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This pdf includes the division of mixed numbers (mixed numerals) and how to divide them with examples for better understanding.

1.
5-9

5-9 Dividing

DividingFractions

Fractionsand

andMixed

MixedNumbers

Numbers

Warm Up

Problem of the Day

Lesson Presentation

L-12

6.NS.1

Course1 1

5-9 Dividing

DividingFractions

Fractionsand

andMixed

MixedNumbers

Numbers

Warm Up

Problem of the Day

Lesson Presentation

L-12

6.NS.1

Course1 1

2.
5-9 Dividing Fractions and Mixed Numbers

Warm Up

Multiply. Write each answer in simplest

form.

1

1. 2 __ • 2 5

2

1

2. 1 __

2

• 3 __

1 __ or 5 1

21 _

2 4 4

1

3. 3 __

3

•3 10

4. 1

__

25 • 1

__

14 11 3

__ or 2 __

4 4

Course 1

Warm Up

Multiply. Write each answer in simplest

form.

1

1. 2 __ • 2 5

2

1

2. 1 __

2

• 3 __

1 __ or 5 1

21 _

2 4 4

1

3. 3 __

3

•3 10

4. 1

__

25 • 1

__

14 11 3

__ or 2 __

4 4

Course 1

3.
5-9 Dividing Fractions and Mixed Numbers

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 cuts; yes, 14 in.

Course 1

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 cuts; yes, 14 in.

Course 1

4.
5-9 Dividing Fractions and Mixed Numbers

Learn to divide fractions and mixed

numbers.

Course 1

Learn to divide fractions and mixed

numbers.

Course 1

5.
5-9 Dividing Fractions and Mixed Numbers

Vocabulary

reciprocal

Course 1

Vocabulary

reciprocal

Course 1

6.
5-9 Dividing Fractions and Mixed Numbers

Reciprocals can help you divide

by fractions. Two numbers are

reciprocals if their product is 1.

Copy to Notebook!

Course 1

Reciprocals can help you divide

by fractions. Two numbers are

reciprocals if their product is 1.

Copy to Notebook!

Course 1

7.
5-9 Dividing Fractions and Mixed Numbers

Additional Example 1A: Finding Reciprocals

Find the reciprocal.

1

__

9

1

__ 1

__

• = 1 Think: 9 of what number is 1?

9

1

__ 1

__ 9

__

• 9 =1 of is 1.

9 9 1

1

__

The reciprocal of 9 is 9.

Course 1

Additional Example 1A: Finding Reciprocals

Find the reciprocal.

1

__

9

1

__ 1

__

• = 1 Think: 9 of what number is 1?

9

1

__ 1

__ 9

__

• 9 =1 of is 1.

9 9 1

1

__

The reciprocal of 9 is 9.

Course 1

8.
5-9 Dividing Fractions and Mixed Numbers

Additional Example 1B: Finding Reciprocals

Find the reciprocal.

2

__

3

2

__ 2

__

• =1 Think: 3 of what number is 1?

3

2 __3 6 2

__ 3

__ • = __ =1 of __ is 1.

3 2 6 3 2

2

__ 3

__

The reciprocal of 3 is 2 .

Course 1

Additional Example 1B: Finding Reciprocals

Find the reciprocal.

2

__

3

2

__ 2

__

• =1 Think: 3 of what number is 1?

3

2 __3 6 2

__ 3

__ • = __ =1 of __ is 1.

3 2 6 3 2

2

__ 3

__

The reciprocal of 3 is 2 .

Course 1

9.
5-9 Dividing Fractions and Mixed Numbers

Additional Example 1C: Finding Reciprocals

Find the reciprocal.

1

3 __

5

1 16

16

__ • =1 Write 3 __ as __.

5 5 5

16 5

__ • __ 80 16 5

__ of __

= __ = 1 is 1.

5 16 80 5 16

16 5

The reciprocal of __ is __ .

5 16

Course 1

Additional Example 1C: Finding Reciprocals

Find the reciprocal.

1

3 __

5

1 16

16

__ • =1 Write 3 __ as __.

5 5 5

16 5

__ • __ 80 16 5

__ of __

= __ = 1 is 1.

5 16 80 5 16

16 5

The reciprocal of __ is __ .

5 16

Course 1

10.
5-9 Dividing Fractions and Mixed Numbers

Check It Out: Example 1A

Find the reciprocal.

1

__

4

1

__ 1

__

• =1 Think: 4 of what number is 1?

4

1 1

__ 4

__ • 4 =1 of __is 1.

4 4 1

1

__

The reciprocal of 4 is 4.

Course 1

Check It Out: Example 1A

Find the reciprocal.

