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Equivalent Fractions Using Multiplication

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Equivalent Fractions Using Multiplication

Fraction circles and multiplication symbols

🔢 Part 1: Finding Equivalent Fractions

1. Fill in the missing numbers to make equivalent fractions using multiplication:

a) 1/3 = ___/9 (multiply by ___)

b) 2/5 = 6/___ (multiply by ___)

c) 3/4 = ___/12 (multiply by ___)

d) 1/2 = 4/___ (multiply by ___)

2. Which fraction is equivalent to 2/3? Circle your answer:

4/6

3/4

2/6

6/8

3. Complete these equivalent fractions:

a) 1/4 × 2/2 = ___/___

b) 3/5 × 3/3 = ___/___

c) 2/7 × 4/4 = ___/___

🎯 Part 2: Multiple Choice & Problem Solving

4. Sarah ate 3/8 of a pizza. Which fraction shows the same amount?

6/16

3/16

6/8

9/16

5. Check ALL the fractions that are equivalent to 1/2:

2/4

3/6

4/6

5/10

6/12

✏️ Part 3: Word Problems

6. Maria colored 3/4 of her drawing. She wants to show this as an equivalent fraction with 12 parts. How many parts out of 12 did she color?

Answer: _____ out of 12 parts

Show your multiplication: 3/4 × ___/___ = ___/12

7. A recipe calls for 2/5 cup of flour. If you want to write this as an equivalent fraction with 20 as the denominator, what would it be?
8. Explain in your own words: Why does multiplying both the numerator and denominator by the same number give you an equivalent fraction?

📝 ANSWER SHEET

Part 1 Answers:

1.

a) 1/3 = 3/9 (multiply by 3)

b) 2/5 = 6/15 (multiply by 3)

c) 3/4 = 9/12 (multiply by 3)

d) 1/2 = 4/8 (multiply by 4)

2. Circle: 4/6 (2/3 × 2/2 = 4/6)

3.

a) 1/4 × 2/2 = 2/8

b) 3/5 × 3/3 = 9/15

c) 2/7 × 4/4 = 8/28

Part 2 Answers:

4. Circle: 6/16 (3/8 × 2/2 = 6/16)

5. Check: 2/4, 3/6, 5/10, 6/12 (All equal 1/2 when simplified)

Part 3 Answers:

6. Answer: 9 out of 12 parts

Show your multiplication: 3/4 × 3/3 = 9/12

7. 8/20 (2/5 × 4/4 = 8/20)

8. Sample answer: When you multiply both the numerator and denominator by the same number, you're essentially multiplying the fraction by 1 (like 2/2 or 3/3). Since multiplying by 1 doesn't change the value, the fraction represents the same amount but is written differently. It's like having the same pizza cut into more pieces - you still have the same amount of pizza.

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