Number and Operations—Fractions
Unlike fractions and mixed numbers
Add and subtract fractions with different denominators, and swap between mixed numbers and improper fractions.
Fractions can only be added when the pieces are the same size. Halves and quarters are different sizes, so 1/2 + 1/4 cannot be added as it stands — one of them has to be rewritten first.
The rule
Change one fraction so both have the same denominator, then add or subtract the top numbers only. The bottom number is the size of the pieces, and that does not change just because you have more of them.
Worked example
What is 1/2 + 1/4?
4 is a multiple of 2, so rewrite the half in quarters: 1/2 = 2/4.
When one denominator divides into the other, only one fraction needs rewriting.
Mixed numbers
A mixed number is a whole number with a fraction beside it, like 2 1/3. An improper fraction says the same thing in pieces alone: 2 1/3 is 7/3, because two wholes are six thirds and one third makes seven.
Try it together
Let us work out 2/3 + 1/6 together.
Sixths are smaller than thirds, and 6 is a multiple of 3 — so the thirds are the ones to rewrite.
1.How many sixths are the same as 2/3? Write your answer as a fraction.
Have a go
Have a go on your own: 1/4 + 3/8 = ? Write your answer as a fraction.
Hint: Rewrite the quarter in eighths first.
Ready to practice?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.