop MenuW
.
5A–D, 6 Q# 3A–E,
a helpxtrr eemse sou
d luoI cGetting It!
orkshop Menu
c.
5E–I, 6 Q# 3C–G, 4,
foI
ceitcaprere momsodeet nsI ju
Got It!
.
5G–L, 6 Q# 3F–J, 4,
egenllha arfo
y deam r’
paper and pencil.models and fraction using Add and subtract
ences.ferdifffer
16–1711–12, 14,
Q# 7–8,
5A–D, 6
Add and subtract
13A–E,15–17 Q# 8–10,
5E–I, 6
13D–H, 15–17 Q# 8–10,
5G–L, 6
20 1
1—4
Name Date
SAB • Grade 5 • Unit 10 • Lesson 6 Workshop: Add and Subtract Fractions410
Copyright © Kendall H
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Student Activity Book - Page 410
TG • Grade 5 • Unit 10 • Lesson 6 • Answer Key 3
Answer Key • Lesson 6: Workshop: Add and Subtract Fractions
*Answers and/or discussion are included in the lesson.
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4. Column A Column BEx. 11�12 2 1�2A. 9�20
1�5B. 144�91
1�10C. 6�35 2 1�4D. 2 5�19 11�2E. 78��100
1�4F. 2 247��500
1�2G. 23��101
3�4H. 20��200 1
5. A. less than 1B. less than 1C. greater than 1D. greater than 1E. less than 1F. greater than 1G. greater than 1H. greater than 1I. less than 1J. less than 2K. less than 2L. greater than 10
6. A. Estimates will vary. Possible response:About 11�2 pounds. 7�8 is almost 1 and 9�16 isjust over 1�2 , so 11�2 pounds is a closeestimate.
B.* 11�2 pounds + 2 1�8 pounds is less than 4 pounds. Possible explanation: 1 poundplus 2 pounds is 3 pounds. When I add thefractions 1�2 plus 1�8 is just a little over 1�2 ,not enough to make another whole.
7. A. I disagree with Shannon. Possibleexplanation: 3�7 cup can’t be right for thesum because she started with 1�2 cup andadded more. She added the denominatorstogether and that is incorrect.
B. 2�5 + 1�2 = 4�10 + 5�10 = 9�10 cup of sugar
4. Find a “friendlier fraction.” Draw a line from a fraction in Column A to afraction in Column B that is close to the first fraction.
Column A Column B
Ex. 11��12 21�2
A. 9��201�5
B. 144��911��10
C. 6��35 21�4
D. 2 5��19 11�2
E. 78��1001�4
F. 2 247��5001�2
G. 23��1013�4
H. 20��200 1
5. For each problem, circle the better estimate. Do not find the exact answer.
A. 2�3 � 3�5 less than 1 greater than 1
B. 2��12 � 1�3 less than 1 greater than 1
C. 7��10 � 8��10 less than 1 greater than 1
D. 1�4 � 4�5 less than 1 greater than 1
E. 1�9 � 1��10 � 1��12 less than 1 greater than 1
F. 7��10 � 3�4 less than 1 greater than 1
G. 11�3 � 1�7 less than 1 greater than 1
H. 2�3 � 6��11 less than 1 greater than 1
I. 13�4 � 3�5 less than 1 greater than 1
J. 16�8 � 1��16 less than 2 greater than 2
K. 9��20 � 7��15 � 5��12 less than 2 greater than 2
L. 31�5 � 4 2�3 � 2 1�2 less than 10 greater than 10
Name Date
Workshop: Add and Subtract Fractions SAB • Grade 5 • Unit 10 • Lesson 6 411
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Student Activity Book - Page 411
6. Mr. Moreno is packing paperback books in boxes to ship to anotherschool.
A. Estimate the weight of the books in Box A. Show or tell how youdecided.
B. Is the weight of both boxes over or under 4 pounds? Do not findan exact answer. Show or tell how you decided.
Add and Subtract
7. Ana and Shannon are baking. Shannon adds 2�5 cup sugar to 1�2 cup brown sugar.
A. Do you agree with Shannon? If you do not, explain why.
9——167—8 � 1—8lb. lb. pounds2
Box A Box B
2 � 1 = 3 and 5 � 2 = 7, so I think � = .We have a little less than cup of sugar.
