Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Vocabulary

equivalent fractionsimproper fractionmixed number

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Different fractions can name the same number.

35 = = 15

256

10

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

=

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

In the diagram = . These are called

equivalent fractions because they are different expressions for the same nonzero number.

35

610

1525

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Find two fractions equivalent to .

Additional Example 1: Finding Equivalent Fractions

57

5 27 2

= 1014

Multiply the numerator and denominator by 2.

5 37 3 = 15

21Multiply the numerator and denominator by 3.

Remember!A fraction with the same numerator and

denominator, such as is equal to 1.2 2

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

5 7

The fractions , , and are equivalent,

but only is in simplest form. A fraction is in

simplest form when the greatest common divisor

of its numerator and denominator is 1.

57

1014

1521

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Check It Out! Example 1

Find two fractions equivalent to .

6 212 2 = 12

24Multiply the numerator and denominator by 2.

6 ÷ 212 ÷ 2

= 36

Divide the numerator and denominator by 2.

612

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Write the fraction in simplest form.

Additional Example 2: Writing Fractions in Simplest Form

1824

Find the GCD of 18 and 24.

The GCD is 6 = 2 • 3.

=1824

Divide the numerator and denominator by 6.

18 = 2 • 3 • 3

24 = 2 • 2 • 2 • 3

18 ÷ 624 ÷ 6 = 3

4

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Write the fraction in simplest form.

Check It Out! Example 2

1545

Find the GCD of 15 and 45.

The GCD is 15 = 3 • 5.

=1545

Divide the numerator and denominator by 15.

15 = 3 • 5

45 = 3 • 3 • 5

15 ÷ 1545 ÷ 15 = 1

3

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

To determine if two fractions are equivalent, simplify the fractions.

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Determine whether the fractions in each pair are equivalent.

Additional Example 3A: Determining Whether Fractions are Equivalent

and 46

2842

Simplify both fractions and compare.

46 = 4 ÷ 2

6 ÷ 2 = 23

2842

= 28 ÷ 1442 ÷ 14 = 2

3

are equivalent because both are equal to . and 46

2842

23

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Additional Example 3B: Determining Whether Fractions are Equivalent

Determine whether the fractions in each pair are equivalent.

and 610

2025

Simplify both fractions and compare.

= 6 ÷ 210 ÷ 2 = 3

52025

= 20 ÷ 525 ÷ 5 = 4

5

610

are not equivalent because their simplestand 2025

610forms are not equal.

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Check It Out! Example 3A

Simplify both fractions and compare.

39 = 3 ÷ 3

9 ÷ 3 = 13

= 6 ÷ 618 ÷ 6 = 1

3

and 39

618

618

Determine whether the fractions in each pair are equivalent.

are equivalent because both are equal to . and 39

618

13

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Check It Out! Example 3B

and 412

948

Simplify both fractions and compare.

= 4 ÷ 412 ÷ 4 = 1

3

948

= 9 ÷ 348 ÷ 3 = 3

16

412

Determine whether the fractions in each pair are equivalent.

are not equivalent because their simplestand 948

412forms are not equal.

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Lesson Quiz

1. Write two fractions equivalent to .

2. Determine if and are equivalent.

3. Write the fraction in simplest form.

4. Write as a mixed number.

5. Write 4 as an improper fraction.

1224

1648

37

317

18217

8

13

no

12

36

,

5 12

4 10