Today’s problem — free all day, every step. Every day has one.
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?
Answer
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 3/7 × 84=36 m. The unspent rope is 84-36=48 m, and 12+36+48=96 m, so every condition is satisfied.
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.
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'.
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.
Worked examples of all 33 patterns and skills, in a booklet you can print.