R2 · Lesson 5: Multiply Fractions & Mixed Numbers

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Why this matters for Grade 6: Dividing fractions (6.NS.1) is really "multiply by the reciprocal." You can't do that without being fluent at multiplying fractions. Every time you solve 3/4 ÷ 1/2 = 3/4 × 2/1, you are using the skills from this lesson.

Learn It

Multiply Fractions & Mixed Numbers

Rule: multiply numerator × numerator and denominator × denominator. Then simplify.

Example 1 — Fraction × fraction
1/2 × 1/3 = (1×1)/(2×3) = 1/6

2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2 (simplified by dividing by 6)

Tip — cross-cancel before multiplying to keep numbers small:
²/₃ × ³/₄: cancel the 3s → ²/₁ × ¹/₄ = 2/4 = 1/2 ✓

Example 2 — Fraction of a whole number
"1/2 of 8" = 1/2 × 8 = 1/2 × 8/1 = 8/2 = 4
"3/4 of 12" = 3/4 × 12/1 = 36/4 = 9

Example 3 — Mixed numbers
1½ × 2: convert 1½ to an improper fraction first.
1½ = (1×2 + 1)/2 = 3/2
3/2 × 2/1 = 6/2 = 3

Try It · Guided

Work These Together

1. What is 1/3 × 1/4?

Hint

Multiply numerators: 1×1=1. Multiply denominators: 3×4=12. Answer: 1/12.

2. What is 1/2 of 10? (i.e., 1/2 × 10)

Hint

1/2 × 10/1 = 10/2 = 5. Or simply: half of 10 is 5.

Practice · On Your Own

You Try

3. What is 2/3 × 3/4? (Give your answer in simplest form.)

Hint

2×3=6, 3×4=12. So 6/12. Simplify: GCF(6,12)=6. 6÷6=1, 12÷6=2. Answer: 1/2.

4. What is 3/4 of 16? (i.e., 3/4 × 16)

Hint

3/4 × 16/1 = 48/4 = 12. Or: 16 ÷ 4 = 4, then 4 × 3 = 12.

5. What is 2½ × 2? (Convert to an improper fraction first.)

Hint

2½ = 5/2. Then 5/2 × 2/1 = 10/2 = 5.

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Exit Ticket

Show What You Know

6. What is 3/5 × 5/6? (Give your answer in simplest form.)

Hint

3×5=15, 5×6=30. So 15/30. Simplify: GCF(15,30)=15. 15÷15=1, 30÷15=2. Answer: 1/2.

7. A recipe needs 1½ cups of sugar. You are making 3 batches. How many cups do you need in total? (Calculate 1½ × 3.)

Hint

1½ = 3/2. Then 3/2 × 3/1 = 9/2 = 4½ cups.

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