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Chapter 5Adding and Subtracting Fractions

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Chapter 5Adding and Subtracting Fractions

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http://ca.gr5math.com/

Lesson 5-1 Rounding Fractions and Mixed Numbers

Lesson 5-2 Estimating Sums and Differences

Lesson 5-3 Adding and Subtracting Fractions with Like Denominators

Lesson 5-4 Problem-Solving Strategy: Act It Out

Lesson 5-5 Adding and Subtracting Fractions with Unlike Denominators

Lesson 5-6 Problem-Solving Investigation: Choose the Best Strategy

Lesson 5-7 Adding and Subtracting Mixed Numbers

Lesson 5-8 Subtracting Mixed Numbers with Renaming

55Adding and Subtracting Fractions



Five-Minute Check (over Chapter 4)

Main Idea

California Standards

Key Concept: Rounding to the Nearest Half

Example 1

Example 2

Example 3

Example 4

5-15-1 Rounding Fractions and Mixed Numbers



• I will round fractions and mixed numbers.



Standard 5MR2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

Standard 5NS1.1 Estimate, round, and manipulate very large (e.g., millions) and very small (e.g. thousandths) numbers.





Round 3 to the nearest half.17



The numerator of is much smaller than

the denominator, and is less than .

17

17

14

Answer: So, 3 rounds to 3.17



A. 4

B. 4

C. 4

D. 4







The numerator of is almost as large as

the denominator, and is greater than .

35

35

14

Answer: So, 5 rounds up to 6.35



B. 5

C. 5

D. 6

A. 6



Find the length of the line segment to the nearest half inch.

Answer: To the nearest half inch, the line segment is 1 in. long.




Find the length of the line segment to the nearest half inch.

A. 1 in.

B. 1 in.

C. 1 in.

D. 2 in.



Niraj needs 5 yards of fabric to make a costume.

Should she buy 5 yards or 6 yards of fabric?

Explain your reasoning.

78

12

Answer: She needs to buy 6 yards because 5 is

more than 5 . If she buys 5 yards, she

will not have enough material.

78

12

12



B. 6

A. 6

C. neither

D. 7

Mahatma needs 6 yards of vinyl to cover the

banquet tables. Should he buy 6 yards or 6 yards?

38

12



Five-Minute Check (over Lesson 5-1)

Main Idea


Example 1

Example 2

Example 3

Example 4

Example 5

5-25-2 Estimating Sums and Differences



• I will estimate sums and differences of fractions and mixed numbers.



Standard 5MR2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

Standard 5NS1.1 Estimate, round, and manipulate very large (e.g., millions) and very small (e.g. thousandths) numbers.



Estimate + .49

78

rounds to . rounds to 1.49

78

Answer: So, + is about + 1 or 1 .49

78



Estimate + .38

56

D. 8

14

B. 1 12

A. 1 5

24

C. 1 14



rounds to 1. rounds to 0.1920

Estimate – .1920

15

Answer: So, – is about 1 – 0 or 1.1920

15



A. 1

B.

C. 2

D. 0

Estimate – .45

23



Round 7 to 7. Round 3 to 4.57

Estimate 7 + 3 .15

57

Answer: So, 7 + 3 is about 7 + 4 or 11.15

57


D. 929


A. 9

B. 10

C. 9

Estimate 6 + 2 .23

59



Estimate 9 – .35

47

Round 9 to 9 . Round to .35

47

Answer: So, 9 – is about 9 – or 9.35

47



A. 7

B. 7

C. 6

D. 7

Estimate 7 – .716

37



The electrician wants to make sure he has enough wire for the job, so he rounds up.

An electrician needs a piece of wire 3 feet long for

one job and a piece 1 feet long for another job.

How much wire should she buy for both jobs?

23

56



Answer: So, the electrician needs about 6 feet of wire.

Estimate 4 + 2 = 6

Round 3 to 4 and 1 to 2.56

23


C. 20 feet


A. 19 feet

B. 18 feet

D. 17 feet

A cowboy needs 8 feet of rope to lasso a horse

and 9 feet to lasso a bull. How much rope should

he buy to lasso both?

