Multiplying fractions
Multiply fractions step by step with a grid model.
Enter two fractions – the calculation and visualisation appear instantly.
How to multiply fractions
Multiplying fractions is actually the simplest operation – no common denominator needed. Multiply numerator by numerator and denominator by denominator:
a/b × c/d = (a·c) / (b·d)
Why this works: “a fraction of a fraction”
Multiplying fractions means “taking a part of a part”. 2/3 × 3/4 reads as “two thirds of three quarters”. In the grid above: we divide the rectangle vertically into 4 parts and take 3 (three quarters), then horizontally into 3 parts and take 2 (two thirds). The overlap of both is the result – 6 cells out of 12 total, i.e. 6/12 = 1/2.
Cross-cancelling
With multiplication you can often simplify before calculating – any numerator with any denominator. For example 2/3 × 3/4: the 2 in the first numerator and the 4 in the second denominator can both be divided by 2, and the 3s cancel each other. This simplifies the calculation and the result comes out already in lowest terms.
Multiplying a fraction by a whole number
Write the whole number as a fraction with denominator 1. For example 5 × 2/3 = 5/1 × 2/3 = 10/3 = 3⅓. So enter the whole number as the numerator and 1 as the denominator.
Tip: the result is automatically simplified to lowest terms.