What Is a Ratio? Comparing Two Quantities

A ratio compares two amounts

A class has $3$ girls for every $2$ boys. That comparison is a ratio, and it is written like this:

$$3 : 2$$

Say it “three to two”. It tells you how the two groups compare in size, and it holds however big the class is.

Three ways to write the same ratio

Form	Looks like	Read as
colon	$3 : 2$	three to two
words	$3$ to $2$	three to two
fraction	$\tfrac{3}{2}$	three to two

All three mean the same thing. The colon form is the most common in a ratio question, and the fraction form is the one that lets you do arithmetic with it later.

Order matters

The first number goes with the first thing named.

Statement	Ratio
girls to boys	$3 : 2$
boys to girls	$2 : 3$

Swapping them describes a different class. Always check which quantity is named first in the question, then write that number first.

Part-to-part and part-to-whole

This is the distinction that decides most ratio questions.

In a class of $3$ girls and $2$ boys there are $5$ students in total.

Comparison	Type	Ratio
girls to boys	part-to-part	$3 : 2$
girls to students	part-to-whole	$3 : 5$
boys to students	part-to-whole	$2 : 5$

A part-to-part ratio compares two groups. A part-to-whole ratio compares one group to the total, so you have to add the parts first to find that total.

A part-to-whole ratio works exactly like a fraction. Girls are $\tfrac{3}{5}$ of the class.

Why ratios are worth having

A ratio holds at any size. That is the whole point of it.

A recipe needs $2$ cups of flour for every $1$ cup of sugar, a ratio of $2:1$. Doubling the recipe gives $4$ cups and $2$ cups — still $2:1$. Making ten times as much gives $20$ and $10$, and that is still $2:1$.

Batches	Flour	Sugar	Ratio
$1$	$2$	$1$	$2:1$
$2$	$4$	$2$	$2:1$
$5$	$10$	$5$	$2:1$

The amounts all change. The relationship between them does not.

That is why ratios describe recipes, maps, mixing paint, and gears. Each one is a rule that has to hold no matter how much you make. A plain count could never do that job, because a count is tied to one particular size.

Worked examples

Common mistakes

Practice problems