Ratios and Rates

A ratio is a comparison of two quantities that shows the relative size of one quantity to another. It can be expressed in different forms, such as a fraction, with a colon (e.g., 3:5), or with the word 'to' (e.g., 3 to 5).

A unit rate is a ratio that compares a quantity to one unit of another quantity. For example, if a car travels 150 miles in 3 hours, the unit rate is 50 miles per hour.

To find a unit rate, divide the total quantity by the number of units. For example, if you have 120 apples and want to find the rate per 10 apples, you divide 120 by 10 to get 12.

A ratio compares two quantities, while a unit rate compares a quantity to one unit of another quantity. For example, a ratio of 3:5 compares 3 apples to 5 oranges, while a unit rate might express how many apples are in one orange.

The ratio of students to desks is 30:15, which simplifies to 2:1.

The formula to calculate a unit rate is: Unit Rate = Total Quantity / Number of Units.

The unit rate is 60 miles per hour, calculated as $$\frac{240 \text{ miles}}{4 \text{ hours}} = 60 \text{ miles per hour}$$ .

A rate is a specific kind of ratio that compares two quantities with different units. For example, speed is a rate that compares distance (miles) to time (hours).

To express a ratio in simplest form, divide both terms of the ratio by their greatest common divisor (GCD). For example, the ratio 8:12 can be simplified to 2:3.

The ratio of flour to sugar is 2:3.