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Daily Math Minute

Number & Operations—Fractions

Multiplying Fractions

Multiplying a fraction or whole number by a fraction.

Advanced20 min lesson3 min readUpdated August 12, 2026Author not yet attributed

Prerequisites

  • Adding & Subtracting Unlike Denominators

What Does It Mean to Multiply by a Fraction?

Whole-number multiplication, like 3 × 4, always made the answer bigger than at least one of the original numbers. So here's something to predict before reading on: will 1/2 × 1/3 be bigger or smaller than both 1/2 and 1/3? Think about what 'half of a third' would actually look like.

Multiplying by a fraction means finding a fraction of a fraction — and taking a fraction of something always makes it smaller, not bigger. 1/2 × 1/3 asks: what is half of one-third? Picture a rectangle split into thirds, with one third shaded. Now split that same rectangle in half the other direction. The overlap — half of that one shaded third — is a much smaller piece: exactly 1/6 of the whole rectangle.

This area-model picture is exactly why multiplying fractions works by multiplying straight across: the numerators multiply together, and the denominators multiply together.

Worked Example — Multiplying Two Fractions

Multiply 2/3 × 3/4. Multiply the numerators: 2 × 3 = 6. Multiply the denominators: 3 × 4 = 12. The product is 6/12, which simplifies to 1/2.

Worked Example — Multiplying a Fraction by a Whole Number

Multiply 5 × 2/3. Write the whole number 5 as the fraction 5/1, then multiply straight across: (5 × 2)/(1 × 3) = 10/3, which can also be written as the mixed number 3 1/3.
23×34=2×33×4=612=12\dfrac{2}{3} \times \dfrac{3}{4} = \dfrac{2 \times 3}{3 \times 4} = \dfrac{6}{12} = \dfrac{1}{2}

Tip

If the answer to a fraction multiplication problem looks bigger than both original fractions, something's gone wrong — multiplying proper fractions together (both less than 1) always produces a smaller result, since you're finding a fraction of a fraction.

Common Mistakes

  • Finding a common denominator before multiplying, a step that belongs to addition and subtraction but isn't needed for multiplication.

    Fraction multiplication doesn't need a common denominator at all — multiply the numerators together and the denominators together directly, regardless of whether the denominators match.

  • Expecting the product of two fractions to be larger than either original fraction, the same way whole-number multiplication usually behaves.

    Multiplying two fractions less than 1 always gives a smaller result than either one, since it means finding a fraction of an already-small piece.

Key Takeaways

  • Multiplying fractions means finding a fraction of a fraction, which is why the result is smaller than both original fractions.
  • Multiply numerators together and denominators together directly — no common denominator needed.
  • A whole number can be multiplied by a fraction by first writing it as a fraction over 1.

Summary

Multiplying fractions finds a fraction of a fraction, using an area-model picture that explains why multiplying straight across works. The final lesson in this unit looks at the reverse operation — dividing with fractions.

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