Dividing fractions
Divide fractions using the reciprocal, step by step.
Enter two fractions – the calculation and visualisation appear instantly.
How to divide fractions
Dividing fractions has a simple rule: keep the first fraction, flip the second (swap numerator and denominator) and multiply instead of dividing:
a/b ÷ c/d = a/b × d/c = (a·d) / (b·c)
Why dividing is done by flipping
Division means “how many times does it fit”. 1/2 ÷ 1/4 asks: “how many quarters fit into a half?” The answer is 2 – and that is exactly what you get when you multiply a half by the reciprocal of a quarter (4/1): 1/2 × 4/1 = 4/2 = 2. The reciprocal is the number that, when multiplied by the original, gives 1 – and dividing by a number is the same as multiplying by its reciprocal.
Step-by-step example
1/2 ÷ 3/4: flip 3/4 to 4/3, then 1/2 × 4/3 = 4/6 = 2/3. So two thirds of three quarters fit into a half.
Dividing a fraction by a whole number
Write the whole number as a fraction with denominator 1. For example 2/3 ÷ 2 = 2/3 ÷ 2/1 = 2/3 × 1/2 = 2/6 = 1/3. So enter the whole number as the numerator of the second fraction and 1 as its denominator.
Tip: the result is automatically simplified to lowest terms.