Ratios and Rates

Ratio

A ratio compares two quantities by division.

Three ways to write:

• Using colon: $3:5$
• Using "to": $3 \text{ to } 5$
• As a fraction: $\frac{3}{5}$

Example: If there are 3 cats and 5 dogs, the ratio of cats to dogs is $3:5$.

Simplifying Ratios

Divide both numbers by their GCF (like simplifying fractions).

Example: $12:18 = \frac{12}{18} = \frac{2}{3} = 2:3$

Rate

A rate is a ratio that compares two different units.

Examples:

• 60 miles per hour: $\frac{60 \text{ miles}}{1 \text{ hour}}$
• \3$per pound:$\frac{$3}{1 \text{ lb}}$
• 25 miles per gallon: $\frac{25 \text{ miles}}{1 \text{ gallon}}$

Unit Rate

A rate with a denominator of 1.

To find unit rate: Divide numerator by denominator.

Example: If you travel 150 miles in 3 hours: $\frac{150 \text{ miles}}{3 \text{ hours}} = 50 \text{ miles per hour}$

Comparing Rates

Find the unit rate for each, then compare.

Example: Which is cheaper: 3 lb for \6$or 5 lb for$$9$?

• First: \frac{\6}{3} = $2$ per lb
• Second: \frac{\9}{5} = $1.80$ per lb

The second option is cheaper!