Use ratio notation, simplify ratios and share a quantity in a given ratio, and solve direct and inverse proportion problems including the unitary method.

What this dot point is asking

WJEC requires you to write and simplify ratios, share a quantity in a given ratio, and solve direct and inverse proportion problems, including with the unitary method. Ratio and proportion run through the whole course, from scale drawings and similar shapes to compound measures and recipes, and they appear on both components, so a confident method for "how much is one part" and "does more mean more or less" earns marks across many topics.

Ratio notation and simplifying

A ratio such as $12 : 18$ compares two quantities. Simplify by dividing every part by their highest common factor: $12 : 18 = 2 : 3$ after dividing by $6$. A ratio can be written in the form $1 : n$ by dividing both parts by the first, which is useful for scales and best-buy comparisons.

Sharing in a ratio

The standard method has three steps: add the parts, divide to find one part, then multiply.

Some questions give you one share and ask for the whole or another share; in that case work out the value of one part from the share you are given, then scale to whatever is asked.

Direct and inverse proportion

Two quantities are in direct proportion if doubling one doubles the other; their ratio stays the same. The unitary method solves these: find the value of one unit, then multiply up. If $5$ pens cost GBP 2, one pen costs $40$p, so $8$ pens cost GBP 3.20.

The key decision is which type you have. Ask: if I increase the first quantity, does the second go up (direct) or down (inverse)?

Changing and combining ratios

WJEC also sets questions where a ratio changes or two ratios must be combined. If the ratio of boys to girls in a club is $2 : 3$ and four more boys join to make it $3 : 4$, you set up the change algebraically: $\dfrac{2x + 4}{3x} = \dfrac{3}{4}$ and solve for $x$, giving the original numbers. Cross-multiplying gives $4(2x + 4) = 9x$, so $8x + 16 = 9x$ and $x = 16$, meaning $32$ boys and $48$ girls originally.

To combine two ratios that share a quantity, scale them so the shared part matches. If $A : B = 2 : 3$ and $B : C = 4 : 5$, make $B$ equal in both: multiply the first by $4$ and the second by $3$, giving $A : B = 8 : 12$ and $B : C = 12 : 15$, so $A : B : C = 8 : 12 : 15$. This linking step turns two two-part ratios into a single three-part ratio you can then share with.

Proportion and graphs

Direct proportion has a clean graphical signature: plotting one quantity against the other gives a straight line through the origin, because $y = kx$ for a constant $k$. The constant $k$ is the gradient and the rate of change. Inverse proportion, $y = \tfrac{k}{x}$, gives a curve that falls away towards both axes without touching them. Recognising these shapes lets you read off or check a proportional relationship from a graph, which links this topic to the straight line graph work in algebra and to compound measures such as speed.

Why this matters

Ratio and proportion are not just a number topic; they reappear as similar shapes and scale factors in geometry, as speed, density and pressure in compound measures, and as exchange rates and best buys in financial problems. WJEC's worded, multi-step questions often hide a proportion calculation inside a context, so recognising the structure quickly and applying the unitary method cleanly is a transferable, high-value skill.