Use ratio notation; simplify ratios and express them in the form $1:n$; divide a quantity in a given ratio; and apply ratio to scale drawings, maps and similar shapes.

What this dot point is asking

The Eduqas ratio content requires you to read and write ratios, simplify them (including to the form $1 : n$), divide a quantity in a given ratio, and apply ratio to scale drawings, maps and similar shapes. Ratio is one of the most heavily used ideas on the paper, appearing in recipes, best-buy comparisons, maps, mixtures and geometry, and because Eduqas weights problem solving (AO3) at a quarter of the marks, ratio questions are often wrapped in a real context. It appears at both tiers, with the basic share-in-a-ratio being a reliable Foundation question and the harder "change in ratio" and similar-shape questions reaching into Higher.

Ratio notation and simplifying

A ratio compares two or more quantities measured in the same units. The order matters: $3 : 2$ is not the same as $2 : 3$.

The form $1 : n$ is found by dividing both parts by the first part, which is useful for comparing scales. So $4 : 10$ becomes $1 : 2.5$. Converting units before simplifying is essential, because a ratio of unlike quantities (centimetres against metres) is meaningless until they match.

Dividing a quantity in a ratio

Sharing a total in a given ratio is a three-step routine.

A harder version gives you one part and asks for the total or another part. If Ben's share is $60$ and the ratio is $2 : 3 : 7$, then one share is $60 \div 3 = 20$, so the total is $12 \times 20 = 240$.

Scale drawings and maps

A scale is a ratio of a drawn or mapped length to the real length. To go from the drawing to real life, multiply by the scale factor; to go from real life back to the drawing, divide. For a scale of $1 : 50$, a wall drawn $6$ cm long is really $6 \times 50 = 300$ cm $= 3$ m. The hardest part is usually the unit conversion at the end, so track centimetres, metres and kilometres carefully.

Similar shapes

Two shapes are similar when one is an enlargement of the other, so corresponding lengths are in the same ratio (the scale factor). If a photo is enlarged so the width goes from $4$ cm to $10$ cm, the scale factor is $\tfrac{10}{4} = 2.5$, and every other length multiplies by $2.5$. At Higher tier, areas scale by the square of the length factor and volumes by the cube, so a scale factor of $2.5$ multiplies areas by $2.5^2 = 6.25$. This length-area-volume relationship is a favourite Higher reasoning point.

Ratio as a fraction of the whole

It often helps to read a ratio as fractions of the total. In a ratio $3 : 5$ the total is $8$ parts, so the first quantity is $\tfrac{3}{8}$ of the whole and the second is $\tfrac{5}{8}$. This view makes "what fraction" and "what percentage" questions immediate: the first share is $\tfrac{3}{8} = 37.5\%$ of the total. It also helps when a ratio must be combined with another, such as turning $a : b$ and $b : c$ into a single three-part ratio $a : b : c$ by scaling so the shared middle value matches. For example $2 : 3$ and $3 : 4$ already share $3$, so they combine directly to $2 : 3 : 4$; if they did not match, you would scale each ratio first.

Why ratio matters

Ratio is the backbone of proportional reasoning, which is why it threads through the whole course. Recipes scale by ratio, currency converts by ratio, best-buy comparisons reduce to a common unit (a unitary ratio), and similar shapes in geometry depend on a constant length ratio. Because Eduqas frames so many of these as worded, multi-step problems, the marks reward not just the arithmetic but the decision about which proportional method fits, so always identify whether you are sharing, scaling or comparing before you calculate.