Carry out the four operations with fractions, convert between fractions, decimals and percentages, find percentages of amounts, work with percentage change, reverse percentages, compound interest and depreciation.

What this dot point is asking

Fractions, decimals and percentages are three ways of writing the same kind of quantity, and CCEA expects you to calculate with each and switch freely between them. You must add, subtract, multiply and divide fractions, convert between the three forms, find a percentage of an amount, handle percentage increase and decrease, solve reverse-percentage problems, and apply compound interest and depreciation. This material runs from M1 to M8 and appears on both the non-calculator and calculator work, where reverse percentages and compound growth are the higher-value question types.

The four operations with fractions

Multiplying and dividing are the easiest. Multiply two fractions by multiplying numerators and multiplying denominators: $\tfrac{2}{3} \times \tfrac{4}{5} = \tfrac{8}{15}$. Divide by multiplying by the reciprocal (turn the second fraction upside down): $\tfrac{2}{3} \div \tfrac{4}{5} = \tfrac{2}{3} \times \tfrac{5}{4} = \tfrac{10}{12} = \tfrac{5}{6}$.

Addition and subtraction need a common denominator. Rewrite both fractions over the lowest common multiple of the denominators, then add or subtract the numerators only: $\tfrac{1}{2} + \tfrac{1}{3} = \tfrac{3}{6} + \tfrac{2}{6} = \tfrac{5}{6}$. With mixed numbers, either convert to improper fractions first or deal with the whole parts and fractional parts separately.

Converting between the three forms

A percentage is "out of 100", so divide by 100 to make a decimal: $42\% = 0.42$. A decimal becomes a fraction using its place value: $0.42 = \tfrac{42}{100} = \tfrac{21}{50}$. A fraction becomes a decimal by dividing the numerator by the denominator: $\tfrac{3}{8} = 3 \div 8 = 0.375$, and then $\times 100$ gives $37.5\%$.

These conversions let you choose the easiest form for a calculation and are essential for ordering a mixed list such as $0.6$, $\tfrac{5}{8}$ and $62\%$.

Percentages of amounts and percentage change

To find a percentage of an amount, convert to a decimal multiplier and multiply: $35\%$ of $240$ is $0.35 \times 240 = 84$. For an increase or decrease, adjust the multiplier: a $15\%$ increase multiplies by $1.15$, and a $20\%$ decrease multiplies by $0.8$.

Reverse percentages, compound interest and depreciation

A reverse percentage gives you the final amount and asks for the original. The final amount equals a known percentage of the original, so find $1\%$ and scale, or divide by the multiplier. If a price including 20 percent VAT is £60, the original is $60 \div 1.2 = \pounds 50$.

Compound interest and depreciation apply the same multiplier repeatedly.

Depreciation works the same way but with a multiplier below 1; a car losing 12 percent of its value each year is multiplied by $0.88$ per year.

Why this matters

Percentages are the most common real-life maths in the exam, covering prices, interest, growth and decay, while fraction fluency underpins algebra, probability and ratio. CCEA reuses the reverse-percentage and compound-growth structures every year, so recognising which type of problem you face is what separates a secure answer from a lost one.