Ratios and Rates

Study Sheet

Ratios and Rates

Comparing two quantities

Rates as Ratios

Concept
The Big Idea

A ratio compares two amounts. A unit rate is a ratio with 11 in the second slot, which makes scaling up easy: just multiply.

Example
Scaling a recipe

If 1212 grams of sugar go with one cup of flour, then 55 cups need 12×5=6012 \times 5 = 60 grams.

In Plain Terms & More Examples

Concept
In plain terms

A ratio compares two amounts. A unit rate rewrites it with 11 in the second slot, which makes scaling as simple as multiplying.

Example
A pay rate

If $60\$60 is earned in 55 hours, the unit rate is 60÷5=$1260 \div 5 = \$12 per hour.

Example
Scaling a ratio

The ratio 2:32 : 3 scaled up by 44 becomes 8:128 : 12.