Part 1: Build and Complete

Equivalent fractions have the same value. You can multiply or divide the numerator and denominator by the same non-zero number.

1. Draw a fraction bar divided into 4 equal parts. Shade 3 parts to show 3/4. Under it, draw a bar divided into 8 equal parts and shade the equivalent amount. Label both fractions.

2. Draw a circle divided into 6 equal parts. Shade 2 parts. Write an equivalent fraction with a denominator of 12.

3. Complete each equivalent fraction.

a) 1/2 = ____/8 b) 3/5 = 12/____ c) 4/7 = ____/21

4. Multiply the numerator and denominator by the same factor.

a) 2/3 × 4 = ____/____ b) 5/8 × 3 = ____/____

5. Divide the numerator and denominator by the same common factor.

a) 12/18 ÷ 6 = ____/____ b) 20/28 ÷ 4 = ____/____

Part 2: Match, Explain and Challenge

6. Simplify each fraction to its simplest form.

a) 8/12 = ______ b) 15/25 = ______ c) 24/36 = ______

7. Match each fraction to an equivalent representation. Write the matching letter.

a) 2/3

b) 3/4

c) 4/5

d) 5/6

A) 15/18

B) 8/10

C) 6/8

D) 10/15

Answers: a) ____ b) ____ c) ____ d) ____

8. Sam says, “1/2 and 2/3 are equivalent because both numerators increased by 1.” Identify Sam’s error and explain how to make an equivalent fraction.

9. Explain why 3/4 and 9/12 represent the same amount. Use words, numbers or a drawing.

10. Challenge: Order these fractions from smallest to largest. Show how equivalent fractions help you compare them: 2/3, 3/4, 5/6.

Teacher note: Curriculum alignment: Te Mātaiaho Mathematics and Statistics, Phase 2 Number—Rational numbers. Descriptor references: NZ-TMA-MATHEMATIC-Y4-6-number-030-DOC112 and NZ-TMA-MATHEMATIC-Y4-6-number-023-DOC112.

Answer Key

1. Drawings should show 3/4 and 6/8 with the same amount shaded.

2. 2/6 = 4/12.

3. a) 4/8 b) 20 c) 12/21.

4. a) 8/12 b) 15/24.

5. a) 2/3 b) 5/7.

6. a) 2/3 b) 3/5 c) 2/3.

7. a) D b) C c) B d) A.

8. Sam added 1 only to the numerators. To make an equivalent fraction, multiply or divide both the numerator and denominator by the same non-zero number.

9. 3/4 × 3/3 = 9/12, so both fractions represent the same amount.

10. 2/3, 3/4, 5/6. For example, using denominator 12: 8/12, 9/12, 10/12.