4-8 Dividing Fractions and Mixed Numbers

Course 2

Warm Up

Problem of the Day

Lesson Presentation

Warm Up Multiply.

Course 2

4-8 Dividing Fractions and Mixed Numbers

1. 7 9

· 3 6

2. 9 8

· 6 5

3. 1 5

2 · 7

4. 2 1 2

· 1 4

7

18

27 20

7

20 or 1

2 77

5 5 or 15

5

8

Problem of the Day

The Jeffers family is putting in a new fence around their yard. The yard is in the shape of a square. If they put nine fence posts on each side of the square, how many posts will be used?

32

Course 2

4-8 Dividing Fractions and Mixed Numbers

Learn to divide fractions and mixed

numbers.

Course 2

4-8 Dividing Fractions and Mixed Numbers

Vocabulary

reciprocal

Insert Lesson Title Here

Course 2

4-8 Dividing Fractions and Mixed Numbers

Course 2

4-8 Dividing Fractions and Mixed Numbers

When you divide 8 by 4 you find how many 4’s there are in 8. Similarly, when you divide

2 by , you find how many ’s there are in 2. 1 3

1 3

There are six ’s in 2. 1 3

Course 2

4-8 Dividing Fractions and Mixed Numbers

Reciprocals can help you divide by fractions. Two numbers are reciprocals if their product

is 1. The reciprocal of is 3 because 1 3

1 3

· 3 = 1 3

· 3 1

= 3 3

= 1.

To divide by a fraction, find its reciprocal and then multiply.

2 ÷ 1 3

= 2 · 3 = 6

Additional Example 1A & 1B: Dividing Fractions

Divide. Write each answer in simplest form.

A. 3 7

÷ 2 5

3 7

÷ 2 5

= 3 7

· 5 2

= 3 7

· 5 · 2

= 15 14

or 1 14

1

Multiply by the reciprocal of . 2 5

B. 3 8

÷ 12

3 8

÷ 12 = 3 8

· 1 12

= 3 8

· 1 12

1

4

=

Multiply by the reciprocal of 12.

1 32

Course 2

4-8 Dividing Fractions and Mixed Numbers

Simplify.

Try This: Example 1A & 1B

Divide. Write each answer in simplest form.

A. 3 5

÷ 1 2

3 5

÷ 1 2

= 3 5

· 2 1

= 3 5

· 2 · 1

= 6 5

or 1 5

1

Multiply by the reciprocal of . 1 2

B. 3 4

÷ 3

3 4

÷ 3 = 3 4

· 1 3

= 3 4

· 1 3

1

1

=

Multiply by the reciprocal of 3.

1 4

Course 2

4-8 Dividing Fractions and Mixed Numbers

Simplify.

Divide. Write each answer in simplest form.

Insert Lesson Title Here

Course 2

4-8 Dividing Fractions and Mixed Numbers

A. 5 2 3

÷ 1 1 4

5 2 3

÷ 1 1 4

= 17 3

÷ 5 4

= 17 3

· 4 5

= 68 15

or 4 8 15

Write mixed numbers as improper fractions.

Multiply by the reciprocal of 5 4

B. 3 4

÷ 2 1 2

3 4

÷ 2 1 2

= 3 4

÷ 5 2

= 3 4

· 2 5

= 3 · 2

4 · 5

1

2 = 3

10

Write 2 as an improper fraction. 1 2

Multiply by the reciprocal of .

5 2

Simplify.

.

Additional Example 2A & 2B: Dividing Mixed Numbers

Divide. Write the answer in simplest form.

Additional Example 2C: Dividing Mixed Numbers

Course 2

4-8 Dividing Fractions and Mixed Numbers

C. 8 2 3

÷ 13 27

8 2 3

÷ 13 27

= 26 3

÷ 13 27

= 26 3

· 27 13

9

1

2

1

= 18 1

or 18

Write 8 as an improper fraction. 2 3

Multiply by the reciprocal of . 13 27

= 26 3

· 27 13 ·

Divide. Write each answer in simplest form.

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Course 2

4-8 Dividing Fractions and Mixed Numbers

A. 3 2 3

÷ 1 1 2

3 2 3

÷ 1 1 2

= 11 3

÷ 3 2

= 11 3

· 2 3

= 22 9

or 2 4 9

Write mixed numbers as improper fractions.

Multiply by the reciprocal of 3 2

B. 3 5

÷ 1 2 5

3 5

÷ 1 2 5

= 3 5

÷ 7 5

= 3 5

· 5 7

= 3 · 5

5 · 7

1

1 = 3

7

Write 1 as an improper fraction. 2 5

Multiply by the reciprocal of .

7 5

Simplify.

.

Try This: Example 2A & 2B

Divide. Write the answer in simplest form.

Try This: Example 2C

Course 2

4-8 Dividing Fractions and Mixed Numbers

C. 7 1 5

÷ 18 5

7 1 5

÷ 18 5

= 36 5

÷ 18 5

= 36 5

· 5_ 18

1

1

2

1

= 2 1

or 2

Write 7 as an improper fraction. 1 5

Multiply by the reciprocal of . 18 5

= 36 5

· 5 18 ·

Additional Example 3: Social Studies Application

Course 2

4-8 Dividing Fractions and Mixed Numbers

The life span of a golden dollar coin is 30 years, while

paper currency lasts an average of 1 years. How many

1 2

times longer will the golden dollar stay in circulation?

30 ÷ 1 1 2

= 30 1

÷ 3 2

Write the number as an improper fraction.

= 30 1

· 2 3

Multiply by the reciprocal of . 3 2

= ·

Simplify. 30 2

1 3

10

1

= 20 1

or 20

The golden dollar will stay in circulation about 20 times longer than paper currency.

·

Try This: Example 3

Course 2

4-8 Dividing Fractions and Mixed Numbers

The average life of a queen ant is approximately 3 years.

The life span of a worker ant is year. How many

3 7

times longer will the queen ant live?

3 ÷ 3 7

= 3 1

÷ 3 7

Write the number as an improper fraction.

= 3 1

· 7 3

Multiply by the reciprocal of . 3 7

= · Simplify.

3 7

1 3

1

1

= 7 1

or 7

The queen ant will live 7 times longer than the worker ant.

·

Lesson Quiz

10

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Course 2

4-8 Dividing Fractions and Mixed Numbers

Divide. Write each answer in simplest form.

1.

2.

8 ÷ 4 5

5 9

÷ 1 8

3. 3 5

÷ 6

4. 2 1 2

÷

5. There are 5 1 4

yards of silk in a roll. If it takes 3 4

of a yard to make one designer scarf, how many scarves can be made from the roll?

7

4 4 9

40 9

or

1 10

3 1 7

35

44