5-8 Dividing Fractions and Mixed Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson.

5-8 Dividing Fractions and Mixed Numbers

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm UpMultiply. Write each answer in simplest form.

1. 2 • 2

2. 1 • 3

3. 3 • 3

4. 2 • 1

5

or 5

10

15__

12__

12__

12__

13__

14__

214__

or 2114__ 3

4__

14_


Problem of the Day

Rachel is building a doghouse. She needs to cut a 12-foot-long board into lengths of 65 in. How many lengths can she cut, and will there be any wood left? If so, how much?

2 lengths; yes, 14 in.


MA.6.A.1.2 Multiply and divide fractions…efficiently.

Also MA.6.A.1.3

Sunshine State Standards


Vocabulary

reciprocal

multiplicative inverse


Reciprocals can help you divide by fractions. Two numbers are reciprocals or multiplicative inverses if their product is 1.


Additional Example 1A: Finding Reciprocals

Find the reciprocal.

19__

19__ • = 1 Think: of what number is 1?

19__1

9__

19__ • 9 = 1 of is 1.

19__ 9

1__

The reciprocal of is 9.19__


Additional Example 1B: Finding Reciprocals


23__

23__ • = 1 Think: of what number is 1?

23__

32__2

3__ • = = 1

66__ of is 1.

23__ 3

2__

The reciprocal of is .23__ 3

2__


15__

165__ • = 1 Write 3 as . 1

5__

516__16

5__ • = = 1

8080__ of is 1.

165__ 5

16__

The reciprocal of is .165__ 5

16__

165__

Additional Example 1C: Finding Reciprocals


3


Check It Out: Example 1A

Find each reciprocal.

18__4

418__

=338__

;833__


Check It Out: Example 1B


5

5 =51__ ; 1

5__


Check It Out: Example 1C


14__2

214__

=94__

;49__


Look at the relationship between the

fractions and . If you switch the

numerator and denominator of a fraction,

you will find its reciprocal. Dividing by a

number is the same as multiplying by its

reciprocal.

34__ 4

3__

24 ÷ 4 = 6 24 • = 614__


Additional Example 2A: Using Reciprocals to Divide Fractions and Mixed Numbers

Divide. Write each answer in simplest form.

÷ 7 87__

87__ ÷ 7 = •

Rewrite as multiplication using the

reciprocal of 7, . 17__

Multiply by the reciprocal.

87

__ 17__

8 • 17 • 7____ =

The answer is in simplest form.

=

849__


When you divide by a proper fraction, the quotient will be greater than the dividend. For example, since there are 8 halves in 4, 4 ½ = 8.

Caution!


Additional Example 2B: Using Reciprocals to Divide Fractions and Mixed Numbers

÷ 56__

56__ ÷ = •

Rewrite as multiplication using the

reciprocal of , . 32__

Simplify before multiplying.

56

__ 32__

5 • 36 • 2____ =

You can write the answer as a mixed number.

=

54__

23__

23__

23__

1

2

Multiply.

= 1

14__


Additional Example 2C: Using Reciprocals to Divide Fractions and Mixed Numbers

2 ÷ 1 34__

Write the mixed numbers as

improper fractions. 2 =

and 1 = 1312__

Rewrite as multiplication.

11 • 12

4 • 13______

=

You can write the answer as a mixed number.

=

3313__

112__

34__

1

3Simplify before multiplying.

= 2

713__

2 ÷ 1 = ÷34

__ 112__ 11

4__ 13

12__ 11

4__

112__

11

4__ 12

13__ •

Multiply. =


Check It Out: Example 2A


710__ 1

5__

÷

710__ 5

1__.

3510__

12__3


Check It Out: Example 2B


34__ 1

8__

÷

74__ 8

1__.

564__

14

1


Check It Out: Example 2C


15__ 1

2 __

÷

115__ 33

2__

215__

2 16

÷

115__ 2

33__.


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz


1. 2.


3. ÷ 20 4. 3 ÷ 2

5. Rhonda put 2 pounds of pecans into -pound

bags. How many bags did Rhonda fill?

111__ 8

13__

47__ 1

2__ 1

2__

34__ 1

4__

111__ 13

8__

135__ 7

5 __ 2

5__, or 1

11 bags


1. Identify the reciprocal of .

A. –15 C.

B. D. 15



2. Identify the reciprocal of .

A. 15 C.

B. 7 D.



3. Divide and identify the answer in the simplest form.

A. C.

B. D.



4. Divide and identify the answer in the simplest form.

A. C.

B. D.



5. In his pet care center, Nelson has pounds

of cat food. He plans to feed a cat with pound

of cat food. How many cats can he feed?

A. 13 cats C. 11 cats

B. 12 cats D. 10 cats


5-8 Dividing Fractions and Mixed Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson.

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