Add, subtract, multiply and divide fractions and mixed numbers; convert between fractions, decimals and percentages; and find a percentage of an amount and one number as a percentage of another.

What this dot point is asking

OCR references N6, N8 and N9 cover calculating with fractions, converting freely between fractions, decimals and percentages, and the core percentage operations of finding a percentage of an amount and writing one quantity as a percentage of another. These three forms are different costumes for the same idea, a proportion, and a strong candidate moves between them without thinking. The skills underpin ratio, proportion, interest and probability, and they are tested heavily on the non-calculator paper, so the by-hand methods must be secure.

The four operations on fractions

Addition and subtraction need a common denominator; multiplication and division do not.

For mixed numbers, convert to improper fractions first. To work out $\tfrac{3}{4} \div 1\tfrac{1}{2}$, write $1\tfrac{1}{2} = \tfrac{3}{2}$, then $\tfrac{3}{4} \div \tfrac{3}{2} = \tfrac{3}{4} \times \tfrac{2}{3} = \tfrac{6}{12} = \tfrac{1}{2}$. Always simplify the final answer, and give it as a mixed number if the question asks.

Converting between the three forms

The three forms convert with a small set of moves.

So $\tfrac{7}{8} = 0.875 = 87.5\%$, and $0.6 = \tfrac{60}{100} = \tfrac{3}{5} = 60\%$. Recognising these instantly is what lets you compare a fraction, a decimal and a percentage in one question and decide which is largest.

Percentages of amounts

There are two routine percentage tasks at this level.

So $15\%$ of $240 = 0.15 \times 240 = 36$, and $18$ out of $40$ as a percentage is $\tfrac{18}{40} \times 100 = 45\%$. On the non-calculator paper, build percentages from easy pieces: $10\%$ is a tenth, $5\%$ is half of that, and $1\%$ is a hundredth, so $15\%$ of $240$ is $24 + 12 = 36$.

Why fluency matters

These conversions are the spine of the Ratio strand and of probability, where answers are often demanded as fractions, decimals or percentages interchangeably. OCR's AO2 marks reward you for choosing the cleanest form for a calculation, for instance turning "$\tfrac{3}{8}$ off" into $37.5\%$ or into $0.375$ depending on whether a calculator is allowed. Showing the conversion explicitly also secures method marks when the final arithmetic slips.