Fraction Calculator with Steps

Enter two fractions and pick an operation — you get the full step-by-step working: how to find the common denominator, which multipliers to use, how to reduce the result and extract the whole part. Every step comes with a formula and an explanation.

Task:

How it works. Fractions can only be added or subtracted when their denominators match — so we first find the LCM of the denominators and convert both fractions. Multiplication is simpler: numerator by numerator, denominator by denominator. Division reduces to multiplying by the reciprocal. Finally the result is reduced via the GCD, and an improper fraction gets its whole part extracted.

FAQ

How do you find a common denominator?

Find the LCM of the denominators — that is the common denominator. Then compute each fraction's multiplier by dividing the LCM by its denominator, and multiply both the numerator and the denominator by it. The value of the fraction does not change.

How do you reduce a fraction?

Find the GCD of the numerator and denominator and divide both by it. For 12/18 the GCD is 6: 12/6 = 2, 18/6 = 3, giving 2/3. If the GCD is 1, the fraction is already in lowest terms.

Why does the fraction flip when dividing?

Dividing by a number is the same as multiplying by its reciprocal. The reciprocal of b/c is c/b — their product is 1. Hence a/b ÷ c/d = a/b · d/c.

What is a mixed number?

An improper fraction written with its whole part extracted: 7/3 = 2 1/3 (two and one third). The whole part is the quotient of the numerator by the denominator; the remainder becomes the numerator of the fractional part.