Today’s problem — free all day, every step. Every day has one.
Priya had some money. She spent of it on art supplies and of the remainder on a canvas tote bag. After that, her aunt gave her $144. The ratio of the total amount she had at the end to the amount she had at first was 5 : 4. How much did Priya have at first?
Answer
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The second fraction is of one piece, not of the whole.
In this one. Choose the number of units so that every cut in the question lands on a whole box — 20 works for the 1/4, for the 2/5 of what remains, and for the 5 : 4 — and then the $144 gift stops being a fraction and becomes an exact 16-unit gap.
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.