Question

What is the difference between ratios and rates ?

Answer 1

Both rates and ratios are a comparison of two numbers.

A rate is simply a specific type of ratio.

The difference is that a rate is a comparison of two numbers with different units, whereas a ratio compares two numbers with the same unit.

For example, in a room full of students, there are $10$ boys and $5$ girls. This means the ratio of boys to girls is $10:5$

If we simplify the ratio, we see that the ratio of boys to girls is $2:1$, since $10÷5=2$ and $5÷5=1$ Thus, there are $2$ boys in the room for every $1$ girl.

Let's say we'd like to buy a soda for each student in the classroom. The local pizza place offers a group discount on soda purchases: $\$10$ for $20$ sodas.

Since we only need $15$ sodas, we're wondering how much each soda costs at the discounted rate. To find out, we'll set up two rates, because we have 2 different units, dollars and number of sodas:

If $\frac{20sodas}{\$10}$, then $\frac{1soda}{x}$

We cross multiply of $x$:

$20x=\$10$

$x=10÷20$

$x=\frac{1}{2}$

Since our unit is $\$$. We'll $\frac{1}{2}$ to dollars. One half of a dollar is $\$0.50$.

Thus the discounted rate for the sodas is $\$.50/1$ soda.