How do you multiply fractions?

To multiply fractions, multiply the numerators together, multiply the denominators together, then simplify: 2/3 × 4/5 = 8/15. Unlike adding, you do not need a common denominator. Convert whole numbers (5 = 5/1) and mixed numbers (1 1/2 = 3/2) to fractions first.

Multiplying fractions, step by step

  1. 1

    Write everything as a plain fraction

    Whole numbers go over 1 (5 = 5/1) and mixed numbers become improper fractions (1 1/2 = 3/2). Once everything is a single fraction, the rule is the same every time.

  2. 2

    Multiply straight across

    Top times top, bottom times bottom: 2/3 × 4/5 = (2 × 4)/(3 × 5) = 8/15. No common denominator, no extra steps — this is genuinely the whole rule.

  3. 3

    Cross-cancel to keep numbers small (optional)

    Before multiplying, divide any numerator and any denominator by a shared factor. In 3/8 × 4/9, the 3 and 9 cancel to 1 and 3, and the 4 and 8 cancel to 1 and 2 — leaving 1/2 × 1/3 = 1/6 with no big numbers to simplify later.

  4. 4

    Simplify the answer

    If you didn't cross-cancel, reduce the result by dividing top and bottom by their greatest common factor. Convert improper answers to mixed numbers if the question expects one: 15/4 = 3 3/4.

Worked examples

Fraction × fraction

2/3 × 4/5

  1. Multiply the numerators: 2 × 4 = 8.
  2. Multiply the denominators: 3 × 5 = 15.
  3. 2/3 × 4/5 = 8/15, which is already in simplest form.

Answer: 8/15

Cross-cancelling first

3/8 × 4/9

  1. Cancel the 3 with the 9 (÷3): the 3 becomes 1 and the 9 becomes 3.
  2. Cancel the 4 with the 8 (÷4): the 4 becomes 1 and the 8 becomes 2.
  3. Multiply what's left: 1/2 × 1/3 = 1/6.
  4. Check without cancelling: 3/8 × 4/9 = 12/72 = 1/6 — same answer, bigger numbers.

Answer: 1/6

Whole number × fraction

5 × 3/4

  1. Write 5 as a fraction: 5 = 5/1.
  2. Multiply across: 5/1 × 3/4 = 15/4.
  3. Convert to a mixed number: 15 ÷ 4 = 3 remainder 3, so 15/4 = 3 3/4.

Answer: 3 3/4 (= 15/4)

Common mistakes to avoid

Finding a common denominator first

Common denominators are for adding and subtracting. Multiplication works straight across — introducing a common denominator gives a correct but needlessly messy calculation.

Multiplying mixed numbers part by part

2 1/2 × 3 is not 6 1/2 (2 × 3 plus 1/2). Convert first: 2 1/2 = 5/2, then 5/2 × 3/1 = 15/2 = 7 1/2. The whole and fraction parts can't be multiplied separately without cross terms.

Expecting the answer to get bigger

Multiplying by a proper fraction makes things smaller — 1/2 × 1/3 = 1/6 because you're taking half of a third. Students who expect multiplication to grow numbers often assume they've made an error when they haven't.

Multiplying fractions — common questions

Do you need a common denominator to multiply fractions?

No. Multiply the numerators together and the denominators together: 2/3 × 4/5 = 8/15. Common denominators are only needed for adding and subtracting.

How do you multiply a fraction by a whole number?

Write the whole number over 1 and multiply across: 5 × 3/4 = 5/1 × 3/4 = 15/4 = 3 3/4. Equivalently, multiply just the numerator by the whole number.

How do you multiply mixed numbers?

Convert each mixed number to an improper fraction first, then multiply across. For 1 1/2 × 2 2/3: 3/2 × 8/3 = 24/6 = 4.

What is cross-cancelling?

Simplifying before you multiply: divide any numerator and any denominator by a common factor. In 3/8 × 4/9 you can cancel 3 with 9 and 4 with 8, leaving 1/2 × 1/3 = 1/6. It's optional — it just keeps the numbers small.

Why does multiplying by a fraction make numbers smaller?

Because "×1/2" means "take half of". Half of 1/3 is 1/6, so 1/2 × 1/3 = 1/6. Multiplying only makes things bigger when the multiplier is greater than 1.

What does 'of' mean in fraction problems?

'Of' means multiply. "Two thirds of 12" is 2/3 × 12 = 24/3 = 8, and "half of a quarter" is 1/2 × 1/4 = 1/8.

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