Rates

Rates

Like ratios, rates compare two different things.

But with rates, you are comparing different units.

If you're travelling at 80 k/h you're comparing the distance to the time (kilometers to hours). You also can find unit rates which compare a quantity to 1 unit. 80km/h is a unit rate because it express how far one would travel in 1 hour.

Finding the unit rate

When you go shopping you might see a package of 12 buns for $1.50 and a package of 8 for 98c. Which is the better deal?

In this case we need to find the unit rate, or how much for 1 bun.

1.50 ÷ 12 = 0.125 or rounded to $0.13

0.98 ÷ 8 = 0.1225 or rounded to $0.12

The package of 8 is the slightly better deal.

In a unit rate the second term is always 1. In other words the quantity would be expressed compared to 1 month or 1 hour or 1 bun.

Changing the units

If you're riding your bike at 30 km/h how far will you go in one minute? Will you make it to your friend's house which is 5 kilometers away in 12 minutes?

In this case we need to convert 30 km/h into kilometers per minute to determine the rate per minute.

Therefore 30 km/h is equivalent to 30 km/60 minutes. Divide both 30 and 60 by 60 to get the rate per 1 minute.

30 km/h ÷ 60 = 0.5 km/minute

So you'll go 0.5 kilometers in a minute.

In 12 minutes you'll go 6 kilometers (12 x 0.5) so you'll make it to your friend's in plenty of time.

Because rates have two different units they can't be expressed as percents like ratios can. A rate of 12 cents a bun cannot be expressed as a percent.