What is multiplying fractions?
Multiplying fractions is simpler than adding them because you don't need a common denominator at all. Multiply the two numerators (top numbers) together, then multiply the two denominators (bottom numbers) together, and simplify the result if you can.
Why it matters
Multiplying fractions is how kids find a fraction of a fraction: half of a half, two-thirds of a cup. It drives ratio and proportion work in Grade 6-7, probability calculations (where "and" means multiply), and every algebra problem that involves fractional rates or scaling.
Worked example
Multiply: 2/3 × 3/4.
- 1
Multiply the numerators: 2 × 3 = 6.
No LCD needed. With multiplication you go straight across the top.
- 2
Multiply the denominators: 3 × 4 = 12.
Straight across the bottom too.
- 3
Write the result: 6/12.
- 4
Simplify: GCF of 6 and 12 is 6. Divide top and bottom by 6: 6 ÷ 6 = 1, 12 ÷ 6 = 2. So 6/12 = 1/2.
You can also simplify BEFORE multiplying by cancelling a numerator with a denominator from the other fraction. 2/3 × 3/4: the 3 in the numerator and the 3 in the denominator cancel to give 2/1 × 1/4 = 2/4 = 1/2. Same answer, smaller numbers to work with.
- 5
Check the result makes sense: two-thirds of three-quarters of something. That should be less than 3/4, and 1/2 is less than 3/4. ✓
Answer
1/2
Common mistakes
- •Trying to find a common denominator before multiplying. That's the addition rule, not the multiplication rule. With multiplication you just multiply straight across.
- •Forgetting to simplify, leaving 6/12 as the answer when 1/2 is the expected simplified form.
- •When multiplying a fraction by a whole number, not rewriting the whole number as a fraction first. 3 × 2/5 should be set up as 3/1 × 2/5 = 6/5. Skipping the /1 causes place-value mix-ups.
- •Cross-cancelling incorrectly by cancelling within the same fraction (numerator with its own denominator) instead of across fractions (one fraction's numerator with the other fraction's denominator).
How Briveli teaches multiplying fractions
Briveli introduces fraction multiplication in Grade 5 starting with a whole number times a fraction, then fraction times fraction, then problems involving mixed numbers, always pairing the algorithm with an area-model visual so students can see why "multiply across" works.
Practice Grade 5 math on Briveli