5-6 Dividing Fractions and Mixed Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson.

5-6 Dividing Fractions and Mixed Numbers

Warm Up

Lesson Presentation

Problem of the Day

Lesson 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.


Learn to divide fractions and mixed numbers.


Vocabulary

reciprocal

multiplicative inverse


Reciprocals can help you divide by fractions. Two numbers are reciprocals 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__

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__


16__

165__

Additional Example 1C: Finding Reciprocals


3


Check It Out: Example 1A


14__


14__

14__ • 4 = 1 of is 1.

14__ 4

1__

The reciprocal of is 4.14__


Check It Out: Example 1B


45__


45__

54__4

5__ • = = 1

2020__ of is 1.

45__ 5

4__


4__


18__

338__ • = 1 Write 4 as . 1

8__

833__33

8__ • = = 1

264 264___ of is 1.

338__ 8

33__


33__

338

__

Check It Out: Example 1C


4


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__ ÷ = •


reciprocal of , . 32__

Simplify before multiplying.

56

__ 32__

5 • 36 • 2____ =

You can write the answer as a mixed number.

=

54__

23__

23__ 2

3__

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______

=


=

3313__

112__

34__

1

3Simplify before multiplying.

= 2

713__

2 ÷ 1 = ÷3

4__ 1

12__ 11

4__ 13

12__ 11

4__

112__

11

4__ 12

13__ •

Multiply. =


Check It Out: Example 2A


÷ 3 23__

23__ ÷ 3 = •


reciprocal of 3, . 13__

Multiply by the reciprocal.

23

__ 13__

2 • 13 • 3____ =

The answer is in simplest form.

=

29__


Check It Out: Example 2B

÷ 710__

710__ ÷ = •


reciprocal of , . 51__

Simplify before multiplying.

710__ 5

1__

7 • 510 • 1____ =


=

72__

15__

15__ 1

5__

1

2

Multiply.

= 3 12__


Check It Out: Example 2C

3 ÷ 1 23__

Write the mixed numbers as

improper fractions. 3 =

and 1 = . 109__

Rewrite as multiplication.

11 • 9

3 • 10______

=


=

3310__

19__

23__

1

3Simplify before multiplying.

= 3

310__

3 ÷ 1 = ÷2

3__ 1

9__ 11

3__ 10

9__ 11

3__

19__

11

3__ 9

10__ •

Multiply. =


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 a -pound

bag. 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 her 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


5-6 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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