Fractions practice: simplifying, adding and multiplying

To multiply fractions, multiply the numerators together and the denominators together, then simplify. To add fractions, first make the denominators equal, then add only the numerators. For example, two thirds times three fifths is six fifteenths, which simplifies to two fifths.

Fractions underpin ratio, probability and algebra, so weaknesses here surface everywhere else. The three operations examined most often are simplifying, adding with different denominators, and multiplying.

The method, step by step

1. Simplify by dividing. Divide top and bottom by their highest common factor.
2. Add with a common denominator. Convert both fractions so the denominators match, then add only the numerators.
3. Multiply straight across. Tops together, bottoms together, then simplify.
4. Divide by flipping. To divide, turn the second fraction upside down and multiply.

Worked example

Common mistakes

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