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

OCR references R4, R5 and R6 cover ratio notation: simplifying ratios, writing them as $1 : n$, dividing a quantity in a given ratio, and applying ratio to scale drawings, maps and similar shapes. Ratio is one of the most heavily examined parts of the qualification because it links to fractions, proportion, geometry and real-life problem solving. It appears on every tier and is a frequent multi-step, multi-mark question that rewards the AO3 problem solving OCR weights at $30$ percent.

Ratio notation and simplifying

A ratio shows the relative sizes of two or more quantities, separated by colons, such as $2 : 3$ or $4 : 1 : 2$. The quantities must be in the same units before you write the ratio, so $50$ cm to $2$ m becomes $50 : 200$, not $50 : 2$.

So $12 : 18$ simplifies to $2 : 3$ (dividing both by $6$), and $5 : 8$ in the form $1 : n$ is $1 : 1.6$ (dividing both by $5$). Writing a ratio as $1 : n$ makes two ratios easy to compare: $3 : 5$ ($1 : 1.67$) is "more spread" than $2 : 3$ ($1 : 1.5$).

Dividing a quantity in a ratio

Sharing in a ratio is the most common ratio task.

The method has three steps: add the parts, find one part, then multiply. To share $560$ g of flour in the ratio $5 : 2$, the total is $7$ parts, one part is $560 \div 7 = 80$ g, so the shares are $400$ g and $160$ g. A frequent variation gives you the difference between two shares, or the value of one share, and asks for the total. If the larger share of a $3 : 5$ split is $200$, then one part is $200 \div 5 = 40$, so the total is $40 \times 8 = 320$.

Scale drawings, maps and similar shapes

A scale is a ratio between a drawing and reality.

Similar shapes are an enlargement of each other, so corresponding lengths are in a fixed ratio called the scale factor. If two triangles are similar with a length scale factor of $3$, every length in the larger is three times the matching length in the smaller, which lets you find a missing side by setting up the ratio.

Ratio questions also appear in "changing the ratio" form, where extra items are added and you must find the new ratio or work back to the original quantities. For example, a bag has red and blue counters in the ratio $2 : 3$; if there are $12$ red counters, then one part is $12 \div 2 = 6$, so there are $18$ blue counters and $30$ in total. These problems reward setting out the parts clearly and tracking what one part is worth, which is the same parts-based thinking that underlies every ratio calculation.

Why ratio matters

Ratio threads through proportion, compound measures, percentages and geometry, and OCR sets it in rich real-life contexts (recipes, currency, mixing, maps) precisely because it tests reasoning. Showing the parts-total-one-part-multiply structure, and stating the direction of any scaling, secures method marks even when an arithmetic slip costs the final answer.