PROBLEM SOLVING

Multi Step Fraction Problems

Learn the reliable method for multi step fraction problems, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

Multi-step fraction problems require each fraction to be applied to the correct whole or remainder.

Picture itPlan, solve, then check
Bowls, fruit, scales and a measuring jug showing ratio and measurement in baking
2 · THE METHOD

Follow these steps

  1. Identify what quantity is the whole at each step.
  2. Calculate one fraction operation at a time.
  3. Convert units or work backwards only after the fraction relationship is clear.
3 · WORKED EXAMPLES

See the method in action

Example 1

A roll contains 420 m. 2/5 is used, then 1/3 of the remainder is given away. How many metres remain?

  1. 2/5 of 420 is 168, leaving 252.
  2. One third of 252 is 84, so 168 m remain.
Answer: 168 m
Example 2

A charity packs 1/3 of 216 boxes in the morning and 1/4 of the remainder in the afternoon. How many boxes are packed altogether?

  1. Morning: 216 ÷ 3 = 72.
  2. The remainder is 144; one quarter is 36.
  3. Altogether 72+36=108.
Answer: 108
4 · ELEVENSPRINT TIP

A useful shortcut

Convert units or work backwards only after the fraction relationship is clear.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.