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 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.

Read the full concept explanation β†’

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 asks how many of that size fit, so you multiply by its reciprocal.

Common stuck point: The procedure for dividing fractions is the easy part; the trap is flipping the first fraction instead of the divisor. Asking "Am I asking how many of a fractional size fit into another amount?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Am I asking how many of a fractional size fit into another amount?

Worked Examples

Example 1

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

Answer

158=178\frac{15}{8} = 1\frac{7}{8}

First step

1
Take the reciprocal of the divisor: 25\frac{2}{5} becomes 52\frac{5}{2}.

Full solution

  1. 2
    Multiply: 34Γ—52=158\frac{3}{4} \times \frac{5}{2} = \frac{15}{8}.
  2. 3
    Convert to a mixed number if desired: 158=178\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 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 3

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 4

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 5

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

Practice Problems

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

Example 1

easy
Compute 56Γ·512\frac{5}{6} \div \frac{5}{12}.

Example 2

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 3

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

Example 4

easy
Compute 34Γ·12\frac{3}{4} \div \frac{1}{2}.

Example 5

easy
Compute 23Γ·4\frac{2}{3} \div 4.

Example 6

easy
Compute 6Γ·136 \div \frac{1}{3}.

Example 7

easy
Compute 56Γ·56\frac{5}{6} \div \frac{5}{6}.

Example 8

easy
Compute 38Γ·34\frac{3}{8} \div \frac{3}{4}.

Example 9

easy
Compute 12Γ·2\frac{1}{2} \div 2.

Example 10

easy
Compute 45Γ·25\frac{4}{5} \div \frac{2}{5}.

Example 11

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

Example 12

medium
How many 14\frac{1}{4}-cup servings are in 33 cups?

Example 13

medium
Compute 56Γ·103\frac{5}{6} \div \frac{10}{3}.

Example 14

medium
Compute 212Γ·342\frac{1}{2} \div \frac{3}{4}.

Example 15

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

Example 16

medium
Compute 35Γ·625\frac{3}{5} \div \frac{6}{25}.

Example 17

medium
Simplify the complex fraction 2345\frac{\frac{2}{3}}{\frac{4}{5}}.

Example 18

medium
Compute 710Γ·710\frac{7}{10} \div \frac{7}{10} and explain quickly.

Example 19

medium
34\frac{3}{4} of a pizza is split among 33 people. How much pizza each?

Example 20

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

Example 21

challenge
Solve for xx: 23Γ·x=49\frac{2}{3} \div x = \frac{4}{9}.

Example 22

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

Example 23

easy
Compute 13Γ·16\frac{1}{3} \div \frac{1}{6}.

Example 24

easy
Compute 25Γ·15\frac{2}{5} \div \frac{1}{5}.

Example 25

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

Example 26

easy
Compute 4Γ·124 \div \frac{1}{2}.

Example 27

easy
Compute 34Γ·3\frac{3}{4} \div 3.

Example 28

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

Example 29

easy
Compute 1Γ·351 \div \frac{3}{5}.

Example 30

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

Example 31

medium
Compute 910Γ·35\frac{9}{10} \div \frac{3}{5}.

Example 32

medium
How many 13\frac{1}{3}-cup servings are in 56\frac{5}{6} cup?

Example 33

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

Example 34

medium
Compute 112Γ·381\tfrac{1}{2} \div \frac{3}{8}.

Example 35

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 36

medium
Compute 49Γ·815\frac{4}{9} \div \frac{8}{15}.

Example 37

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

Example 38

hard
Simplify the complex fraction 35910\dfrac{\frac{3}{5}}{\frac{9}{10}}.

Example 39

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

Example 40

hard
Compute 12βˆ’1314+112\dfrac{\frac{1}{2} - \frac{1}{3}}{\frac{1}{4} + \frac{1}{12}}.

Example 41

hard
Solve for xx: 34Γ·x=98\frac{3}{4} \div x = \frac{9}{8}.

Example 42

hard
Compute 1415Γ·710\frac{14}{15} \div \frac{7}{10}.

Example 43

challenge
If abΓ·cd=cdΓ·ab\frac{a}{b} \div \frac{c}{d} = \frac{c}{d} \div \frac{a}{b} and both fractions are positive, what must be true about ab\frac{a}{b} and cd\frac{c}{d}?
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Background Knowledge

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

multiplying fractionsinverse operations