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[Pages:12]Reteach

Chapter 9

Grade 5

Name

Lesson 1 Reteach

Round Fractions

Round Up If the numerator is almost as large as the denominator, round the number up to the next whole number.

Example:

_9__ 10

rounds

to

1.

9 is almost as large as 10.

_ Round

to

1 2

If the numerator is about half of the

denominator, round the fraction to _12_.

Example:

_3_ 5

rounds

to

_1 _ 2

.

3 is about half of 5.

Date

9 10

0

1

3 5

0

1

Copyright ? The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.

Round Down

If the numerator is much smaller than the

1

denominator, round the number down to

5

the previous whole number.

0

1

Example:

_1_ 5

rounds

to

0.

1 is much smaller than 5.

Round each fraction to 0, --12, or 1. Use a number line if needed.

1.

_ 8 9

2.

_ 1 10

3.

_ 5 8

4.

_ 2 7

5.

_ 9 16

6.

_ 1 12

7.

_ 2 3

8.

_ 5 7

9.

_ 4 9

10.

_ 5 11

11.

_ 1 8

Grade 5 ? Chapter 9 Add and Subtract Fractions

12.

_ 7 8

69

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Date

Lesson 2 Reteach

Add Like Fractions

Follow these steps to add fractions with like denominators.

_ _ Find

3 8

+

1 8

.

Step 1

Add the numerators. Use the like denominator.

_ 3

8

+

_ 1

8

=

_ 4

8

So,

_ 3

8

+

_ 1

8

=

_ 4

8

or

_12 .

Step 2

Write the sum in simplest form. Divide the numerator and denominator by their greatest common factor.

_ 4

8

=

_ 4 ? 4 8 ? 4

or

_ 1

2

Copyright ? The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.

Add. Write each sum in simplest form. Draw a picture or use models to check.

1.

_ 5 7

+

_ 4 7

=

2.

_ 1 4

+

_ 1 4

=

3.

_ 3 10

+

_ 1 10

=

4.

_ 7 8

+

_ 5 8

=

5.

_ 11 12

+

_ 7 12

=

6.

_ 3 10

+

_ 2 10

=

7.

_ 1 3

+

_ 3 3

=

8.

_ 1 2

+

_ 1 2

=

9.

_ 1 9

+

_ 3 9

=

10.

_ 1 7

+

_ 4 7

=

11.

_ 1 10

+

_ 5 10

=

70

12.

_ 1 6

+

_ 3 6

=

Grade 5 ? Chapter 9 Add and Subtract Fractions

Name

Date

Lesson 3 Reteach

Subtract Like Fractions

Follow these steps to subtract fractions with like denominators.

_ _ Find

8 9

-

2 9

.

Step 1

Subtract the numerators. Use the like denominator.

_ 8

9

-

_ 2

9

=

_ 6

9

So,

_ 8

9

-

_ 2

9

=

_ 6

9

or

_23 .

Step 2

Write the difference in simplest form. Divide the numerator and denominator by their greatest common factor.

_ 6 9

=

_ 6 ? 3 9 ? 3

or

_ 2 3

Subtract. Write each difference in simplest form. Draw a picture or use models to check.

1.

_ 5 7

-

_ 4 7

=

2.

_ 3 4

-

_ 1 4

=

Copyright ? The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.

3.

_ 3 10

-

_ 1 10

=

4.

_ 7 8

-

_ 5 8

=

5.

_ 11 12

-

_ 7 12

=

6.

_ 3 10

-

_ 2 10

=

7.

_ 4 6

-

_ 1 6

=

8.

_ 4 5

-

_ 2 5

=

9.

_ 8 9

-

_ 4 9

=

10.

_ 14 15

-

_ 8 15

=

11.

_ 7 8

-

_ 1 8

=

12.

_ 9 10

-

_ 4 10

=

Grade 5 ? Chapter 9 Add and Subtract Fractions

71

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Date

Lesson 5 Reteach

Add Unlike Fractions

When adding fractions with unlike denominators, it helps to write the

problems in vertical form.

_ _ Find

7 8

+

2 . 3

Step 1 Step 2

Find the least common denominator (LCD). Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, . . . Multiples of 8: 8, 16, 24, . . . The LCD is 24.

Rename each fraction using the LCD.

_ 7 8

=

_ 21 24

_ 2 3

=

_ 16 24

Copyright ? The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.

Step 3

Write the problems vertically. Add.

_ 7 8

=

_ 21 24

+

_ 2 3

=

+

_ 16 24

_ 37 24

or

1

_ 13 24

Add. Write each sum in simplest form.

1.

_ 3 8

+

_ 5 6

Multiples of 8:

Multiples of 6:

LCD:

So,

_ 3 8

+

_ 5 6

=

2.

_ 11 12

+

_ 3 4

Multiples of 12:

Multiples of 4:

LCD:

So,

_ 11 12

+

_ 3 4

=

3.

_ 4 5

+

_ 2 3

=

4.

_ 3 5

+

_ 9 10

=

5.

_ 9 10

+

_ 5 6

=

6.