1

__

4

1

__ 1

__

• =1 Think: 4 of what number is 1?

4

1 1

__ 4

__ • 4 =1 of __is 1.

4 4 1

1

__

The reciprocal of 4 is 4.

Course 1

11.
5-9 Dividing Fractions and Mixed Numbers

Check It Out: Example 1B

Find the reciprocal.

4

__

5

4

__ 4

__

• =1 Think: 5 of what number is 1?

5

4 __5 20 4

__ 5

__ • = __ = 1 of __ is 1.

5 4 20 5 4

4

__ 5

__

The reciprocal of 5 is 4 .

Course 1

Check It Out: Example 1B

Find the reciprocal.

4

__

5

4

__ 4

__

• =1 Think: 5 of what number is 1?

5

4 __5 20 4

__ 5

__ • = __ = 1 of __ is 1.

5 4 20 5 4

4

__ 5

__

The reciprocal of 5 is 4 .

Course 1

12.
5-9 Dividing Fractions and Mixed Numbers

Check It Out: Example 1C

Find the reciprocal.

1

4 __

8

33 1 33.

Write 4 __ as __

__ • =1

8 8 8

33 8

__ • __ 264 33 8

__ of __

= ___ = 1 is 1.

8 33 264 8 33

33

__ 8

__

The reciprocal of 8 is 33 .

Course 1

Check It Out: Example 1C

Find the reciprocal.

1

4 __

8

33 1 33.

Write 4 __ as __

__ • =1

8 8 8

33 8

__ • __ 264 33 8

__ of __

= ___ = 1 is 1.

8 33 264 8 33

33

__ 8

__

The reciprocal of 8 is 33 .

Course 1

13.
5-9 Dividing Fractions and Mixed Numbers

Look at the relationship between the

3

__ 4

__

fractions 4 and 3 . 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.

1

__

24 ÷ 4 = 6 24 • 4 = 6

Copy to Notebook!

Course 1

Look at the relationship between the

3

__ 4

__

fractions 4 and 3 . 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.

1

__

24 ÷ 4 = 6 24 • 4 = 6

Copy to Notebook!

Course 1

14.
5-9 Dividing Fractions and Mixed Numbers

Additional Example 2A: Using Reciprocals to

Divide Fractions and Mixed Numbers

Divide. Write each answer in simplest form.

8

__ ÷7

7

8

__ 8 1 Rewrite as multiplication using the

÷ 7 =__ • __ 1

__

7 7 7 reciprocal of 7, .

7

8•1

= ____ Multiply by the reciprocal.

7•7

8

= __ The answer is in simplest form.

49

Course 1

Additional Example 2A: Using Reciprocals to

Divide Fractions and Mixed Numbers

Divide. Write each answer in simplest form.

8

__ ÷7

7

8

__ 8 1 Rewrite as multiplication using the

÷ 7 =__ • __ 1

__

7 7 7 reciprocal of 7, .

7

8•1

= ____ Multiply by the reciprocal.

7•7

8

= __ The answer is in simplest form.

49

Course 1

15.
5-9 Dividing Fractions and Mixed Numbers

Additional Example 2B: Using Reciprocals to

Divide Fractions and Mixed Numbers

5 2

__ ÷ __

6 3

5 __

__ 2 __5 3 Rewrite as multiplication using the

÷ = •__ 2

__ 3

__

6 3 6 2 reciprocal of 3 , 2 .

1

5•3

= ____ Simplify before multiplying.

6•2

2

5

= __ Multiply.

4

1

__ You can write the answer as a

=1

4 mixed number.

Course 1

Additional Example 2B: Using Reciprocals to

Divide Fractions and Mixed Numbers

5 2

__ ÷ __

6 3

5 __

__ 2 __5 3 Rewrite as multiplication using the

÷ = •__ 2

__ 3

__

6 3 6 2 reciprocal of 3 , 2 .

1

5•3

= ____ Simplify before multiplying.

6•2

2

5

= __ Multiply.

4

1

__ You can write the answer as a

=1

4 mixed number.

Course 1

16.
5-9 Dividing Fractions and Mixed Numbers

Additional Example 2C: Using Reciprocals to

Divide Fractions and Mixed Numbers

3 1

2 __ ÷ 1 __

4 12

Write the mixed numbers as

3 1 11 13 3 11

2 __ ÷ 1 __ = __ ÷ __ improper fractions. 2 __ = __

4 12 4 12 1 13 4 4

and 1 __ = __

12 12

11 12

= __ • __ Rewrite as

4 13 multiplication.

11 • 123

______

= Simplify before multiplying.

4 • 13

1

33

= __ Multiply.

