Dividing Fractions — How to Divide Fractions Step by Step

Dividing fractions is built on one simple rule: multiply by the reciprocal of the divisor. Once you understand why that works, the Keep-Change-Flip method is not a trick to memorise but a logical shortcut. This guide walks through every case — proper fractions, whole numbers, and mixed numbers — with worked examples at each step.

Dividing fractions answers the question: how many times does one fraction fit into another? For example, $\frac{3}{4}÷\frac{1}{4}$ asks "how many quarters fit into three-quarters?" — the answer is 3.

This is no different from whole-number division (12 ÷ 3 = 4 asks how many 3s fit into 12), just applied to parts of a whole. The key fact: dividing by a number is mathematically identical to multiplying by its reciprocal. That insight is what makes the Keep-Change-Flip method work.

To divide any two fractions, follow three steps:

1. Keep the first fraction exactly as it is.
2. Change the division sign (÷) to multiplication (×).
3. Flip the second fraction — swap its numerator and denominator to get its reciprocal.

Then multiply straight across: numerator × numerator for the new numerator, denominator × denominator for the new denominator. Simplify the result if possible.

The reciprocal of a fraction $\frac{\mathrm{a}}{\mathrm{b}}$ is simply $\frac{\mathrm{b}}{\mathrm{a}}$. The reciprocal of 2/5 is 5/2; the reciprocal of 3/7 is 7/3.

Example 1: Divide two proper fractions

Divide $\frac{3}{4}÷\frac{2}{5}$:

1. Keep: $\frac{3}{4}$
2. Change: ÷ to ×
3. Flip: $\frac{2}{5}$ becomes $\frac{5}{2}$

$\frac{3}{4}\times \frac{5}{2}=\frac{3\times 5}{4\times 2}=\frac{15}{8}=1\frac{7}{8}$

Example 2: Divide fractions with a common factor — simplify first

Divide $\frac{4}{9}÷\frac{8}{3}$:

After flipping: $\frac{4}{9}\times \frac{3}{8}$ — cross-cancel 4 and 8 (÷4), and 3 and 9 (÷3):

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

Dividing a whole number by a fraction

Write the whole number as a fraction over 1, then apply Keep-Change-Flip:

For $6÷\frac{3}{4}$: rewrite as $\frac{6}{1}\times \frac{4}{3}=\frac{24}{3}=8$.

The result (8) is larger than 6 — dividing by a fraction less than 1 always produces a bigger number.

Dividing mixed numbers

Convert each mixed number to an improper fraction first, then apply Keep-Change-Flip:

For $2\frac{1}{2}÷1\frac{1}{4}$: convert to $\frac{5}{2}÷\frac{5}{4}$, then:

$\frac{5}{2}\times \frac{4}{5}=\frac{20}{10}=2$

• Dividing Fractions Worksheets

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

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• Dividing Fractions Game Worksheets

  Make learning more engaging with game-style worksheets, including division 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 division means for fractions comes before working through the Keep-Change-Flip 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 dividing 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 dividing 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 division is not an isolated skill — it underpins large areas of mathematics and real-world problem solving from Grade 5 upwards.

Foundation for Ratio and Proportion

Dividing fractions is the arithmetic behind unit rates and proportional reasoning — topics that appear throughout science, cooking, construction, and financial maths. Students who are fluent at fraction division reach these topics with one less barrier.

Builds Conceptual Understanding

Fraction division teaches an important and counter-intuitive insight: dividing by a fraction less than 1 produces a larger result. Understanding why — rather than just memorising the rule — builds a deeper number sense that carries through algebra and beyond.

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 division 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.