Ratios and Rates

A ratio is a comparison of two quantities by division, showing how many times one value contains or is contained within the other.

Ratios can be written in three ways: using a colon (e.g., 5:7), using the word 'to' (e.g., 5 to 7), or as a fraction (e.g., \(\frac{5}{7}\)).

A unit rate is a ratio that compares a quantity to one unit of another quantity, often expressed as 'per' something (e.g., miles per hour).

To find a unit rate, divide the first quantity by the second quantity to determine how much of the first quantity corresponds to one unit of the second.

The ratio of boys to girls is 5:7.

The ratio of chocolate lovers to vanilla lovers is 2:3.

The ratio of red to blue marbles is 3:1.

To convert an hourly rate to a per minute rate, divide the hourly rate by 60.

Serena makes $4 per minute.

The rate is 10 miles per hour.