13

67




Main Idea and Vocabulary


Key Concept: Add Like Fractions

Key Concept: Subtract Like Fractions

Example 1

Example 2

Example 3

5-35-3 Adding and Subtracting Fractions with Like Denominators

Adding and Subtracting Fractions with Like Denominators



• I will add and subtract fractions with like denominators.

• like fractions



Standard 5NS2.3 Solve simple problems, including ones arising in concrete situations, involving the addition and subtraction of fractions and mixed numbers (like and unlike denominators of 20 or less), and express answers in the simplest form.







Find the sum of + .79

39

79

39

Estimate 1 + = 1



79

+ 39

= 7 + 39

Add the numerators.

= 109

= 19

1

Simplify.

Write as a mixed number.

Check for Reasonableness

Compare 1 to the estimate. 1 is about 1 .19

19

12



A. 1

C.

D. 1

Find the sum of + .23

13

B. 36



Find – . Write in simplest form.1215

215

1215

– 215

= 12 – 215

Subtract the numerators.

1015

23

= or Simplify.



C.

D.

B.

A. 39

Find – . Write in simplest form.69

39



1318

– 718

= 13 – 718


618

13

= or Simplify.

During track practice, Casey ran of a mile, and

Ruben ran of a mile. How much farther did

Casey run than Ruben?

1318

718

Answer: Casey ran of a mile further than Ruben.13



D. 1 yard

Joy’s hair is of a yard long. Janelle’s is of

a yard long. How much longer is Joy’s hair than

Janelle’s?

1516

716

A. yard 816

B. yard 12

C. yard 2232




Main Idea


Example 1: Problem-Solving Strategy

5-45-4 Problem-Solving Strategy: Act It Out



• I will solve problems by acting them out.



Standard 5MR2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.



Standard 5NS2.3 Solve simple problems, including ones arising in concrete situations, involving the addition and subtraction of fractions and mixed numbers.



Jacqui is using a roll of craft paper to make five

art projects. Each project uses the same amount

of paper. The roll of craft paper had 11 yards on

it. She already used 2 yards for one project. Is

Jacqui going to have enough paper for four more

projects?

14

58


Understand

What facts do you know?


• The roll of paper had 11 yards on it.

• 2 of the roll of paper was used for one art

project.

• Each project uses the same amount of paper.


Understand

What do you need to find?


• Does Jacqui have enough craft paper for four more art projects?


Plan


Act out the problem by marking the floor to show

a length of 11 yards. Then mark off the amount

used in the first project and continue until there

are a total of five projects marked.


Solve

Answer: There is not enough paper for 4 additional projects.



Check

Look back. You can estimate.


Round 2 to 2 .

2 + 2 + 2 + 2 + 2 = 12

So, 11 yards will not be enough for five

projects.




Main Idea and Vocabulary


Key Concept: Add or Subtract Unlike Fractions

Example 1

Example 2

Example 3

Example 4

5-55-5 Adding and Subtracting Fractions with Unlike Denominators

Common Denominators



• I will add and subtract fractions with unlike denominators.

• unlike fractions








Find + .47

12



One Way: Use a model.

47

12

114+ = 1



Write the problem.

Rename using the LCD, 14.

Add the fractions.

The least common denominator of and is 14.

12

47+

1 × 72 × 7

4 × 27 × 2+

=

=

714

814+

714

814+1514

Another Way: Use the LCD.



Find + .610

38

A. 3940

B. 9

18

C. 7880

D. 1880



Find – .23

25



One Way: Use a model.

23

25

415– =



Another Way: Use the LCD.

Write the problem.


Subtract the fractions.

23

25–

2 × 53 × 5

2 × 35 × 3–

=

=

1015

615–

1510

615–415


23

25



Find – . Write in simplest form. 34

12

A. 22

B. 12

C. 14

D. 28


Use the table to find the fraction of adopted dogs in one town that are either golden retrievers or mixed breed.




Find + . 110

730

The least common denominator of and is 30.110

730

Write the problem.


Add the fractions.

110

730+

1 × 310 × 3

7 × 130 × 1

+ =

= 330

730+

330

730+

1030



Answer: So, of the total adopted dog breeds are

golden retriever or mixed breed.

13



D. 10 pounds

B. 9 pounds

José and his brother each had a jar of marbles.

