3-11 Dividing Fractions and Mixed Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation...

3-11 Dividing Fractions and Mixed Numbers

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm UpMultiply.

1. 79

· 36

2.98

· 65

3.15

2 ·7

4. 212

· 114

7182720

720

or 1

2775 5

or 15

258 8

or 3 1


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


MA.7.A.3.2 …Divide…fractions…including solving problems in everyday contexts.Also MA.7.A.5.2

Sunshine State Standards


Vocabulary

reciprocal

multiplicative inverse


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.


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.


Check It Out: Example 1

Divide. Write the answer in simplest form.

A. 35

÷ 12

B. 47

÷ 20

35

÷ 12

= 35

· 21

= 65

= 151

47

÷ 20 =47

· 120

1

= 135

5



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


Check It Out: Example 2ADivide. Write the answer in simplest form.

35

÷125

35

÷125

= 35

÷ 75

= ·

= 3 7

135

57

1


Check It Out: Example 2B

16

÷3 14

2

16

÷3 14

2 = 19 6

÷ 94

19 6

= 49

·2

3

3827

= = 11 27

1



Check It Out: Example 2C


558

÷ 59

45 8

÷ 5 9

= 45 8

· 9 51

5 58

÷ 59

=

= 81 8

= 18

10

9


Check It Out: Example 2D


429

÷ 23

2

38 9

÷ 8 3

= 38 9

· 3 84

4 29

÷ 23

=

= 1912

= 7 12

1

19

2

1

3


Additional Example 3: Consumer ApplicationAnthony bought several pounds of fruit at the farmer’s market. He first purchased strawberries. Then he picked up 1 times as many pounds of bananas as strawberries. He finally selected 3 more pounds of apples than bananas. Anthony purchased 6 pounds of apples. How many pounds of strawberries did he buy?

19

13

Subtract the fractions then subtract the integers.

The amount of bananas purchased is 2 lb.

79

34

Step 1: Find the amount of bananas Anthony purchased.

6 – 3 79

19

= 5 – 3 79

10 9

= 39

2 = 13

2

19

Regroup: 6 = 5 + + 99

19

Simplify.

Work backward from the amount of apples Anthony purchased to the amount of strawberries.


Additional Example 3: Consumer Application

Write mixed numbers as improper fractions.

13

The amount of strawberries purchased is 1 lb.

2 1 34

13

= 74

7 3

or 1 13

= 43

74

Multiply by the reciprocal of .

Simplify.

Step 2: Find the amount of strawberries purchased. The amount is times as much as the amount of bananas purchased, so divide the amount of bananas by .

34

134

1

= 47

73

= 47

73 1

1


Check It Out: Example 3

Hannah is putting her loose change into rolls. She has the most number of penny rolls. There are times as many dime rolls as penny rolls. There are times as many quarter rolls as dime rolls. If there are 15 quarter rolls, how many penny rolls does Hannah have?

56 3

10

There are 15 quarter rolls.

10 3

50 1

There are15 ÷ 3 10

= 15 1

· = 50dime rolls1

5

There are 50 ÷ 5 6

= · 65

= 60penny rolls1

10


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz

10


1.

2.

8 ÷ 45

59

÷ 18

3. 35

÷ 6

5. Roy cuts yard of silk from a roll. Susan then takes of the remaining silk on the roll. If there are 5 yards of silk after Susan’s cut, how much was on the roll before Roy’s cut?

14

34

4 49

40 9

or

110

34. 212

÷ 17

3544

14

7 yards34


1. Divide. Write your answer in simplest form.

10 ÷

A. 6

B. 18

C. 12

D. 24


5 6



÷

A. or 4 C.

B. or 2 D.


20 5

20 7

4 35

3 35

4 7

1 5

6 7



÷ 15

A. or 9 C.

B. 24 D. or


75 8

1 24

3 15

5 8

3 8

1 5


4. Multiply. Write your answer in simplest form.

3 ÷ 5

A. C. or 1

B. D. 27


50

8123

27

81

50

1 3

2 5

31

50

3-11 Dividing Fractions and Mixed Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation...

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