Lesson 23: Ratio

New Concept

A ratio is a way to describe a relationship between numbers. It can be written as $7 \text{ to } 3$, $7:3$, or $\frac{7}{3}$. A rate is a ratio of measures.

What’s next

This is just the start. Next, we'll use these ideas in worked examples, like finding a team's win-loss ratio and calculating average speed.

Property

A ratio is a way to describe a relationship between numbers. Ratios can be written in several forms, such as $13 \text{ to } 15$, $13:15$, or $\frac{13}{15}$.

Examples

• A team wins 7 games and loses 3. The win-loss ratio is $\frac{7}{3}$.
• In a class with 13 boys and 15 girls, the ratio of boys to girls is $\frac{13}{15}$.
• If a zoo has 5 tigers and 12 lions, the ratio of tigers to lions is $\frac{5}{12}$.

Explanation

Think of a ratio as a 'comparison recipe.' It tells you how much of one thing you have compared to another, like cats to dogs or wins to losses. The order you write it in is super important—a win-loss ratio is different from a loss-win ratio! We usually write them as fractions because it keeps things clear and simple to compare.

Property

A rate is a ratio of measures that compares two different units. Common rates include speed ($\frac{\text{distance}}{\text{time}}$), mileage ($\frac{\text{distance}}{\text{fuel used}}$), and unit price ($\frac{\text{price}}{\text{quantity}}$).

Examples

• Jeremy rode his bike 60 miles in 4 hours, so his speed was $\frac{60 \text{ miles}}{4 \text{ hours}} = 15$ miles per hour.
• A 4-quart container of milk costs 2.48 dollars, so the cost is $\frac{2.48 \text{ dollars}}{4 \text{ quarts}} = 0.62$ dollars per quart.
• A car travels 280 miles on 10 gallons of gas, so its mileage is $\frac{280 \text{ miles}}{10 \text{ gallons}} = 28$ miles per gallon.

Explanation

A rate is a special kind of ratio that's always on the move! It compares two different types of measurements, like miles and hours or dollars and pounds. The word 'per' is your big clue, as in 'miles per hour.' Rates are incredibly useful for figuring out everything from your car's speed to the best deal on snacks at the store.