Number – fractions (including decimals)
Comparing and ordering fractions
Compare fractions with the same bottom number and with the same top number, and put a set of fractions in order.
A fraction has two jobs written into it. The bottom number says how many equal pieces the whole was cut into, and the top number says how many of those pieces you have. Both matter, and comparing two fractions means asking which number is doing the work — sometimes it is the top, sometimes the bottom.
Two easy comparisons
If the bottom numbers match, the pieces are the same size, so more pieces means more cake: 5/8 beats 3/8. If the top numbers match, you have the same number of pieces, so the smaller the pieces the less you have — and a bigger bottom number means smaller pieces. That is why 1/3 is larger than 1/5, even though 5 is larger than 3.
Worked example
Which is larger, 1/3 or 1/5?
Both have a single piece on top.
So the question is purely about how big one piece is.
Try it together
Now let us put 1/2, 1/8 and 1/4 in order together, smallest first.
Every one of these is a single piece, so the bottom number alone decides the size.
1.Which of the three bottom numbers is the largest?
Have a go
Have a go on your own. Fill in the missing number: 3/4 = ?/8
Hint: The bottom number has doubled.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.