Holt CA Course 1

4-5 Dividing Fractions and Mixed Numbers

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Holt CA Course 1

4-5 Dividing Fractions and Mixed Numbers

Warm UpMultiply.

1.

2.

3.

4.

718

2720

720

or 1

2775 5

or 15

258 8

or 3 1

Holt CA Course 1

4-5 Dividing Fractions and Mixed Numbers

NS2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation.Also covered: NS2.2, NS2.4

California Standards

Holt CA Course 1

4-5 Dividing Fractions and Mixed Numbers

Reciprocals can help you divide by fractions. Two numbers are reciprocals or multiplicative inverses if their product is 1. The reciprocal of is 3 because

13

13

3= 13

31

= 33

= 1.

Dividing by a number is the same as multiplying by its reciprocal.

6 ÷ 3 = 26 ÷ 3 = 2 13

6 6 = 2 = 2

same answer

reciprocals

Holt CA Course 1

4-5 Dividing Fractions and Mixed Numbers

You can use this rule to divide by fractions.

Holt CA Course 1

4-5 Dividing Fractions and Mixed Numbers

Vocabularyreciprocal

multiplicative inverse

Holt CA Course 1

4-5 Dividing Fractions and Mixed NumbersAdditional Example 1: Dividing Fractions

Divide. Write each answer in simplest form.

A. 37 ÷ 2

537

÷ 25

= 37 ·

52

= 37

· 5· 2

=1514

or 114

1

Multiply by the reciprocal of . 25

B. 38

÷ 12

38

÷ 12 =38

· 112

=38

· 112

1

4

=

Multiply by the reciprocal of 12.

132

Simplify.

Holt CA Course 1

4-5 Dividing Fractions and Mixed Numbers

Divide. Write each answer in simplest form.

A. 523

÷ 1 14

5 23

÷ 114

= 17 3

÷ 54

= 17 3

· 45

= 6815

or 4 815

Write mixed numbers as improper fractions.

Multiply by the reciprocal of 54

B. 34

÷ 212

34

÷ 2 12

= 34

÷ 52

= 34

· 25

=3 · 24 · 5

1

2= 3

10

Write 2 as an improper fraction.12

Multiply by the reciprocal of . 52

Simplify.

.

Additional Example 2: Dividing Mixed Numbers

Holt CA Course 1

4-5 Dividing Fractions and Mixed NumbersAdditional Example 3: Social Studies Application

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

paper currency lasts an average of 1 years. How many12

times longer will the golden dollar stay in circulation?

30 ÷ 1 12

= 30 1

÷ 32

Write the number as an improper fraction.

=30 1

· 23

Multiply by the reciprocal of .32

= ·Simplify.

30 21 3

10

1= 20

1or 20

The golden dollar will stay in circulation about20 times longer than paper currency.

·

Holt CA Course 1

4-5 Dividing Fractions and Mixed NumbersCheck It Out! Example 1

Divide. Write each answer in simplest form.

A. 35 ÷ 1

235

÷ 12

= 35 ·

21

= 35

· 2· 1

=65

or 151

Multiply by the reciprocal of . 12

B. 34

÷ 3

34

÷ 3 = 34

· 13

=34

· 13

1

1

Multiply by the reciprocal of 3.

1= 4

Simplify.

Holt CA Course 1

4-5 Dividing Fractions and Mixed Numbers

Divide. Write each answer in simplest form.

A. 323

÷ 1 12

3 23

÷ 112

= 11 3

÷ 32

= 11 3

· 23

= 22 9

or 2 4 9

Write mixed numbers as improper fractions.

Multiply by the reciprocal of 32

B. 35

÷ 125

35

÷ 1 25

= 35

÷ 75

= 35

· 57

=3 · 55 · 7

1

1

= 3 7

Write 1 as an improper fraction.25

Multiply by the reciprocal of . 75

Simplify.

.

Check It Out! Example 2

Holt CA Course 1

4-5 Dividing Fractions and Mixed Numbers

Check It Out! Example 3

The average life of a queen ant is approximately 3 years.The life span of a worker ant is year. How many 3

7times longer will the queen ant live?

3 ÷ 37

= 31

÷37 Write the number as an improper fraction.

=31

· 73

Multiply by the reciprocal of .37

= · Simplify.3 71 3

1

1= 7

1or 7

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

·

Holt CA Course 1

4-5 Dividing Fractions and Mixed NumbersLesson Quiz

10

Divide. Write each answer in simplest form.

1.

2.

8 ÷ 45

59

÷ 18

3. 35

÷ 6

5. There are 5 14

yards of silk in a roll. If it takes 34

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

7

4 49

40 9

or

110

34. 212

÷ 17

3544