Practice Dividing Fractions in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Dividing by a fraction means multiplying by its reciprocal: abΓ·cd=abΓ—dc=adbc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}. This works because division asks 'how many groups of this size fit?'

Imagine you have 2 cups of flour and each serving of a recipe needs 13\frac{1}{3} cup. How many servings can you make? You are asking 'how many one-thirds fit into 2?'β€”that is 2Γ·13=62 \div \frac{1}{3} = 6 servings. Division by a fraction counts how many pieces of that size fit inside the whole.

Showing a random 20 of 50 problems.

Example 1

easy
Divide 34Γ·25\frac{3}{4} \div \frac{2}{5}.

Example 2

medium
Show that ab÷ab=1\frac{a}{b} \div \frac{a}{b} = 1 whenever a≠0a \ne 0 and b≠0b \ne 0.

Example 3

challenge
Explain, using a number line, why 34Γ·18=6\tfrac{3}{4} \div \tfrac{1}{8} = 6.

Example 4

easy
Compute 12Γ·2\frac{1}{2} \div 2.

Example 5

hard
Compute 223Γ·1192\tfrac{2}{3} \div 1\tfrac{1}{9}.

Example 6

medium
Compute 1112Γ·16\frac{11}{12} \div \frac{1}{6}.

Example 7

easy
Compute 12Γ·14\frac{1}{2} \div \frac{1}{4}.

Example 8

medium
A roll of tape is 154\frac{15}{4} m long. Each piece needs to be 38\frac{3}{8} m. How many full pieces?

Example 9

medium
A ribbon is 78\frac{7}{8} of a metre long. It is cut into pieces that are each 14\frac{1}{4} of a metre. How many pieces are there?

Example 10

medium
Compute 23Γ·49\frac{2}{3} \div \frac{4}{9}.

Example 11

medium
Compute 78Γ·1416\frac{7}{8} \div \frac{14}{16}.

Example 12

easy
Compute 67Γ·27\frac{6}{7} \div \frac{2}{7}.

Example 13

easy
Compute 58Γ·14\frac{5}{8} \div \frac{1}{4}.

Example 14

hard
A construction crew can pour 35\tfrac{3}{5} of a concrete pad per hour. How long does it take to pour 910\tfrac{9}{10} of a pad?

Example 15

medium
Compute 512Γ·109\frac{5}{12} \div \frac{10}{9}.

Example 16

easy
Compute 1Γ·351 \div \frac{3}{5}.

Example 17

challenge
Simplify 12+1316\frac{\frac{1}{2} + \frac{1}{3}}{\frac{1}{6}}.

Example 18

hard
A container holds 910\frac{9}{10} of a litre of juice. Each glass holds 320\frac{3}{20} of a litre. How many full glasses can be filled?

Example 19

challenge
Why does 'invert and multiply' work for fraction division?

Example 20

medium
A board 78\frac{7}{8} m long is cut into 18\frac{1}{8}-m pieces. How many pieces?
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