Equivalent Fractions
1/2 and 4/8 are the same amount, cut a different number of ways. Fill in the missing number to make two fractions match, then do it the other way round and cancel one down to its simplest form.
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Why doing the same to the top and the bottom works
Take 1/2 of a chocolate bar and cut every piece in half. You have not eaten anything and you have not been given anything — but now the bar is in 4 pieces and you have 2 of them. That is 2/4, and it is the same amount as 1/2.
That is the whole rule. Cutting the pieces into n makes the bottom number n times bigger, and it makes the number of pieces you are holding n times bigger too. Do it to one and not the other, and you really have changed the amount.
Simplifying is the same move backwards
Cancelling 6/8 down to 3/4 is gluing the pieces back together in pairs. Find a number that goes into the top and the bottom, divide both by it, and keep going until nothing does. A fraction is in its simplest form when the only number that divides both is 1.
Both directions live in this one tool on purpose. Practised separately, they turn into two unrelated tricks — “make it into eighths” and “cancel it down” — instead of one idea you can run either way.
The mistake to watch for
Adding instead of multiplying. Going from 2/3 to something over 9, the bottom went up by 6 — but it also went up three times, and it is the three times that matters. 2/3 is 6/9, not 5/9.
School levels
School levels are a guide only. They show where a skill is usually taught in each country and are not taken from, aligned to, or endorsed by any curriculum authority. Your school may cover it earlier or later.