3-7 Dividing Fractions and Mixed Numbers

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

3-7 Dividing Fractions and Mixed Numbers

Warm UpMultiply.

1. 7 9

· 36

2. 98

· 65

3. 15

2 ·7

4. 212

· 114

7182720

720

or 1

2775 5

or 15

258 8

or 3 1

3-7 Dividing Fractions and Mixed Numbers

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

3-7 Dividing Fractions and Mixed Numbers

Learn to divide fractions and mixed numbers.

3-7 Dividing Fractions and Mixed Numbers

Vocabulary

reciprocal

3-7 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.

2 ÷ 13

= 2 · 3 = 6

3-7 Dividing Fractions and Mixed Numbers

Additional Example 1: Dividing Fractions

Divide. Write each answer in simplest form.

A. 37 ÷ 2

537

÷ 25

= 37 ·

52

= 37

· 5· 2

=1514

or 1141

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.

3-7 Dividing Fractions and Mixed Numbers

Check 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.

14

Simplify.

3-7 Dividing Fractions and Mixed Numbers

Divide. Write each answer in simplest form.

A. 523

÷ 114

5 23

÷ 114

= 17 3

÷ 54

= 17 3

· 45

= 6815

or 4 815

Write mixed numbers as improperfractions.

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

3-7 Dividing Fractions and Mixed Numbers

Divide. Write the answer in simplest form.

Additional Example 2: Dividing Mixed Numbers

C. 8 23

÷ 1327

8 23

÷ 1327

= 26 3

÷ 1327

= 26 3

· 2713

9

1

2

1

= 18 1

or 18

Write 8 as an improper fraction.23

Multiply by the reciprocal of . 1327

=26 3

· 2713·

3-7 Dividing Fractions and Mixed Numbers

Divide. Write each answer in simplest form.

A. 323

÷ 112

3 23

÷ 112

= 11 3

÷ 32

= 11 3

· 23

= 22 9

or 2 4 9

Write mixed numbers as improperfractions.

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

3-7 Dividing Fractions and Mixed Numbers

Divide. Write the answer in simplest form.

Check It Out: Example 2

C. 7 15

÷ 18 5

7 15

÷ 18 5

= 36 5

÷ 18 5

= 36 5

· 5_18

1

1

2

1

= 21

or 2

Write 7 as an improper fraction.15

Multiply by the reciprocal of . 18 5

= 36 5

· 518·

3-7 Dividing Fractions and Mixed Numbers

Additional 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.

·

3-7 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.

·

3-7 Dividing Fractions and Mixed Numbers

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

3-7 Dividing Fractions and Mixed Numbers

Lesson 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

3-7 Dividing Fractions and Mixed Numbers

1. Divide. Write your answer in simplest form.

10 ÷

A. 6

B. 18

C. 12

D. 24

Lesson Quiz for Student Response Systems

5 6

3-7 Dividing Fractions and Mixed Numbers

2. Divide. Write your answer in simplest form.

÷

A. or 4 C.

B. or 2 D.

Lesson Quiz for Student Response Systems

20 5

20 7

4 35

3 35

4 7

1 5

6 7

3-7 Dividing Fractions and Mixed Numbers

3. Divide. Write your answer in simplest form.

÷ 15

A. or 9 C.

B. 24 D. or

Lesson Quiz for Student Response Systems

75 8

1 24

3 15

5 8

3 8

1 5

3-7 Dividing Fractions and Mixed Numbers

4. Multiply. Write your answer in simplest form.

3 ÷ 5

A. C. or 1

B. D. 27

Lesson Quiz for Student Response Systems

50

8123

27

81

50

1 3

2 5

31

50

3-7 Dividing Fractions and Mixed Numbers

5. A blacksmith has 6 pounds of iron with

him. If it takes of a pound to make one

lock, how many locks can he make from the iron?

A. 9 locks

B. 11 locks

C. 12 locks

D. 13 locks

Lesson Quiz for Student Response Systems

1 2

1 2