JENECONKMaths Universe

Dividing Fractions

Ages 10–14

Difficulty adapts to you

Dividing Fractions

To divide by a non-zero fraction, multiply by its reciprocal. The reciprocal of a/b is b/a, provided a is not zero.

Your goals

  • ✓You can divide one fraction by another.
  • ✓You can use reciprocal, divisor correctly.
  • ✓You can multiply by the reciprocal of the non-zero divisor.

Words to know

reciprocal:
A non-zero fraction turned upside down; the reciprocal of a/b is b/a.
divisor:
The number or fraction you divide by.

Examples

  • 12/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
  • 21/2 ÷ 3 = 1/2 ÷ 3/1 = 1/2 × 1/3 = 1/6.

Check these

  • • Do not take the reciprocal of the first fraction or divide by zero.
  • • Keep every number, symbol, label, and unit in its correct place.
  • • Show enough working to check how you reached your answer.

Helpful habits

  • • Read the whole question before choosing what to do.
  • • Show one clear step at a time and check each step.
  • • If you are stuck, draw a model, try smaller numbers, or revisit the example.

Now try your own

Create your own dividing fractions example, solve it, and explain how you checked it.

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Helpful Hints

“Try drawing a picture to help you see the answer.”