Today’s problem — free all day, every step. Every day has one.
Rope — fencing area A and area B
A farmer had 96 m of rope. He used of it to fence area A, and of the remainder to fence area B. How many metres of rope did he use for area B?
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The farmer used 36 m of rope for area B. Check: area A used 1/8 × 96=12 m, leaving 96-12=84 m; area B used 3…
The pattern behind it: Branching
The second fraction is of one piece, not of the whole.
In this one. Cut the whole into 8 equal units so area A lands on exactly 1 unit; the remainder is then exactly 7 equal units, so 3/7 of the remainder is simply 3 of those units.
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.
Try one like it
Standard A dress and a handbag — Mei's savings Mei spent $48 on a dress. This was 3/8 of her savings. After buying the dress, she spent 1/5 of the remaining savings on a handbag…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.