Number
Adding and subtracting fractions
Add and subtract fractions, including ones with different denominators.
Fractions with the same bottom number are easy to add: they are already the same size of piece, so you just count them. Three eighths plus two eighths is five eighths, in the same way that three apples plus two apples is five apples.
Watch out
Never add the bottom numbers. 1/4 + 1/4 is 2/4, not 2/8. The bottom number tells you what size the pieces are, and adding does not change their size.
The trouble starts when the bottom numbers disagree, because then you are trying to add two different sizes of piece. The fix is always the same: rewrite one of them so both are counting the same size.
Worked example
What is 1/2 + 1/4?
Halves and quarters are different sizes, so change the half into quarters. 1/2 is the same as 2/4.
Multiply the top and the bottom by the same number and the value does not change — you have just cut each piece in two.
Try it together
Your turn: 2/3 + 1/6
Thirds and sixths are different sizes, so one of them has to change. Six is a multiple of three, so it is the thirds that move.
1.2/3 is the same as how many sixths? Type just the top number.
Have a go
Have a go on your own: 1/4 + 1/3
Hint: Turn both into twelfths: 1/4 is 3/12 and 1/3 is 4/12.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.