Dividing Fractions - Big Ideas Learning

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Spanish

2.5

Dividing Fractions

How do you divide by a fraction?

1

ACTIVITY: Dividing by a Fraction

Work with a partner.

8 ‾ 16

〞

b. Describe the pattern of the red numbers.

Use the pattern to complete the table.

8‾8

1

8‾4

2

8‾2

4

8‾1

8

1

2

c. The division 8 ‾ 〞 can be read as ※How many halves

are in 8?§ Use the completed table to answer this

question. Then draw a model that shows your answer.

d. Use the pattern in the table to complete the following.

1

2

8 ‾ 〞 = 16 = 8 ℅ 〞

2

1

1

2

8‾〞

1

Invert 〞 and multiply.

2

1

4

8‾〞

1

8 ‾ 〞 = 32 =

4

1

8

8‾〞

1

8

8 ‾ 〞 = 64 =

2

ACTIVITY: Dividing by a Fraction

Work with a partner.

2

3

a. Draw a model for 3 ‾ 〞. Use the model to answer the question

※How many two-thirds are in 3?§

1

1

b. Complete the table in two ways.

First use the model. Then use the

※invert and multiply§ rule that

you found in Activity 1. Compare

your answers.

1

2

3

3‾〞

2

3

6‾〞

2

3

9‾〞

2

3

12 ‾ 〞

70

Chapter 2

1

2

a. Describe the pattern of the blue numbers.

Multiplying and Dividing Fractions

English

Spanish

3

ACTIVITY: Dividing by a Fraction

Work with a partner. Write the division problem and answer it using a model.

a. How many halves are in five halves?

1

1

1

2

b. How many sixths are in three halves?

1

2

1

2

1

2

c. How many three-fourths are in 3?

1

1

1

d. How many four-fifths are in 8?

1

1

1

1

1

1

1

1

1

1

e. How many three-tenths are in 6?

1

f.

1

1

1

How many halves are in a fourth?

1

4

1

4

1

4

1

4

4. IN YOUR OWN WORDS How do you divide by a fraction? Give an example.

Use what you learned about dividing fractions to complete

Exercises 11每18 on page 75.

Section 2.5

Dividing Fractions

71

English

2.5

Spanish

Lesson

Lesson Tutorials

Two numbers whose product is 1 are reciprocals. To write a reciprocal

of a number, write the number as a fraction. Then invert the fraction.

Key Vocabulary

reciprocals, p. 72

Invert

When y

you invert a g

glass,,

EXAMPLE

Study Tip

When any number is

multiplied by 0, the

product is 0. So, the

number 0 does not

have a reciprocal.

y

you turn it over.

Writing Reciprocals

1

Original Number

Fraction

Reciprocal

Check

a.

〞

3

5

〞

3

5

〞

5

3

〞℅〞=1

3

5

5

3

b.

〞

9

5

〞

9

5

〞

5

9

〞℅〞=1

9

5

5

9

c.

2

〞

2

1

〞

1

2

〞℅〞=1

2

1

1

2

Write the reciprocal of the number.

Exercises 7每10

3

4

1. 〞

7

2

3. 〞

2. 5

4

9

4. 〞

Dividing Fractions

Words

To divide a number by a fraction, multiply the number by the

reciprocal of the fraction.

Numbers

Algebra

72

Chapter 2

1

5

3

4

1

5

4

3

〞‾ 〞= 〞℅ 〞

a

b

c

d

a

b

d

c

〞 ‾ 〞 = 〞 ℅ 〞, where b, c, and d ≧ 0

Multiplying and Dividing Fractions

English

Spanish

EXAMPLE

2

Dividing a Fraction by a Fraction

1

6

2

3

Find 〞 ‾ 〞.

1

6

2

3

1

6

3

2

2

3

〞‾〞=〞℅〞

1℅3

=〞

6℅2

3

2

Multiply by the reciprocal of 〞, which is 〞.

1

Multiply fractions. Divide out the common factor 3.

2

1

4

=〞

EXAMPLE

3

Simplify.

Dividing a Whole Number by a Fraction

3

A piece of wood is 3 feet long. How many 〞 -foot pieces can be cut from

4

the piece of wood?

3

4

Method 1: Draw a diagram. Mark each foot on the diagram. Then divide

1

4

each foot into 〞 -foot sections.

3

4

Count the number of 〞 -foot pieces of wood. There are four.

1 ft

3

4

3

4

So, four 〞 -foot pieces can be cut from the piece of wood.

3

4

3

4

Method 2: Divide 3 by 〞 to find the number of 〞 -foot pieces.

2 ft

3

4

4

3

Multiply by the reciprocal of 〞, which is 〞.

3℅4

3

Multiply. Divide out the common factor 3.

3

4

3‾〞=3℅〞

3

4

1

=〞

4

3

1

=4

3

4

Simplify.

3

4

So, four 〞 -foot pieces can be cut from the piece of wood.

3 ft

Divide. Write the answer in simplest form.

Exercises 11每26

2

7

1

3

1

2

5. 〞 ‾ 〞

1

8

6. 〞 ‾ 〞

3

8

1

4

7. 〞 ‾ 〞

2

5

3

10

8. 〞 ‾ 〞

1

2

9. How many 〞-foot pieces can be cut from a 7-foot piece of wood?

Section 2.5

Dividing Fractions

73

English

Spanish

EXAMPLE

4

Evaluating an Algebraic Expression

4

5

Evaluate a ‾ b when a = 〞 and b = 2.

4

5

4

5

a‾b=〞‾2

4

5

Substitute 〞 for a and 2 for b.

1

2

1

2

=〞℅〞

2

4℅1

5℅2

Multiply by the reciprocal of 2, which is 〞.

=〞

Multiply fractions. Divide out the common factor 2.

1

2

5

=〞

Simplify.

Evaluate the expression x ‾ y for the given values of x and y.

Exercises 32每35

1

2

11. x = 〞, y = 10

2

3

5

8

13. x = 4, y = 〞

10. x = 〞, y = 3

1

3

12. x = 〞, y = 4

EXAMPLE

5

Using Order of Operations

3

8

5

6

Evaluate 〞 + 〞 ‾ 5.

3

8

5

6

3

8

5

6

1

5

1

5

〞+〞‾5=〞+〞℅〞

Multiply by the reciprocal of 5, which is 〞.

1

3 5℅1

=〞+〞

8 6℅5

5

6

1

3 1

=〞+〞

8 6

9

24

1

5

Multiply 〞 and 〞. Divide out the common factor 5.

Simplify.

4

24

=〞+〞

Rewrite fractions using the LCD 24.

13

24

=〞

Add.

Evaluate the expression.

Exercises 47每 55

74

Chapter 2

4

5

2

5

14. 〞 + 〞 ‾ 4

15.

Multiplying and Dividing Fractions

3

8

3

4

1

6

〞‾〞?〞

16.

8

9

〞‾2‾8

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