_ 7 10

+

_ 3 4

=

72

7.

_ 5 8

+

_ 2 5

=

8.

_ 3 4

+

_ 5 6

=

Grade 5 ? Chapter 9 Add and Subtract Fractions

Name

Date

Lesson 7 Reteach

Subtract Unlike Fractions

_ _ You can draw models to help subtract fractions with unlike denominators.

Find

3 4

-

1 3

.

Show

models

for

_3 _ 4

and

_1 _ 3

.

_1_

_1_

_1_

_ 3

4

4

4

4

_1_

_ 1

3

3

Find

the

LCD

of

_3 _ 4

and

_13_.

Multiples of 4: 4, 8, 12, ...

Multiples of 3: 3, 6, 9, 12, ...

The

LCD

of

_3 _

4

and

_1 _

3

is

12.

Use models to show how

many

twelfths

are

in

_3 _ 4

,

how many twelfths are

and in _13_.

_1__ _1__ _1__ _1__ _1__ _1__ _1__ _1__ _1__ _3 12 12 12 12 12 12 12 12 12 4

_ 9 12

_1__ _1__ _1__ _1__ _1 12 12 12 12 3

_ 4 12

Take away models to

subtract

_4__ 12

.

So,

_3 _ 4

-

_1_ 3

=

_15_2_.

_1__ _1__ _1__ _1__ _1__ _1__ _1__ _1__ _1__

12 12 12 12 12 12 12 12 12

_ 3 4

-

_ 1 3

_ 9 12

-

_ 4 12

=

_ 5 12

Copyright ? The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.

Use fraction models to subtract the fractions. Write each difference in simplest form.

1.

_ 3 4

-

_ 5 12

2.

_ 1 2

-

_ 2 5

3.

_ 9 10

-

_ 3 5

_ 12

-

_ 12

=

_-_ =

_-_ =

Subtract. Write each difference in simplest form.

4.

_ 1 2

-

_ 3 8

=

5.

_ 5 6

-

_ 7 12

=

6.

_ 11 12

-

_ 1 4

=

7.

_ 2 3

-

_ 1 2

=

8.

_ 9 20

-

_ 2 5

=

9.

_ 7 8

-

_ 1 3

=

Grade 5 ? Chapter 9 Add and Subtract Fractions

73

Name

Date

Lesson 8 Reteach

Problem Solving: Determine Reasonable Answers

Linden

buys

1

_3 _ 4

pounds

of

cashew

nuts

and

1_13_

pounds

of

peanuts.

He

mixes

the nuts together. About how many pounds of nuts are there altogether?

Step 1 Understand

Step 2 Plan

What do you know? ? You know the amount of cashew nuts and the amount of peanuts.

What do you need to find? ? You need to find about how many pounds of nuts there are altogether.

You can use estimation to find a reasonable answer.

Step 3 Solve

Step 4 Check

Round each amount to the nearest whole number. Then add.

1_43 2

1_13 1

Linden bought about 2 + 1 or 3 pounds of nuts.

Is the answer reasonable?

Yes,

because

1_34

+

1_13

=

3

_ 1 12

.

Copyright ? The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.

74

Grade 5 ? Chapter 9 Add and Subtract Fractions

Name

Date

Lesson 8 Reteach

Problem Solving: Determine Reasonable Answers (continued)

Determine a reasonable answer to solve each problem.

1. Renata bought 0.85 pound of pine nuts and 0.9 pound of macadamia nuts. Is 1 pound, 2 pounds, or 2.5 pounds the most reasonable estimate for how many pounds of nuts she purchased altogether?

2.

One container pineapple and

haansot2h_58e_ rphoausn1d_7s8_

of pounds

of pineapple. Sani buys both

containers. Which is the most

reasonable estimate for how many

pounds of pineapple he bought in all:

4 pounds, 5 pounds, or 6 pounds?

Copyright ? The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.

3. From the beginning of a trail, Claire

hiked

4

_3 _ 8

she hiked

miles to the

2

_5 _ 8

miles

to

lake. Then the nature

center. Is 5 miles, 6 miles, or 7 miles

the most reasonable estimate for how

far Claire hiked altogether?

4. At the beginning of the week there were 2.85 pounds of jelly beans in a jar. By the end of the week, there were 1.7 pounds of jelly beans in the jar. Which is the most reasonable estimate for how many jelly beans were eaten during the week: 0.5 pound, 1 pound, or 2 pounds?

5.

In the

morning,

Kevin's

cat eats

_1 _ 2

of

a

can of cat food. In the afternoon, the

cat eats evening,

_1 _ 4

of

the

a can of food.

cat

eats

_4 _ 5

of

a

In the can of

food. Which is the most reasonable

estimate for the amount of food the

cat eats throughout the day: 1 can,

2 cans, or 3 cans?

6. A DVD player costs $154.98. A portable digital music player costs $174.49. Is $15, $20, or $25 the most reasonable estimate for how much more the digital music player costs?

Grade 5 ? Chapter 9 Add and Subtract Fractions

75

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