1—2
1—2
2—53—7
2–5
1–2
Shannon
.rr.ap of sug 2ss thanee ltltie a lve haW
.7 2ink so I th, 2 = 7 7, �d 5 3 an= 1 �2
7 —3= .5—2
2 —1 1 cu
2 —— 11�
5–2
2–1
Name Date
SAB • Grade 5 • Unit 10 • Lesson 6 Workshop: Add and Subtract Fractions412
Copyright © Kendall H
unt Publishing Company
Student Activity Book - Page 412
Answer Key • Lesson 6: Workshop: Add and Subtract Fractions
4 TG • Grade 5 • Unit 10 • Lesson 6 • Answer Key
Copyright © Kendall H
unt Publishing Company
8. A. I disagree with Ana. She only added thewhole numbers and she should have addedthe fractions too because they make anotherwhole cup.
B. 2 2�3 + 2 3�4= 2 8�12 + 2 9�12= 417�12= 5 5�12 cups flour
9. A. 1�4 cup of chocolate chips =
��8 cup of chocolate chips
B. 1 cup of crispy rice cereal
=��8 cup of crispy rice cereal
C. 2 3�4 cups of flour =��8 cups of flour
D. 11�2 cups of sugar =��8 cups of sugar10. A. 2 2�3 – 1 5�8 = 1 1�24 more cups of flour
B. 1 1�24 + 1 5�8 = 1 1�24 + 115�24 = 216�24 = 2 2�3
2
8
22
12
B. Exactly how much does Shannon have when she combines the two sugars? Use the models to show the sum.
� �
8. Ana needs 2 3�4 cups of flour for one recipe and 2 2�3 cups foranother recipe. She measuresthe flour she has in her kitchenand she has 5 cups. A. Do you agree with Ana? Why or why not?
B. Exactly how much flour does Ana need to make both recipes?
9. Ana can only find a 1�8 -cup measure. How many1�8 of a cup will she need to
equal the amounts she needs?
A. 1�4 cup of chocolate chips = ��8 cup of chocolate chips
B. 1 cup of crispy rice cereal = ��8 cup of crispy rice cereal
C. 2 3�4 cups of flour = ��8 cups of flour
D. 11�2 cups of sugar = ��8 cups of sugar
2–5
——10
1–2
� ——10
�5–2 ——
10——�
2–1 � ——�
10——
5 10 2 10
1–88–1
I will estimate 2 � 2 is 4, so 5 cups of flour should be more than enough to make the receipes.
1
eicee the rkmae than enrbe mops of fso 5 cu
e 2 timatsl eilI w
.sepeio h tugoe than end lu shoruolps of f
, 2 is 4�e 2
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Workshop: Add and Subtract Fractions SAB • Grade 5 • Unit 10 • Lesson 6 413
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10. A. Ana measures 15�8 of a cup of flour. How many more cups does she need to make 22�3 cups of flour? Show your work and include anumber sentence.
B. Show how to check your answer with addition.
For Questions 11–12, read about how Chris and Carla solve 4�5 � 3��20 . Theyknow they need to add the same parts together and that fifths are differentfrom twentieths. They want to rename the fractions. Here is how they findcommon denominators so they can rename 4�5 and
3��20 with equivalentfractions.
Chris’s Way
Chris multiplies the two denominators together: 5 � 20 � 100. 100 is a commondenominator for 5 and 20.
Chris multiplied 5 � 20 to get 100, so he multiplies the numerator anddenominator by 20 to find an equivalent fraction.
4 � 20���5 ���20 � 80��100
Chris multiplied 20 � 5 to get 100, so he multiplies the numerator anddenominator by 5 to find an equivalent fraction.
3 � 5����20 � 5�� 15��100
Now he is able to add hundredths: 80��100 � 15��100 =95��100. He rewrites it in
simplest form: 19��20.
To decide what the numerator will change to, I think about what I multiplied 5 by to get 100, and what I multiplied 20 by to get 100.
Chrisplitlut I mhad w, an010
t I mhat wuboink aI thmut the nhade wcio deTTo de
.0t 10eo gy td 20 bieplt eo gy td 5 bieplitlut I m
, oo, e tghanl cilr wotarraem
isChr
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SAB • Grade 5 • Unit 10 • Lesson 6 Workshop: Add and Subtract Fractions414
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Student Activity Book - Page 414
TG • Grade 5 • Unit 10 • Lesson 6 • Answer Key 5
Answer Key • Lesson 6: Workshop: Add and Subtract Fractions
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Carla’s Way
To solve 4�5 � 3��20 , Carla looks at the denominators and thinks about their multiplesuntil she finds a common one. The Multiplication and Division Facts chart in theStudent Guide Reference section helps. If she can’t find a common multiple, shejust multiplies the denominators together to find one like Chris does.
