Simplify ratios, divide a quantity in a given ratio, use the unitary method, solve best-buy and scale problems, and work with direct and inverse proportion including compound measures.

What this dot point is asking

Ratio and proportion sit in the CCEA Number and Algebra strand and test whether you can compare quantities and scale them correctly. You must simplify ratios, divide a quantity in a given ratio, use the unitary method for best buys and recipes, work with map and model scales, and solve direct and inverse proportion problems, including compound measures such as speed, density and pressure. These questions are heavily contextual, which means they also carry AO2 and AO3 reasoning marks, and they appear on every module from M1 to M8.

Simplifying and writing ratios

A ratio such as $4 : 6$ compares two quantities of the same kind. Simplify by dividing every part by their highest common factor: $4 : 6 = 2 : 3$. Ratios can also be written in the form $1 : n$ by dividing both parts by the first, which is useful for comparing scales. Always make sure both quantities are in the same units before simplifying, so $50\text{ cm} : 2\text{ m}$ must first become $50 : 200 = 1 : 4$.

Sharing in a given ratio

To divide a quantity in a ratio, add the parts to find the total number of parts, divide the quantity by that to find one part, then multiply each share. Sharing £350 in the ratio $3 : 4$ gives $7$ parts, one part is $350 \div 7 = 50$, so the shares are £150 and £200. The check is that the shares add back to the original total.

The unitary method, best buys and scales

The unitary method finds the cost or size of one unit, then scales to the amount you need. For a best buy, work out the price per gram or per item for each option and compare. For a scale, the same idea converts between map distance and real distance: on a $1 : 25\,000$ map, $1\text{ cm}$ represents $25\,000\text{ cm} = 250\text{ m}$.

Direct and inverse proportion

In direct proportion, two quantities increase together at a constant rate, so $y = kx$ for some constant $k$. Doubling one doubles the other. Recipes, currency conversion and unit pricing are direct proportion.

In inverse proportion, one quantity rises as the other falls, so $y = \tfrac{k}{x}$ and their product is constant. More workers take less time; more pumps fill a tank faster. The reliable method is to find the constant product (the total work) and divide.

Compound measures

Compound measures combine two different units. The three CCEA expects are speed, density and pressure.

Why this matters

Ratio and proportion connect arithmetic to real situations of money, mixing, scaling and rates, so they reward exactly the reasoning CCEA prizes in AO2 and AO3. The same proportional thinking returns in similar shapes, trigonometry, and the rates-of-change ideas in graphs, so a secure grasp here pays off across the whole course.