Do maths with two fractions. The answer is always made as simple as possible, and shown as a decimal and, where useful, a mixed number.
To add or subtract, both fractions are put over a common denominator first.
To multiply, the numerators and denominators are multiplied straight across.
To divide, the second fraction is flipped and then multiplied.
The result is divided by the greatest common divisor to reduce it to lowest terms.
Add / subtract: a/b ± c/d = (a×d ± c×b) ÷ (b×d)
Multiply: a/b × c/d = (a×c) ÷ (b×d)
Divide: a/b ÷ c/d = (a×d) ÷ (b×c)
Adding one half and one third.
First fraction: 1/2
Second fraction: 1/3
Common denominator: 2 × 3 = 6
Convert: 1/2 = 3/6 and 1/3 = 2/6
Add the numerators: 3 + 2 = 5
Result: 5/6, already in lowest terms
Answer: 5/6 (0.8333…)
Why do I need a common denominator to add fractions?
Because the bottom number of a fraction shows how big each piece is. You cannot add halves to thirds directly, just like you cannot add metres to feet — both have to be changed to the same size of piece first.
Why does dividing by a fraction make the answer bigger?
Dividing asks how many of the second fraction fit into the first. There are four quarters in one whole, so 1 ÷ 1/4 = 4. Dividing by a number smaller than one always makes the result bigger.
What is a mixed number?
A whole number combined with a fraction, like 2 1/3 instead of 7/3. Both are equal — a mixed number is just easier to picture.