N4NumberFoundation

Fractions

A fraction shows a part of a whole. Once you can find equivalent fractions, the four operations all become straightforward — the golden rule for adding and subtracting is a common denominator.

40 min Video by Maths Genie AQA GCSE Maths

Adding and Subtracting FractionsWatch the walkthrough, then read the notes below.

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What you'll learn

Simplify fractions and find equivalent fractions
Add and subtract fractions
Multiply and divide fractions
Work with mixed numbers

Equivalent fractions

Multiplying or dividing top and bottom by the same number gives an equal fraction: $\frac{1}{2} = \frac{2}{4} = \frac{5}{10}$ . Dividing to the smallest whole numbers is called simplifying.

Adding and subtracting

You can only add or subtract fractions when the bottoms (denominators) are the same. Rewrite each fraction with a common denominator, then add or subtract the tops.

\frac{a}{b} + \frac{c}{d} = \frac{a d + b c}{b d}

Common denominator, then add the numerators.

1Common denominator is 12.

\frac{1}{3} = \frac{4}{12}

\frac{1}{4} = \frac{3}{12}

\frac{4}{12} + \frac{3}{12} = \frac{7}{12}

Answer

\frac{7}{12}

Tip — For multiplying, just multiply tops and bottoms. To divide, “keep, flip, multiply” (multiply by the reciprocal).

Remember these

\frac{a}{b} \times \frac{c}{d} = \frac{a c}{b d}

Multiply tops and bottoms.

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Divide = multiply by the reciprocal.

Watch out for these

Adding fractions by adding tops and bottoms:

\frac{1}{3} + \frac{1}{4} = \frac{2}{7}

Use a common denominator first:

\frac{4}{12} + \frac{3}{12} = \frac{7}{12}

Flipping the wrong fraction when dividing.

Keep the first fraction, flip the second, then multiply.

Key takeaways

Equivalent fractions: multiply/divide top and bottom by the same number.
Add/subtract only with a common denominator.
Multiply across; divide by flipping the second fraction.

Test yourself

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