José’s jar weighs 3 pounds. His brother’s is 5

pounds. How much do their jars weigh altogether?

C. 8 pounds

A. 8 pounds




a – c = 34

13

–

= 3 × 34 × 3

1 × 43 × 4

–

= 912

412

– Simplify.

= 512


ALGEBRA Evaluate a – c if a = and c = .13

Replace a with and c with .13

34

Rename and using the LCD, 12.

13

34



ALGEBRA Evaluate d – f if d = and f = .38

23

B. 7

24

A. 14

C. 13

D. 4

16




Main Idea


Example 1: Problem-Solving Investigation

5-65-6 Problem-Solving Investigation: Choose the Best Strategy



• I will choose the best strategy to solve a problem.



Standard 5MR2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.





STACY: My teacher asked me to find the average monthly precipitation for Redding, California. I found a chart that shows the averages during certain months.



YOUR MISSION: Find the difference between the average precipitation for the month with the greatest average and the month with the lowest average.



Understand

What facts do you know?

• You know the precipitation averages for 3 months.

What do you need to find?

• You need to find the difference between the average precipitation for the month with the greatest average and the month with the lowest average.



Plan

You can use logical reasoning to solve the problem.



Solve

Rewrite each fraction using the LCD, 20.


Order the fractions from least to greatest:

.


Solve

Subtract the lowest average from the greatest average.


So, the difference between the greatest

average and the lowest average is in.


Check


Look back at the problem. Estimate

Since , the answer is reasonable.




Main Idea


Key Concept: Add and Subtract Mixed Numbers

Example 1

Example 2

Example 3

Example 4

Example 5

5-75-7 Adding and Subtracting Mixed Numbers



• I will add and subtract mixed numbers.








Estimate 6 – 3 = 3

Subtract the fractions.

Subtract the whole numbers.

51112

– 29

12

51112

– 29

12

212

32

12

Find 5 – 2 .1112

912



Answer: So, the answer is 3 .16



Find 4 – 2 .68

38

A. 2 28

B. 230

C. 2 38

D. 38



Write the problem.

Rename the fractions using the LCD, 15.

Add the fractions. Then add the whole numbers.

34 1

+53 2

3 × 51 × 5

5 × 32 × 3

155

+156 +

1511

4 155

3 156

7 1511

Find 4 + 3 .13

25

The LCD of and is 15.13

25



B. 6

C. 7

A. 6

Find 5 + 1 .34

18

D. 6 68


First, use the LCD to rename the fractions. Then add.


Answer: So, Jorge jogged 9 miles altogether.1112

Jorge jogged 4 miles on Saturday. He jogged 5

miles on Monday. How many miles did he jog

altogether?

16

34

4 + 5 = 4 + 5 9

12

= 91112



D. 7

C. 1

Emanuel has 3 inches of ribbon. Lolita has 4

inches. How much ribbon do they have altogether?

221

37

A. 4 1121

B. 71121


e – f


= 9 712 – 3 1

4

= 9 712 – 3 3

12

= 6 412

= 6 13

ALGEBRA Evaluate e – f if e = and f = . 9 712 3 1

4

Replace e with and f with .

712

9 14

3

Rename.

Subtract.

Simplify.



ALGEBRA Evaluate c – d if c = 3 and d = 1 . 35

16

B. 23

30

A. 2 36

C. 2 1330

D. 2 2630



g + h = 2 59 + 4 1

2

= 2 1018 + 4 9

18

= 6 1918

= 6

Rename.

Add.

Write as a mixed number.1918

ALGEBRA Evaluate g + h if g = and h = .2 59 4 1

2

Replace g with and h with

.

2 59

4 12

+ 1181

or 7 118



B. 7

D. 8

ALGEBRA Evaluate a + b if a = and b = .3 78 4 3

8

A. 7 108

C. 7 28




Main Idea


Example 1

Example 2

Example 3

5-85-8 Subtracting Mixed Numbers with Renaming



• I will subtract mixed numbers involving renaming.






Find – . 4 38 2 5

8

4 = 3118

38



4 38

2 58

–

3118

2 58

–

Rename as .438

3118

Subtract.1 68



B. 2

C. 2

D. 2

Find 6 – 3 .