4�5 � 3��20
The common multiple is 20.
Carla needs to rename 4�5 so that it has a common denominator of 20. Shemultiplies 5 � 4 to get 20, so she also multiplies the numerator by 4 and finds an equivalent fraction.
4 � 4����5 � 4 � 16��20
Now she is able to add twentieths: 16��20 � 3��20 = 19��20 .
12. Find common denominators and equivalent fractions Carla’s way to solvethe problems. You can check your work with fraction circle pieces.
A. 2�5 � 3��10 Number sentence
B. 5��12 � 2�3 Number sentence
C. 3�4 � 1�8 Number sentence
Sometimes I take a shortcut. I look at the denominators and see if 5 � some number equals 20. I know that 5 � 4 � 20, so the common denominator is 20.
Multiples of 5: 5, 10, 15, 20, 25, 30 . . .
Multiples of 20: 20, 40, 60, 80 . . .
, so the c 20� 4 �5 �f 5 d see ian
s I teimtemSo
, 20Multiples of 20:
Multiples of 5: 5, 10, 15,
r is 20otinamon denmomo, so the c I kn.ls 20 equarmbeue nm so�
t the denok ao I l.tt.cutre a shokas I t
40, 60, 80 . . .
, 25, 30 . . . 200, 15,
.r is 20t w thao I kn
s rotinamot the den
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SAB • Grade 5 • Unit 10 • Lesson 6 Workshop: Add and Subtract Fractions416
Copyright © Kendall H
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Student Activity Book - Page 416
11. A. The common denominator is .2 �����3 � = ��
1 �����4 � = ��
8�12 + 3�12 = 11�12B. The common denominator is .
4 �����5 � = ��
1 �����2 � = ��
8�10 – 5�10 = 3�10C. Possible response:
1 �����2 � = ��2�4 + 3�4 = 5�4 = 11�4
12. A. 4�10 + 3�10 = 7�10B. 5�12 + 8�12 = 13�12 = 11�12C. 6�8 – 1�8 = 5�8
12
12
3
3
3
12
8
4
4
10
10
5
5
5
10
8
2
2
4
2
2
2
11. Find common denominators and equivalent fractions Chris’s way to solvethe problems. You can check your work with fraction circle pieces.
A. Solve 2�3 � 1�4 . The common denominator is .
2 ���3 �������� 1 ���4 ��������
Write the new number sentence and solve it.
B. Solve 4�5 � 1�2 . The common denominator is .
4 ���5 �������� 1 ���2 ��������
Write the new number sentence and solve it.
C. Chris is solving 1�2 � 3�4 . He multiplies 2 � 4 and finds the commondenominator 8. Find a common denominator other than 8 to solve1�2 � 3�4 .
1 ���2 ��������
Write the new number sentence and solve it. Write the answer insimplest form.
� 3�4 �
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Workshop: Add and Subtract Fractions SAB • Grade 5 • Unit 10 • Lesson 6 415
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Answer Key • Lesson 6: Workshop: Add and Subtract Fractions
6 TG • Grade 5 • Unit 10 • Lesson 6 • Answer Key
13. Solve the problems using a paper-and-pencil strategy. Estimate to makesure your answers are reasonable. Write your answer in simplest form.
A. 2�5 � 2�3 �
B. 11��3 � 5�2 �
C. 21�8 � 11�4 �
D. 6�8 � 2�7 �
E. 4 1�4 � 3 5��12 �
F. 4 8��11 � 21�3 �
G. 12��5 � 9��13 �
H. 3 7�9 � 23�4 �
14. Choose fraction pairs that equal 1. Write number sentences to show thepairs you choose. Use fraction circle pieces.7�8
1�33�4
4�61�8
5��102�8
4�8
Number sentence
Number sentence
Number sentence
Number sentence
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Workshop: Add and Subtract Fractions SAB • Grade 5 • Unit 10 • Lesson 6 417
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15. Make each number sentence true. You cannot use the digits that arealready in each problem.
A. ���5 ����3 � 1 B. 2��� �
3��� � 1�2
C. ���8 �5
��� � 1�2 D. 9��� ����8 � 1
E. 4��� �
4��� � 1�4
F. Explain how you know your answer to Question 15B is correct by usingfraction circle pieces. Draw or describe the pieces you use.
