Multiplying Fractions
Multiplying fractions follows a straightforward rule: multiply the numerators together and multiply the denominators together, then simplify the result. This operation appears in CCSS standards starting in grade 4 with whole number multiplication and expanding to full fraction multiplication in grade 5. The process differs from adding fractions because no common denominator is needed.
Why it matters
Fraction multiplication appears frequently in real-world calculations involving scaling and proportions. A baker making 34 of a recipe that calls for 23 cup flour needs to calculate 23 × 34 = 12 cup. Construction workers calculating material needs often multiply dimensions given as mixed numbers, like finding the area of a 2 14 by 1 38 foot section. In medicine, dosage calculations frequently involve multiplying fractions when adjusting prescriptions. The skill becomes essential for algebra, where multiplying rational expressions builds directly on fraction multiplication rules. Advanced mathematics courses like calculus rely heavily on fraction manipulation for derivatives and integrals.
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 quarter of 13?
Answer: 112
- Multiply straight across → 112 — 'Of' means multiply: 1/4 x 1/3. Numerator x numerator over denominator x denominator.
- Simplify → 112 — Divide numerator and denominator by their GCD.
- Verify → 112 ✓ — Answer.
A recipe calls for 45 cup of milk. You make 24 of the recipe. How much milk do you need?
Answer: 25
- Multiply straight across → 820 — Scaling a recipe means multiplying. Numerator x numerator over denominator x denominator.
- Simplify → 25 — Divide numerator and denominator by their GCD.
- Verify → 25 ✓ — Answer.
A recipe calls for 29 cup of milk. You make 45 of the recipe. How much milk do you need?
Answer: 845
- Multiply straight across → 845 — Scaling a recipe means multiplying. Numerator x numerator over denominator x denominator.
- Simplify → 845 — Divide numerator and denominator by their GCD.
- Verify → 845 ✓ — Answer.
Common mistakes
- Adding numerators and denominators instead of multiplying, such as writing 1/2 × 1/3 = 2/5 instead of 1/6
- Forgetting to simplify the final answer, leaving 6/12 instead of reducing to 1/2
- Converting mixed numbers incorrectly before multiplying, turning 1 1/2 into 1/2 instead of 3/2