A. 3



18 15

10 910

–

18 210

–

Find – . 18 15 10 9

10

Step 1

10 910


18 210


10 910

–

17 1210

–

Step 2

10 910

7 310



B. 5

C. 4

A. 4

D. 4 68

Find 15 – 10 . 38

14



18 34

– 2 78

A new bag of flour contains 18 cups of flour. If a

baker uses cups for a bread recipe, how much

flour is left?

2 78

18 68

– 2 78

17 148

– 2 78

15 78



A new bag of sugar contains 17 cups of sugar. If a

chef uses 3 in a pie, how much sugar is left?

23

89

A. 16 159

B. 1479

C. 13 79

D. 13 159




Five-Minute Checks

Adding and Subtracting Fractions with Like Denominators

Common Denominators


Lesson 5-1 (over Chapter 4)

Lesson 5-2 (over Lesson 5-1)








(over Chapter 4)

Graph the point on a coordinate plane.

A. A

(3, 2)

B. B

C. C

D. D


(over Chapter 4)


(0, 2)

A. A

B. B

C. C

D. D


(over Chapter 4)


(1 , 3)12

A. A

B. B

C. C

D. D


(over Chapter 4)


(4, 3 )12

A. A

B. B

C. C

D. D


C. 12

(over Lesson 5-1)

B. 1

D. 2

Round to the nearest half.59

A. 112


(over Lesson 5-1)

C. 1

D. 4


A. 412

B. 12


A. 7

(over Lesson 5-1)

B. 6

D. 1

C. 612



(over Lesson 5-1)

A. 5

C. 4

D. 1

B. 412



C. 112

(over Lesson 5-2)

B.12

Estimate + .712

89

A. 1

D. 2


B. 1

(over Lesson 5-2)

Estimate – . 1920

15

12A. 1

D. 0

C. 12


D. 7

(over Lesson 5-2)

B. 6 12

A. 6

C. 8

Estimate 4 + 2 .45

17


C. 3

(over Lesson 5-2)

B. 312

A. 4

D. 2

Estimate 7 – 4 .910

1113


D. 114

(over Lesson 5-3)

A.108

B.12

C. 128

Write + in simplest form.78

38


B. 115

(over Lesson 5-3)


35

A.6

10

C. 65

D. 112


A.4

13

(over Lesson 5-3)

D. 4

B. 15

13

C. 14

13

Write – in simplest form.1113

713


C. 12

(over Lesson 5-3)

A.8

16

D. 48


716

B. 16

16


A. Rita, Calvino, Ramla, Alkas, Seki

B. Seki, Calvino, Alkas, Ramla, Rita

C. Seki, Alkas, Ramla, Calvino, Rita

D. Seki, Calvino, Ramla, Alkas, Rita

(over Lesson 5-4)

Use the Act It Out strategy to solve this problem. Ramla is taller than Alkas but shorter than Calvino. Rita is the tallest of the group. Seki is the shortest of the group. Order the students in the group from shortest to tallest.


C. 78

(over Lesson 5-5)


14

A. 1416

B. 68

D. 6

12


B. 12

(over Lesson 5-5)


13

C. 13

A. 29

D. 36


D. 1

15

(over Lesson 5-5)

A. 2115

C. 34


1115

B. 9

15


A. 3

16

(over Lesson 5-5)

B. 12

C. 45


716

D. 14


(over Lesson 5-6)

Use one of these strategies to solve the problem

below: act it out, make a table, guess and check, or

use logical reasoning. To decorate a corridor

exhibit, Alicia needed yd of blue trim, yd of red

trim, and yd of white trim. How many yards of

trim will Alicia use?

910

12

34


B. 2 yd3

20

D. 2 yd

(over Lesson 5-6)

A. yd1316

C. yd4360


C. 934

(over Lesson 5-7)

A.788

B. 968

Write 7 + 2 in simplest form.18

58

D. 938


D. 89

10

(over Lesson 5-7)

A. 87

10

B. 837

Write 5 + 3 in simplest form.25

12

C. 835


B. 727

(over Lesson 5-7)

C. 517

Write 9 – 2 in simplest form.57

37

D. 27

A. 1217


C. 27

12

(over Lesson 5-7)

A. 4

B. 3112

D. 242

Write 4 – 2 in simplest form.56

14

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