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P6 The equal concept

Today’s problem — free all day, every step. Every day has one.

370 visitors — who bought a raffle ticket

A charity fun fair had 370 visitors, made up of children and adults. of the children and of the adults bought a raffle ticket. The number of children who did not buy a raffle ticket is twice the number of adults who did not buy one. How many adults did not buy a raffle ticket?

One step of the worked solution to 370 visitors — who bought a raffle ticket, drawn in pencil.
9 steps, drawn in pencil

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The pattern behind it: The equal concept

The question tells you a part of one pile equals a part of another.

In this one. Make the numerator the same. The matching numerator 6 makes one group on each side the same size; then the denominator gives the total number of same-sized units, so children : adults = 27 : 10.

the two shaded parts are the same sizePile Aa third of APile Ba fifth of B

How to spot it

Two different groups each get their own fraction or percentage, and the question links them with 'the same as', 'twice as many as', or a shared cost across different units.

Common mistake

Children compare the two fractions without first relating them to a common whole. A smaller fraction of a larger group can be bigger than a larger fraction of a smaller group.

Try one like it

Challenging 810 workers — who finished on time A factory has 810 workers, made up of assembly-line workers and packing workers. 7/12 of the assembly-line workers and 8/9 of the …
All 5 with 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.