Think of a ratio as a recipe instruction. If a cake recipe says "mix flour and butter in the ratio 2 : 1," it's telling you exactly how the two ingredients relate to each other — for every 2 scoops of flour, you need 1 scoop of butter. It doesn't tell you the total amount of cake mixture; it just tells you the balance between the two ingredients.

That's the core idea: a ratio compares one part of a whole to another part — not a part to the whole (that job belongs to fractions, which we'll get to in a second).

Order Matters — Always

In any ratio question, whoever or whatever gets mentioned first in the sentence takes the first position in the ratio. This trips up more students than anything else in this topic, so get it locked in now.

If the question said "butter and flour," the ratio would flip to 1 : 2. Same numbers, completely different meaning if you get the order wrong.

Parts of a Whole

The numbers in a ratio tell you how many "parts" each quantity is made of. Add them up to find the total number of parts in the whole thing.

This is where a lot of the confusion in this topic actually lives, so let's nail the distinction with a picture in your head: imagine a pizza cut into 8 slices, shared between two people — the first person gets 5 slices, the second gets 3.

Notice the number 8 (the total slices) shows up automatically in the fraction, but it never appears inside the ratio itself — you get it by adding 5 + 3. This is a really common place to lose marks: writing "5 : 8" when the question asks for a ratio, when it should be a fraction 5⁄8, or vice versa.

One more key difference: fractions can be turned into percentages or decimals (5⁄8 = 62.5%), but a ratio like 5 : 3 has no percentage equivalent on its own — it's purely a comparison between two parts.

This works exactly like equivalent fractions — multiply or divide every part of the ratio by the same number, and the relationship between the parts stays identical, even though the numbers look different.

Simplifying a Ratio

A ratio is in its simplest form when every value is a whole number and there's no common factor left between them. Divide every part by the highest common factor (HCF) to get there in one clean step.

This is the single most common ratio skill you'll be tested on, and honestly it's just a three-step dance once you've done it a couple of times.

Once you're comfortable sharing a total, examiners like to twist the question so that instead of giving you the total straight away, they give you something a bit more indirect. There are three common twists:

A) Given the DIFFERENCE Between Two Parts

Instead of "the total is X," you're told "one person got $30 more than the other." Now you compare the difference in parts to the difference in actual value.

B) Given ONE Quantity, Find the Other

You know one actual value (e.g. "Kacey gets $50" in an 8:5 ratio) and need to find the rest.

C) Combining Two Two-Part Ratios into a Three-Part Ratio

Sometimes you're given two separate ratios that share a common quantity — like "Kerry : Kacey = 8 : 5" and "Kacey : Kylie = 1 : 2." Kacey is the link. To combine them, scale each ratio so that Kacey's value matches in both, then join them together.

Direct proportion means two quantities move in the same direction, at the same rate. Double one, and the other one doubles too. Triple one, the other triples. Think of buying multiple boxes of cereal — buy twice as many boxes, and you get twice as much cornflakes. The ratio between the two quantities never changes.

Best Value for Money

A classic direct-proportion question: which product is cheaper "per unit"? Always compare prices for the same size unit (e.g. price per kg) — never compare raw prices of different-sized packages directly.

Inverse proportion is the opposite relationship: as one quantity increases, the other decreases by the same factor (and vice versa). Picture a group of workers finishing a job — the more workers you add, the less time the job takes. Triple the workers, and the time gets divided by 3, not multiplied.