How to Add, Subtract, and Simplify Fractions

Fractions follow a small set of dependable rules: to add or subtract you need a common denominator, to multiply you go straight across, and to divide you flip the second fraction and multiply. Then you simplify by dividing the top and bottom by their greatest common divisor. Let's walk through each one, and you can verify every step with our free fraction calculator.

Adding and subtracting: find a common denominator

You can only add or subtract fractions once the denominators match. Take 1/4 + 1/6. The smallest common denominator is 12, so rewrite them as 3/12 and 2/12, then add the numerators: 3/12 + 2/12 = 5/12. Subtraction works the same way: 3/4 - 1/6 becomes 9/12 - 2/12 = 7/12.

Multiplying: straight across

Multiplying is the easy one — no common denominator needed. Multiply the numerators together and the denominators together. For 2/3 x 3/4, that's (2 x 3) / (3 x 4) = 6/12, which simplifies to 1/2.

Dividing: flip and multiply

To divide, multiply by the reciprocal of the second fraction (flip its top and bottom). So 1/2 / (3/4) becomes 1/2 x 4/3 = 4/6, which simplifies to 2/3. If you can remember "keep, change, flip," you'll never miss it.

Simplifying: divide by the GCD

A fraction is in lowest terms when the numerator and denominator share no common factor other than 1. Take 8/12: the greatest common divisor of 8 and 12 is 4, so divide both by 4 to get 2/3. If you can't spot the GCD right away, just keep dividing by any shared factor — 8/12 to 4/6 to 2/3 gets you there too.

Practice until it's automatic

These four moves cover almost everything you'll do with fractions. When you want to check an answer or see the work, use the fraction calculator, and for converting parts of a whole into percentages, the percentage calculator pairs nicely. To have a patient explanation on demand, COSMIQ's free voice tutor is free for every learner.

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