Check-In: Questions 16–17
16. Solve the problems. Show your work.
A. 3�8 � 4�5 B. 5 3�4 � 2 1��16 C. 2 5��12 � 1 2�3
D. Choose one problem from Question 16A–C. Show or tell howestimation can help you check the reasonableness of your answer.
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SAB • Grade 5 • Unit 10 • Lesson 6 Workshop: Add and Subtract Fractions418
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Student Activity Book - Page 418
Copyright © Kendall H
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13. A. 11�15B. 6 1�6C. 7�8D. 26�56E. 5�6F. 213�33G. 36�65H. 619�36
14. 7�8 + 1�8 = 1;1�3 + 4�6 = 1;3�4 + 2�8 = 1;5�10 + 4�8 = 1
15. Answers may vary. Possible responses given.
A. ��5 –��3 = 1
B. 2�� + 3�� = 1�2
C. ��8 + 5�� = 1�2
D. 9�� +��8 = 1
E. 4�� – 4�� = 1�4
F. Possible response: 2�10 + 3�10 = 1�2 with fractioncircle pieces is 2 purples + 3 purples = 1 pink.
16. A. 3�8 + 4�5 =15�40 + 32�40 = 47�40 = 17�40
B. 5 3�4 – 2 1�16 = 23�4 – 33�16 =92�16 – 33�16 = 59�16 = 311�16
C. 2 5�12 + 12�3 = 2 5�12 + 1 8�12 = 313�12 = 4 1�12
D. Responses will vary. Possible response: Myanswer of 4 1�12 is reasonable because 2 5�12 isclose to 2 1�2 . 2 1�2 + 1 2�3 is a little more than 4,like 4 1�12 .
15 6
2
4
10 10
20
18
8 16
TG • Grade 5 • Unit 10 • Lesson 6 • Answer Key 7
Answer Key • Lesson 6: Workshop: Add and Subtract Fractions
SAB • Grade 5 • Unit 10 • Lesson 6 Workshop: Add and Subtract Fractions420
Copyright © Kendall H
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Exp
ec-tation
Ch
eck In
Com
men
ts
E1
E3
E5
E9
E8
E7
E10
Find Fraction Sums and D
ifferencesC
heck-In:Q#
16–17Feedback
BoxFind equivalent fractions. [Q
# 16–17]
Represent addition and subtraction of
fractions with num
ber sentences. [Q# 17]
Solve word problem
s involving addition and subtraction of fractions. [Q
# 17]
Find comm
on denominators and use them
to add and subtract fractions. [Q
# 16–17]
Estimate sum
s and differences of fractions. [Q# 16D
]A
dd and subtract fractions. [Q# 16–17]
Choose from
among estim
ation and com
putation strategies. [Q# 17C
]
Yes . . .
Yes, bu
t . . .N
o, but . . .
No. . .
MP
E2. F
ind
a strategy. I choose good tools and an efficient strategy for solving the problem
. [Q
# 16–17]
MP
E3. C
heck
for reasonablen
ess. I look back at my
solution to see if my answ
er makes sense. If it does
not, I try again. [Q# 16D
]
MPE
1. Kn
ow th
e problem
. I read the problem
carefully. I know the questions to answ
er and what
information is im
portant. [Q# 17]
MP
E5. S
how
my w
ork. I show
or tell how I arrived at
my answ
er so someone else can understand m
y thinking. [Q
# 16–17]
Nam
eDate
Student Activity Book - Page 420
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17. A.* 3 1�2 cups of granola;7�8 + 7�8 + 7�8 + 7�8 = 28�8 = 3 1�2 cups of granola
B.* 1�6 cup more of granola; 3 2�3 – 3 1�2 = 3 4�6 – 3 3�6 = 1�6 cup of granola
C. Answers will vary.
17. John needs to pack carefully because he does not have any extra roomin his small backpack. He wants to pack one serving of granola for eachbreakfast on his hiking trip. One serving of granola is 7�8 cups.
A. How many cups of granola should John pack in a container so thathe and Mark can each have exactly one serving for breakfast for two days? Show how you solved the problem.
Number sentence
B. The container in John’s backpack can hold 3 2�3 cups. How many morecups of granola can he fit into the container? Show how you solvedthe problem.
Number sentence
C. How did you decide whether to estimate or find an exact answer inQuestions 17A and 17B?
Choose to play either Circle Duets to practice adding fractions or the Closest togame to practice estimating and subtracting fractions. Both games are in theStudent Activity Book.
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Workshop: Add and Subtract Fractions SAB • Grade 5 • Unit 10 • Lesson 6 419
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*Answers and/or discussion are included in the lesson.