Adding and subtracting fractions
Add and subtract fractions step by step with a common denominator and a bar model.
Enter two fractions – the calculation and visualisation appear instantly.
How to add fractions
We can only add fractions when they have the same denominator – that is, when the whole is divided into equally sized parts. Then we just add the numerators (the number of parts) and keep the denominator:
a/b + c/d = (a·d + c·b) / (b·d)
Why this works: we convert each fraction to the common denominator b·d. We multiply the first by d and the second by b. Now both have equally sized parts and the numerators can be added.
Step-by-step example
1/2 + 1/3: the common denominator is 6. 1/2 = 3/6 (multiply by three), 1/3 = 2/6 (multiply by two). Now 3/6 + 2/6 = 5/6. The bar shows that a half and a third together take up five sixths.
Subtracting fractions
Subtraction works the same way – we just subtract the numerators instead of adding: a/b − c/d = (a·d − c·b) / (b·d). For example 3/4 − 1/2 = 3/4 − 2/4 = 1/4.
Least common denominator
The product b·d always works, but sometimes gives an unnecessarily large number. The least common denominator (the least common multiple of the denominators) gives smaller numbers. The result is then simplified to lowest terms anyway – the calculator does that automatically.
Tip: the result is automatically simplified to lowest terms. You'll recognise a mixed number (e.g. 1¼) when the numerator is larger than the denominator.