Lesson 1: Understanding Ratios and Unit Rates

Property

A ratio is a type of quotient used to compare two numerical quantities. The ratio of $a$ to $b$ is written $\frac{a}{b}$. A ratio can be expressed as a decimal instead of a common fraction.

Examples

• In a class with 15 boys and 12 girls, the ratio of boys to girls is $\frac{15}{12}$, which simplifies to $\frac{5}{4}$.

• A recipe calls for 2 cups of sugar for every 5 cups of flour. The ratio of sugar to flour is $\frac{2}{5}$.

Property

A rate is a ratio of two quantities.
The unit rate is the amount of one quantity that corresponds to 1 unit of the other quantity.
The designation of unit rate must be clear about the choice and order of the units.

For a ratio $a:b$ with $b \neq 0$, the unit rate is $\frac{a}{b}$ units of the first quantity per 1 unit of the second quantity.

Examples

• If you pay 9 dollars for 3 sandwiches, the unit rate is found by dividing: $9 \div 3 = 3$ dollars per sandwich.
• A cyclist travels 30 miles in 2 hours. The unit rate for her speed is $30 \div 2 = 15$ miles per hour.
• A team scores 45 points in 3 quarters. Their unit rate is $45 \div 3 = 15$ points per quarter.