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Branching

Mr Lim’s salary — amount saved

Mr Lim spent of his salary on household and medical expenses, with of the household expenses equal to of the medical fees. He gave of the remainder to his mother and saved the rest; his mother received $150 more than the medical fees. How much did he save?

One step of the worked solution to Mr Lim’s salary — amount saved, drawn in pencil.
7 steps, drawn in pencil

See all 7 steps

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The pattern behind it: Branching

The second fraction is of one piece, not of the whole.

In this one. Use the same small unit throughout every branch so amounts from different branches can be compared directly.

All of it$81books4/9 → $36the rest5/9 → $45a game1/3 of $45 = $15left$30

How to spot it

A second fraction arrives after the first and is attached to a piece rather than to the whole — 'of the remainder', 'of what was left', or 'of the ones that were red'.

Common mistake

Children take the second fraction of the original total instead of the piece it was named against, which makes the amount come out too big.

More on this pattern →

The 33 problem patterns

All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.

A PDF, and a note when new solutions go up.