Fractions in 10 Minutes
Recipes, measurements, splitting a bill: fractions turn up all the time. Here's everything you need, one short step at a time.
What a fraction means
A fraction is a number of equal parts. The bottom number (the denominator) says how many parts make a whole. The top number (the numerator) says how many parts you have.
A fraction is also a division: 3/4 means 3 ÷ 4 = 0.75.
Equivalent fractions and simplifying
Multiply or divide the top and bottom by the same number and the fraction keeps its value: 1/2 = 2/4 = 50/100.
To simplify, divide top and bottom by the biggest number that goes into both (the greatest common factor).
- Both 18 and 24 divide by 6
- 18 ÷ 6 = 3 and 24 ÷ 6 = 4
- 18/24 = 3/4
Not sure of the biggest factor? Divide by any shared number, like 2 or 3, and repeat until nothing else goes into both.
Adding and subtracting
You can only add or subtract fractions when the bottoms match. If they don't, rewrite them with a common denominator first.
- A number both 3 and 4 go into: 12
- 1/3 = 4/12 and 1/4 = 3/12
- Add the tops: 4 + 3 = 7
- 1/3 + 1/4 = 7/12
Common mistake: adding the bottoms too. 1/3 + 1/4 is not 2/7; that's smaller than either of them.
Mixed numbers like 2½ are easiest as improper fractions: 2½ = 5/2 (2 × 2 + 1 = 5 halves).
Multiplying and dividing
Multiply: top × top, bottom × bottom. No common denominator needed.
Divide: flip the second fraction and multiply. (“Keep, change, flip.”)