Lesson 1: What is a Ratio?

Property

A ratio shows the relative sizes of two values by dividing one value into the other. The ratio of $a$ to $b$ is sometimes denoted by $a : b$, and it is computed as the quotient $\frac{a}{b}$.

Examples

• A classroom has 24 students and 2 teachers. The ratio of students to teachers is $\frac{24}{2}$, which simplifies to $\frac{12}{1}$ or 12 to 1.
• A recipe calls for 3 cups of flour and 2 cups of sugar. The ratio of flour to sugar is 3 to 2, or $\frac{3}{2}$.
• In a parking lot, there are 50 cars and 15 trucks. The ratio of cars to trucks is $\frac{50}{15}$, which simplifies to $\frac{10}{3}$. For every 10 cars, there are 3 trucks.

Explanation

A ratio is a way to compare two quantities by division. Think of it as a recipe: 'for every $a$ of this, you have $b$ of that'. Simplifying the ratio makes this relationship easier to understand at a glance.

Property

A ratio compares two numbers or two quantities that are measured with the same unit. The ratio of $a$ to $b$ is written $a$ to $b$, $\frac{a}{b}$, or $a:b$.

Examples

• The ratio 20 to 36 can be written as $20\ \text{to}\ 36$, $20:36$, and $\frac{20}{36}$, which simplifies to $\frac{5}{9}$.

• The ratio 45 to 18 can be written as $45\ \text{to}\ 18$, $45:18$, and $\frac{45}{18}$, which simplifies to $\frac{5}{2}$.