Warm UpName a common factor for each pair.

1. 5 and 10

2. 9 and 12

3. 20 and 24

4. 10 and 14

5. 6 and 8

6. 8 and 15

5

3

4

Course 2

3-8 Equivalent Fractions and Mixed Numbers

2

2

1

Possible answers:

Learn to identify, write, and convert between equivalent fractions and mixed numbers.

Course 2

3-8 Equivalent Fractions and Mixed Numbers

Vocabulary

equivalent fractionsimproper fractionsmixed number

Insert Lesson Title Here

Course 2

3-8 Equivalent Fractions and Mixed Numbers

In some recipes the amounts of ingredients are given as fractions, and sometimes those fractions do not equal the fractions on a measuring cup. Knowing how fractions relate to each other can be very helpful.

Different fractions can name the same number.

35 = = 15

256

10

Course 2

3-8 Equivalent Fractions and Mixed Numbers

=

To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same number.

35

= 3 · 25 · 2

= 1525

= 15 ÷ 525 ÷ 5

= 35

Course 2

3-8 Equivalent Fractions and Mixed Numbers

610

In the diagram = . These are called equivalent fractions because they are different expressions for the same nonzero number.

35

610

1525

Remember!

is in simplest form because the greatest

common factor of 3 and 5 is 1.

35

Course 2

3-8 Equivalent Fractions and Mixed Numbers

Find a fraction equivalent to the given fraction.

Additional Example 1: Finding Equivalent Fractions

A.

5757 = 5 · 3

7 · 3= 15

21Multiply numerator and denominator by 3.

B. 18241824

= 18 ÷ 224 ÷ 2

= 912

Divide numerator and denominator by 2.

Course 2

3-8 Equivalent Fractions and Mixed Numbers

Try This: Example 1

Insert Lesson Title Here

Find a fraction equivalent to the given fraction.

A.

3838 = 3 · 2

8 · 2= 6

16Multiply numerator and denominator by 2.

B.

= 6 ÷ 312 ÷ 3

= 24

Divide numerator and denominator by 3.

612

Course 2

3-8 Equivalent Fractions and Mixed Numbers

612

To determine if two fractions are equivalent, find a common denominator and compare the numerators.

Course 2

3-8 Equivalent Fractions and Mixed Numbers

You can also put both fractions into simplest form and see if they are equal.

Write the fractions with a common denominator. Then determine if they are equivalent.

Additional Example 2A: Determining Whether Fractions are Equivalent

A. and 46

2842

Both fractions can be written with a denominator of 3.46 = 4 ÷ 2

6 ÷ 2 = 23

2842

= 28 ÷ 1442 ÷ 14 = 2

3The numerators are equal, so the fractions are equivalent.

Course 2

3-8 Equivalent Fractions and Mixed Numbers

Additional Example 2B: Determining Whether Fractions are Equivalent

Write the fractions with a common denominator. Then determine if they are equivalent.

B. and 610

2025

Both fractions can be written with a denominator of 50.

= 6 · 510 · 5 = 30

502025

= 20 · 225 · 2 = 40

50

The numerators are not equal, so the fractions are not equivalent.

610

Course 2

3-8 Equivalent Fractions and Mixed Numbers

Try This: Example 2A

Insert Lesson Title Here

Write the fractions with a common denominator. Then determine if they are equivalent.

Both fractions can be written with a denominator of 3.39 = 3 ÷ 3

9 ÷ 3 = 13

= 6 ÷ 618 ÷ 6 = 1

3The numerators are equal, so the fractions are equivalent.

Course 2

3-8 Equivalent Fractions and Mixed Numbers

A. and 39

618

618

Try This: Example 2B

Insert Lesson Title Here

Write the fractions with a common denominator. Then determine if they are equivalent.

B. and 412

948

Both fractions can be written with a denominator of 96.

= 4 · 812 · 8 = 32

969

48= 9 · 2

48 · 2 = 1896

The numerators are not equal, so the fractions are not equivalent.

412

Course 2

3-8 Equivalent Fractions and Mixed Numbers

85= 13

5

85 is an improper

fraction. Its numerator is greater than itsdenominator.

1 35

is a mixednumber. Itcontains both awhole numberand a fraction.

Course 2

3-8 Equivalent Fractions and Mixed Numbers

A. Write

Additional Example 3: Converting Between Improper Fractions and Mixed Numbers

135 as a mixed number.

First divide the numerator by the denominator.

135

= 2 35

Use the quotient and remainder to write a mixed number.

B. Write 7 23 as an improper fraction.

First multiply the denominator and whole number,and then add the numerator.

237

+

= 3 · 7 + 23 = 23

3

Use the result to write the improperfraction.

Course 2

3-8 Equivalent Fractions and Mixed Numbers

Try This: Example 3

A. Write 156 as a mixed number.

First divide the numerator by the denominator.

156

= 2 36

Use the quotient and remainder to write a mixed number.

B. Write 8 13 as an improper fraction.

First multiply the denominator and whole number,and then add the numerator.

138

+

= 3 · 8 + 13 = 25

3

Use the result to write the improperfraction.

Course 2

3-8 Equivalent Fractions and Mixed Numbers

12

= 2