Teaching Models

Ratio and Proportion

A ratio compares two numbers or two quantities. The two numbers being compared are called terms. A ratio can be written in three different ways.

a to b   
a over b

Each is read as “the ratio of a to b.”

Two ratios are equivalent if they represent the same number. To find equivalent ratios, each term in the ratio must be multiplied or divided by the same number.

equivalent rations

So twelve-eighteenths, twenty-four-thirty-sixths, 6/9, two-thirds, and thirty-six-fifty-fourths are all equivalent ratios.

A rate is a special ratio that compares two quantities that have different units of measure. If the second term in a rate is 1, the ratio is called a unit rate. Unit rates are often described as a quantity per unit of time or per item. Students will frequently encounter rates, such as being in a car traveling 30 miles per hour, making a long distance telephone call that costs 20¢ per minute, skating at an ice rink that costs $10 for 2 hours, and so on.

Scale drawings make use of ratios in that the scale of the drawing is the ratio of the measurements of the drawn object to the corresponding measurements of the real object. In some scale drawings, the scale involves the same unit of measure, such as 2 cm:10 cm. In other scale drawings, the scale involves different units of measure, such as 1 in.:200 mi. Blueprints and maps are two common scale drawings that students may be familiar with.

Teaching Model 18.2: Equivalent Ratios

Houghton Mifflin Math Grade 5