Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

NS2.4 Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g. to find a common denominator to add two fractions or to find the reduced form of a fraction).Also covered: NS1.1

California Standards

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

VOCABULARY CARDS

• Numerator

• Denominator

• Equivalent Fractions• Improper Fraction• Mixed Number• Simpliest Form

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 .

Teacher 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

Student Practice 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.

Teacher 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.

Student Practice 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.

Teacher 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

Teacher Example 3B:

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

Student Practice 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

Student Practice 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

85 = 13

5

85 is an improper

fraction. Its numerator is greater than itsdenominator.

135 is a mixed

number. Itcontains both awhole numberand a fraction.

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

4A. Write

Teacher Example 4:

Converting Between Improper Fractions and Mixed Numbers135

as a mixed number.

First divide the numerator by the denominator.

135

= 2 35

Use the quotient and remainder to write the mixed number.

4B. Write 7 23 as an improper fraction.

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

2233

+

= 3 7 + 23 = 23

3

Use the result to write the improperfraction.

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Student Practice 4:

4A. Write 156 as a mixed number.

First divide the numerator by the denominator.

156

= 2 36

Use the quotient and remainder to write the mixed number.

4B. Write 8 13

as an improper fraction.

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

113388

+

= 3 8 + 13 = 25

3

Use the result to write the improperfraction.

12

= 2

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