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§ Fractions

Multiplying Fractions

§ Fractions

Multiplying Fractions

CCSS.5.NFCCSS.6.NS3 min read

Students often struggle with multiplying fractions because they expect it to work like adding fractions, but multiplication actually follows simpler rules. When Emma's class learns that 1/2 × 1/3 equals 1/6, they discover that multiplying fractions makes numbers smaller, not larger.

§ 01

Why it matters

Multiplying fractions appears in countless real-world scenarios that students encounter daily. Recipe scaling requires this skill when making 23 of a batch that calls for 34 cup of flour. Construction projects use fraction multiplication to calculate areas like a 58-inch by 34-inch board section. Sports statistics rely on these calculations when a player hits 35 of their free throws in 23 of their games. Financial literacy connects to fraction multiplication when calculating discounts—finding 34 of a $20 item during a sale. Garden planning uses these skills to determine planting areas when a plot is 78 feet by 56 feet. The CCSS 5.NF standards emphasize these practical applications because fraction multiplication builds foundational skills for algebra, geometry, and advanced mathematics concepts students will encounter in higher grades.

§ 02

How to solve multiplying fractions

Multiplying fractions — how to

  • Multiply the numerators together.
  • Multiply the denominators together.
  • Simplify the result to lowest terms.

Example: 23 × 34 = 612 = 12.

§ 03

Worked examples

Beginner§ 01

What is a third of 12?

Answer: 16

  1. Multiply straight across → 1/6 — 'Of' means multiply: 1/3 x 1/2. Numerator x numerator over denominator x denominator.
  2. Simplify → 1/6 — Divide numerator and denominator by their GCD.
  3. Verify → 1/6 ✓ — Answer.
Easy§ 02

45 x 12 = _______

Answer: 25

  1. Multiply straight across → 4/10 — Numerator x numerator over denominator x denominator.
  2. Simplify → 2/5 — Divide numerator and denominator by their GCD.
  3. Verify → 2/5 ✓ — Answer.
Medium§ 03

A garden plot is 68 m wide and 411 m long. What is the area?

Answer: 311

  1. Multiply straight across → 24/88 — Area = width x length. Numerator x numerator over denominator x denominator.
  2. Simplify → 3/11 — Divide numerator and denominator by their GCD.
  3. Verify → 3/11 ✓ — Answer.
§ 04

Common mistakes

  • Students add instead of multiply, writing 1/2 × 1/3 = 2/5 instead of 1/6 because they apply addition rules to multiplication problems.
  • Students multiply denominators but add numerators, calculating 2/3 × 1/4 = 3/12 instead of 2/12, mixing operations within the same problem.
  • Students forget to simplify final answers, leaving 6/12 instead of reducing to 1/2, missing the lowest terms requirement.
  • Students convert mixed numbers incorrectly, turning 1 1/2 × 2/3 into 1/2 × 2/3 instead of 3/2 × 2/3, losing the whole number portion.
  • Students cross-cancel incorrectly, reducing 4/5 × 3/8 by canceling 4 and 8 to get 1/5 × 3/2 instead of recognizing no common factors exist.
§ 05

Frequently asked questions

Why does multiplying fractions make the answer smaller?
Multiplication by fractions represents taking a part of something. When you multiply 1/2 × 1/3, you're finding 1/3 of 1/2, which must be smaller than the original 1/2. This differs from whole number multiplication where numbers get larger.
Do I cross-multiply when multiplying fractions?
No, cross-multiplication applies to solving proportions, not multiplying fractions. For fraction multiplication, multiply straight across: numerator times numerator over denominator times denominator. Cross-cancellation before multiplying can simplify calculations but isn't required.
How do I multiply mixed numbers?
Convert mixed numbers to improper fractions first. Change 2 1/3 to 7/3 and 1 1/4 to 5/4, then multiply normally: 7/3 × 5/4 = 35/12. Convert back to mixed numbers if needed: 35/12 = 2 11/12.
When should students learn to cross-cancel before multiplying?
Introduce cross-cancellation after students master basic fraction multiplication, typically in 6th grade per CCSS 6.NS standards. Start with obvious examples like 2/3 × 3/4 where the 3s cancel, making calculation easier before multiplying.
What's the connection between 'of' and multiplication in word problems?
The word 'of' in fraction contexts means multiplication. '1/3 of 1/2' translates to 1/3 × 1/2. This language connection helps students identify when to multiply fractions in real-world problems involving parts of parts.
§ 06

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