13

7

__ You can write the answer as a

=2

13 mixed number.

Course 1

Additional Example 2C: Using Reciprocals to

Divide Fractions and Mixed Numbers

3 1

2 __ ÷ 1 __

4 12

Write the mixed numbers as

3 1 11 13 3 11

2 __ ÷ 1 __ = __ ÷ __ improper fractions. 2 __ = __

4 12 4 12 1 13 4 4

and 1 __ = __

12 12

11 12

= __ • __ Rewrite as

4 13 multiplication.

11 • 123

______

= Simplify before multiplying.

4 • 13

1

33

= __ Multiply.

13

7

__ You can write the answer as a

=2

13 mixed number.

Course 1

17.
5-9 Dividing Fractions and Mixed Numbers

Check It Out: Example 2A

Divide. Write each answer in simplest form.

2

__ ÷3

3

2

__ 2 1 Rewrite as multiplication using the

÷ 3 =__ • __ 1

__

3 3 3 reciprocal of 3, .

3

2•1

= ____ Multiply by the reciprocal.

3•3

2

= __ The answer is in simplest form.

9

Course 1

Check It Out: Example 2A

Divide. Write each answer in simplest form.

2

__ ÷3

3

2

__ 2 1 Rewrite as multiplication using the

÷ 3 =__ • __ 1

__

3 3 3 reciprocal of 3, .

3

2•1

= ____ Multiply by the reciprocal.

3•3

2

= __ The answer is in simplest form.

9

Course 1

18.
5-9 Dividing Fractions and Mixed Numbers

Check It Out: Example 2B

7 1

__ ÷ __

10 5

7

__ 1 __

__ 7 5

__ Rewrite as multiplication using the

÷ = • 1 __

__ 5

10 5 10 1 reciprocal of 5 , 1 .

1

7•5

= ____ Simplify before multiplying.

10 • 1

2

7

= __ Multiply.

2

1 You can write the answer as a

= 3 __

2 mixed number.

Course 1

Check It Out: Example 2B

7 1

__ ÷ __

10 5

7

__ 1 __

__ 7 5

__ Rewrite as multiplication using the

÷ = • 1 __

__ 5

10 5 10 1 reciprocal of 5 , 1 .

1

7•5

= ____ Simplify before multiplying.

10 • 1

2

7

= __ Multiply.

2

1 You can write the answer as a

= 3 __

2 mixed number.

Course 1

19.
5-9 Dividing Fractions and Mixed Numbers

Check It Out: Example 2C

2 1

3 __ ÷ 1 __

3 9

2

__ 1

__ 11

__ 10 Write the mixed numbers as

__

3 ÷1 = ÷ 2

__ 11

__

3 9 3 9 improper fractions. 3 =

3 3

1

__ 10

__

and 1 = .

9 9

11 9

= __ • __ Rewrite as

3 10 multiplication.

11 • 9 3

______

= Simplify before multiplying.

3 • 10

1

33

= __ Multiply.

10

3

__ You can write the answer as a

=3

10 mixed number.

Course 1

Check It Out: Example 2C

2 1

3 __ ÷ 1 __

3 9

2

__ 1

__ 11

__ 10 Write the mixed numbers as

__

3 ÷1 = ÷ 2

__ 11

__

3 9 3 9 improper fractions. 3 =

3 3

1

__ 10

__

and 1 = .

9 9

11 9

= __ • __ Rewrite as

3 10 multiplication.

11 • 9 3

______

= Simplify before multiplying.

3 • 10

1

33

= __ Multiply.

10

3

__ You can write the answer as a

=3

10 mixed number.

Course 1

20.
5-9 Dividing Fractions and Mixed Numbers

Lesson Quiz

Find the reciprocal.

1

__ 11

__ 8

__ 13

__

1. 2.

13 8

11 1

Divide. Write each answer in simplest form.

4 1

__ 13 1 __ 2

7 , or 1 __

3. __ ÷ 20 4.__ ÷__

2 5

7 35 2 2 5

3

__ 1

__

5. Rhonda put 2 4 pounds of pecans into a 4 -pound

bag. How many bags did Rhonda fill?

11 bags

Course 1

Lesson Quiz

Find the reciprocal.

1

__ 11

__ 8

__ 13

__

1. 2.

13 8

11 1

Divide. Write each answer in simplest form.

4 1

__ 13 1 __ 2

7 , or 1 __

3. __ ÷ 20 4.__ ÷__

2 5

7 35 2 2 5

3

__ 1

__

5. Rhonda put 2 4 pounds of pecans into a 4 -pound

bag. How many bags did Rhonda fill?

11 bags

Course 1