What a Ratio Says

A recipe with 3 cups of flour for every 2 cups of milk has a ratio of 3 to 2.

Ratio compares two amounts, saying how much of one goes with the other.

Three ways to write it

The same ratio is written 3 to 2, or 3 : 2, or 3/2. All three are read "three to two".

Order matters

3 : 2 flour to milk is not the same recipe as 2 : 3. Say which quantity comes first.

Part to part, part to whole

With 3 cups of flour and 2 of milk there are 5 cups in all, so flour to total is 3 : 5.

A ratio compares, it does not count

A ratio of 3 : 2 says that for every 3 of the first thing there are 2 of the second. It does not say there are exactly 3 and 2 — there might be 30 and 20, or 300 and 200. What a ratio fixes is the relationship, not the amounts.

Order matters

A paint mix of 3 : 2 red to blue is not the same as 2 : 3 red to blue. The first is redder. Always write down which quantity each number refers to, because a ratio with its labels lost is worse than useless — it is confidently wrong half the time.

Part to part, and part to whole

If a class has 3 girls to 2 boys, the part-to-part ratio is 3 : 2 and the class has 5 parts altogether. So girls are 3 out of 5 of the class, which is 3/5. Ratios and fractions are related but ask different questions, and confusing them is a real source of error.

Where ratios show up

Recipes, map scales, paint mixing, gear ratios, exchange rates, screen aspect ratios and concrete mixes are all ratios. In every case what matters is the relationship holding as the quantities scale. That is why ratios earn a whole chapter.