Rates & Ratios

A ratio is a comparison of two quantities by division, showing how many times one value contains or is contained within the other.

The word 'to' is used to express the relationship between two quantities in a ratio, indicating how many parts of one quantity there are for every part of another.

Rate = Distance ÷ Time. For example, if a person travels 182.4 miles in 3 hours, the rate is 182.4 ÷ 3 = 60.8 miles per hour.

Price per unit = Total Price ÷ Number of Units. For example, if 6 gallons of gasoline cost $15.00, the price per gallon is $15.00 ÷ 6 = $2.50.

Average rate of work = Total Work ÷ Total Time. For example, if Lynnette washes 95 cars in 5 days, she washes 95 ÷ 5 = 19 cars per day.

To find jumps per minute, divide the total jumps by the total time in minutes. So, 40 jumps ÷ 4 minutes = 10 jumps per minute.

A unit rate is a ratio that compares a quantity to one unit of another quantity, often expressed as 'per' something, like miles per hour or price per item.

To convert a ratio into a fraction, write the first quantity as the numerator and the second quantity as the denominator. For example, a ratio of 3:4 can be written as 3/4.

Rates are a specific type of ratio that compares two different units, such as speed (miles per hour) or price (dollars per item).

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