Dividing Fractions Examples in Math

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

Dividing by a fraction by multiplying by its reciprocal (inverting the divisor and multiplying).

Imagine you have 2 cups of flour and each serving of a recipe needs \frac{1}{3} cup. How many servings can you make? You are asking 'how many one-thirds fit into 2?'—that is 2 \div \frac{1}{3} = 6 servings. Division by a fraction counts how many pieces of that size fit inside the whole.

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: Dividing by a fraction is the same as multiplying by its reciprocal—'keep, change, flip.'

Common stuck point: Students flip the wrong fraction (the dividend instead of the divisor).

Sense of Study hint: Circle the second fraction (the one after the division sign) and flip only that one, then multiply normally.

Worked Examples

Example 1

easy
Divide \frac{3}{4} \div \frac{2}{5}.

Solution

  1. 1
    Take the reciprocal of the divisor: \frac{2}{5} becomes \frac{5}{2}.
  2. 2
    Multiply: \frac{3}{4} \times \frac{5}{2} = \frac{15}{8}.
  3. 3
    Convert to a mixed number if desired: \frac{15}{8} = 1\frac{7}{8}.

Answer

\frac{15}{8} = 1\frac{7}{8}
Dividing by a fraction is equivalent to multiplying by its reciprocal. This 'keep-change-flip' rule works because division asks 'how many groups of the divisor fit into the dividend.'

Example 2

medium
A ribbon is \frac{7}{8} of a metre long. It is cut into pieces that are each \frac{1}{4} of a metre. How many pieces are there?

Practice Problems

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

Example 1

easy
Compute \frac{5}{6} \div \frac{5}{12}.

Example 2

hard
A container holds \frac{9}{10} of a litre of juice. Each glass holds \frac{3}{20} of a litre. How many full glasses can be filled?
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Background Knowledge

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

multiplying fractionsinverse operations