Today’s problem — free all day, every step. Every day has one.
Ravi had some money saved in his piggy bank. He spent of it on a video game and of the remainder on a pair of headphones. After that, his uncle gave him $112. The ratio of the total amount he had at the end to the amount he had at first was 5 : 4. How much did Ravi have at first?
Answer
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The second fraction is of one piece, not of the whole.
In this one. Cut the starting amount into 20 units — the smallest number of boxes that survives a quarter cut, then two-fifths of what remains, and a 5 : 4 comparison — and the uncle's $112 stops being a stray number and becomes a clean gap of 16 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.