A pie, and fractions to choose from. Can it be written with smaller numbers, or not?
Simplifying fractions
Practise simplifying fractions, from 6/8 = 3/4 to 18/24 = 3/4: seeing when it can be done, dividing the numerator and denominator, and writing the answer as small as it goes.
First: equivalent fractions. Later also: the division tables. To divide both 18 and 24 by 6, a pupil has to see that division without long thought.
Usually taught in Year 4–5 in England and Wales, around ages 8 to 10. Every pupil goes at their own pace; this is a guide, not a requirement.
The first of 6 exercises in this topic. See them all
Simplifying fractions: example sums with their answers
Simplifying, with diagrams
46=23
Simplifying
69=23
As small as it goes
4048=56
More than a whole
2012=53
Simplifying fractions
Worksheets
Free to print, in colour or black and white, with the answers separate.
How it fits together
The arrows point to what can be done next. Whatever sits inside a box belongs to it.
Needed first
Fractions
Can come next
first this, then that belongs to
Divide the numerator and denominator by the same number. The pie stays the same, the numbers get smaller.
More than one pie, in small pieces. Which picture shows the same amount, in bigger pieces?
Divide the numerator and denominator by the same number: 21/35 = 3/5.
Dividing once is not enough here: 18/24 is 9/12, but it goes smaller still: 3/4.
A fraction above one can get smaller too: 14/12 = 7/6.
Why it matters
It is hard to see how much 18/24 is. Everyone sees 3/4 at once, and it is exactly the same amount. That is why so many sums ask for an answer as small as it goes.
Simplifying is not a new kind of sum, but equivalent fractions run the other way: the same amount, in bigger pieces. A pupil who has it will find adding, multiplying and dividing fractions easier each time.
How to approach it
Start with the pictures: can this pie be shown with fewer pieces? Then the pupil divides: find a number that goes into both the numerator and the denominator, and divide both. 6/8 becomes 3/4, because 6 and 8 can both be divided by 2.
Sometimes dividing once is not enough. 18/24 becomes 9/12, but that goes smaller still: 3/4. At each answer, ask the pupil: can the numerator and denominator still be divided by the same number?
When is it secure?
When the pupil gets all 10 sums right in 50 seconds or less. Answers only come that quickly once they come from memory.