Multiplying Fractions Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Multiplying Fractions.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Multiplying two fractions by multiplying the numerators together and the denominators together.

\frac{2}{3} \times \frac{3}{4} means 'two-thirds of three-quarters.' Take \frac{3}{4} of something, then take \frac{2}{3} of that result.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Multiply straight across—numerator times numerator, denominator times denominator. No common denominator needed.

Common stuck point: Students expect the product to be larger, but multiplying by a fraction less than 1 makes the result smaller.

Sense of Study hint: Simplify by canceling common factors between any numerator and any denominator before you multiply across -- it keeps the numbers small.

Worked Examples

Example 1

easy
Multiply \frac{2}{3} \times \frac{5}{7}.

Solution

  1. 1
    Multiply the numerators: 2 \times 5 = 10.
  2. 2
    Multiply the denominators: 3 \times 7 = 21.
  3. 3
    The product is \frac{10}{21}, which is already in simplest form since \gcd(10, 21) = 1.

Answer

\frac{10}{21}
To multiply fractions, multiply numerator by numerator and denominator by denominator. No common denominator is needed, unlike addition.

Example 2

medium
Compute \frac{4}{9} \times \frac{3}{8}.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Multiply \frac{3}{5} \times \frac{2}{9}.

Example 2

medium
A tank is \frac{3}{4} full. If \frac{2}{5} of the water is used, what fraction of the tank is still full?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

fractionsmultiplication