Calculate with fractions and mixed numbers, convert freely between fractions, decimals and percentages, and convert a recurring decimal to an exact fraction (Higher tier).

What this dot point is asking

WJEC asks you to calculate fluently with fractions and mixed numbers using all four operations, to convert freely between fractions, decimals and percentages, and at Higher tier to convert a recurring decimal into an exact fraction. These three forms are one idea written three ways, and questions move between them constantly, so converting quickly and calculating accurately, especially without a calculator on Unit 1, protects marks across the whole paper.

Calculating with fractions

The four operations each have their own method.

Adding and subtracting need a common denominator. Rewrite both fractions over the lowest common multiple of the denominators, then add or subtract the numerators only: $\tfrac{2}{3} + \tfrac{1}{4} = \tfrac{8}{12} + \tfrac{3}{12} = \tfrac{11}{12}$.

Multiplying is the easiest: multiply numerators together and denominators together, cancelling first where possible: $\tfrac{3}{5} \times \tfrac{10}{9} = \tfrac{30}{45} = \tfrac{2}{3}$.

For mixed numbers, always convert to improper fractions first, calculate, then convert back at the end.

Converting between the three forms

Fractions, decimals and percentages are interchangeable.

A short table to memorise: $\tfrac{1}{2} = 0.5 = 50\%$, $\tfrac{1}{4} = 0.25 = 25\%$, $\tfrac{1}{5} = 0.2 = 20\%$, $\tfrac{1}{3} = 0.\dot{3} = 33.\dot{3}\%$. Recognising these on sight saves time on the non-calculator paper.

Recurring decimals to fractions (Higher)

A recurring decimal has a digit or block that repeats forever, shown with dots over the first and last repeating digits. Every recurring decimal is exactly equal to a fraction.

The trick is to multiply by powers of ten that make the repeating tails identical, so they cancel on subtraction.

Finding a fraction of an amount and one as a fraction of another

Two everyday operations come up constantly. To find a fraction of an amount, multiply: $\tfrac{3}{5}$ of $40$ is $\tfrac{3}{5} \times 40 = 24$, or equivalently divide by the denominator and multiply by the numerator ($40 \div 5 = 8$, then $\times 3 = 24$). To write one quantity as a fraction of another, put the part over the whole and simplify: $18$ out of $24$ is $\tfrac{18}{24} = \tfrac{3}{4}$. These feed directly into percentage and probability work, where "what fraction" and "what percentage" questions are routine.

Ordering and comparing mixed forms

A frequent non-calculator task is to order a mixed list such as $\tfrac{3}{5}$, $0.58$ and $62\%$. Convert everything to the same form, usually decimals: $\tfrac{3}{5} = 0.6$, $62\% = 0.62$, and $0.58$ is already a decimal. Ordered smallest to largest that is $0.58, \tfrac{3}{5}, 62\%$. Converting to a common form removes any guesswork, and decimals are usually the quickest common form because comparing them is just reading digits left to right.

Why this matters

These conversions and calculations are the backbone of the percentage, ratio, probability and statistics work later in the course; a probability written as $\tfrac{3}{8}$ may need expressing as a decimal or percentage, and an interest calculation runs on fraction-decimal fluency. Because WJEC examines fractions heavily on the non-calculator Unit 1, secure written methods here pay off across both components.