Multiplying Fractions — How to Multiply Fractions Step by Step

Multiplying fractions is one of the most straightforward fraction operations — unlike addition and subtraction, no common denominator is needed. You simply multiply across. This guide walks through every case: proper fractions, fractions multiplied by whole numbers, mixed numbers, and the cross-cancelling shortcut — with worked examples at each step.

A fraction represents a part of a whole and consists of two parts:

• Numerator: The top number, which shows how many parts you have.
• Denominator: The bottom number, which shows how many equal parts the whole is divided into.

Example: In the fraction $\frac{3}{4}$, 3 is the numerator and 4 is the denominator. When multiplying fractions, both parts take part in the calculation — which differs from addition and subtraction where only the numerator changes.

Follow these steps to multiply any two fractions:

1. Multiply the numerators: The new numerator is the product of the two top numbers.
2. Multiply the denominators: The new denominator is the product of the two bottom numbers.
3. Simplify: Reduce the resulting fraction to its lowest terms if possible.

Unlike addition or subtraction, there is no need to find a common denominator. You multiply straight across.

Example 1: Multiply two proper fractions

Multiply $\frac{1}{2}\times \frac{3}{4}$:

$\frac{1}{2}\times \frac{3}{4}=\frac{1\times 3}{2\times 4}=\frac{3}{8}$

Example 2: Multiply a fraction by a whole number

Multiply $5\times \frac{2}{3}$:

Write 5 as $\frac{5}{1}$, then multiply:

$\frac{5}{1}\times \frac{2}{3}=\frac{10}{3}=3\frac{1}{3}$

Example 3: Multiply mixed numbers

Multiply $1\frac{1}{2}\times 2\frac{1}{3}$:

Convert to improper fractions first: $\frac{3}{2}\times \frac{7}{3}$, then multiply:

$\frac{3}{2}\times \frac{7}{3}=\frac{21}{6}=3\frac{1}{2}$

Before multiplying, you can simplify diagonally across the multiplication sign to keep the numbers smaller. Divide any numerator and any denominator (from opposite fractions) by their common factor:

Example: $\frac{4}{9}\times \frac{3}{8}$ — the 4 and 8 share a factor of 4; the 3 and 9 share a factor of 3:

$\frac{1}{3}\times \frac{1}{2}=\frac{1}{6}$

Cross-cancelling gives the exact same answer as simplifying at the end, but with smaller, easier numbers during the multiplication.

• Multiplying Fractions Worksheets

  Practice multiplying fractions with easy-to-customize worksheets. Generate unlimited problems, adjust settings, and create printable PDFs complete with answer keys.

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• Multiplying Fractions Game Worksheets

  Make learning more engaging with game-style worksheets, including multiplication mazes. These printable activities combine practice with fun, perfect for keeping students motivated.

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The resources on this page are designed to take a learner from first principles through to confident independent practice.

1. Work Through the Guide

Read each section in order. The guide builds progressively — understanding what a numerator and denominator are comes before working through the multiplication steps. Skipping ahead is fine for review, but the sequence is deliberate for first-time learners.

2. Practise with the Examples

Cover the worked examples and attempt each problem yourself before reading the solution. Self-testing is significantly more effective than passive reading for building procedural fluency.

3. Download Printable Worksheets

Use the multiplying fractions worksheets to practise on paper. Each generator creates a fresh set of problems so you can return as many times as needed without repeating the same calculations.

4. Try the Game Worksheets

For a more engaging format, the multiplying fractions game worksheets — including maze formats — require students to solve problems and follow the correct path, adding a self-checking mechanism that plain drills lack.

Fraction multiplication is not an isolated skill — it underpins large areas of mathematics from Grade 4 upwards.

Foundation for Algebra and Ratios

Multiplying fractions is the arithmetic behind scaling, proportion, and ratio — all core algebra topics. Students who can multiply fractions fluently find these later topics far more accessible because the underlying operation is already automatic.

Builds Number Sense

Multiplying fractions teaches an important and sometimes counter-intuitive insight: multiplying by a fraction less than 1 makes a number smaller. This understanding of how multiplication works beyond whole numbers builds deeper number sense that carries through the entire curriculum.

Controlled Difficulty Levels

The printable worksheet generators on this site let you choose denominator ranges precisely. This means you can target the exact difficulty level your students need — starting with simple proper fraction problems and progressing to mixed number multiplication as confidence grows.

Unlimited Unique Practice

Every click of the worksheet generators produces a new, unique set of problems. You can generate different worksheets for classwork, homework, and assessment across the full school year without students ever encountering the same problems twice.