Multiplying Fractions
Multiplying fractions challenges 5th-grade students more than any other fraction operation, with success rates dropping to 40% according to NAEP data. The conceptual leap from 'multiplication makes numbers bigger' to understanding that 2/3 × 1/4 equals 1/6 requires targeted practice across CCSS.5.NF standards.
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Why it matters
Fraction multiplication appears in cooking measurements when scaling recipes by 34, construction projects requiring 23 of a 58-inch board, and financial literacy when calculating 14 of a $20 allowance. Students need this skill for proportional reasoning in 6th grade, where they'll multiply 35 × 15 to find parts of quantities. Research shows students who master fraction multiplication by 5th grade score 23% higher on algebra assessments. The cross-multiplication pattern (numerator × numerator, denominator × denominator) builds foundation skills for rational expressions in high school mathematics and real-world problem solving involving partial quantities.
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.
Worked examples
What is a third of 12?
Answer: 16
- Multiply straight across → 1/6 — 'Of' means multiply: 1/3 x 1/2. Numerator x numerator over denominator x denominator.
- Simplify → 1/6 — Divide numerator and denominator by their GCD.
- Verify → 1/6 ✓ — Answer.
What is 35 of 13?
Answer: 15
- Multiply straight across → 3/15 — 'Of' means multiply: 3/5 x 1/3. Numerator x numerator over denominator x denominator.
- Simplify → 1/5 — Divide numerator and denominator by their GCD.
- Verify → 1/5 ✓ — Answer.
A recipe calls for 46 cup of milk. You make 38 of the recipe. How much milk do you need?
Answer: 14
- Multiply straight across → 12/48 — Scaling a recipe means multiplying. Numerator x numerator over denominator x denominator.
- Simplify → 1/4 — Divide numerator and denominator by their GCD.
- Verify → 1/4 ✓ — Answer.
Common mistakes
- ✗Adding denominators instead of multiplying: students write 1/2 × 1/3 = 2/5 instead of 1/6
- ✗Cross-multiplying like equivalent fractions: writing 2/3 × 1/4 = 8/3 instead of 2/12 = 1/6
- ✗Forgetting to simplify final answers: leaving 6/12 instead of reducing to 1/2
- ✗Converting mixed numbers incorrectly: writing 2 1/3 × 1/2 as 3/3 × 1/2 instead of 7/3 × 1/2
Practice on your own
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