Ratio and rate refer to two basic math concepts. A ratio represents a comparison of two numbers or quantities, and is often written with a colon. For example, if a person has three cats and two dogs, the ratio of cats to dogs can be written as "3:2." This is read as "three to two." A rate is a type of ratio that involves two different units of measurement. For example, if a person runs three miles in 30 minutes, he runs at a rate of one mile every 10 minutes. This can be written as "one mile:10 minutes" or as "one mile every 10 minutes."

### Calculating Ratios

Calculate each number or quantity. Some problems may give you the two numbers; other problems may require you to compare one quantity with the total of all numbers. For example, if a person has three apples, two oranges and five strawberries, and you must find the ratio of oranges to total fruit, add up the total quantity of fruit. There are two oranges and 10 total pieces of fruit.

Simplify the ratio by dividing both sides by the greatest common factor. In a ratio of two oranges and 10 total pieces of fruit, the greatest common factor is two. Dividing each side by two results in 1 and 5.

Write the ratio with a colon in between the two numbers, or the word "to." For example, one orange and five pieces of fruit can be written "1:5" or "1 orange to 5 pieces of fruit."

### Calculating Rate

Write down both measurements. For example, if a car travels 20 miles in 40 minutes, write down 20 miles and 40 minutes. Make sure to always write down the units in rate problems.

Simplify the rate by dividing each number by the greatest common factor. For example, the greatest common factor in 20 and 40 is 20. Dividing both sides by 20 results in 1 and 2.

Express the rate as "1 mile per 2 minutes," or "1 mile:2 minutes."

#### Tip

Always write down units when solving or expressing rates.