Comparing & Scaling Vocabulary

Rate

A comparison of quantities measured in two different units is called a rate. A rate can be thought of as a direct comparison of two sets (20 cookies for 5 children) or as an average amount (4 cookies per child). A rate such as 5.5 miles per hour can be written as 5.5miles/1hour, or 5.5 miles : 1 hour.

Ratio

A comparison of two quantities expressed with a phrase such as 'the ratio of 3 to 5' which means '3 for every 5.' Such ratio comparisons are often written as common fractions and in the special notation 3 : 5.

Equation

A number sentence in which an equal sign is present. An example is the equation 27=42x.

Part-to-Part Ratio

A part-to-part ratio represents a relationship between one part of a whole and another part of the whole. For example, in a recipe that calls for 2 cans of juice concentrate and 3 cans of water, the ratios 2 : 3 and 3 : 2 are part-to-part ratios.

Part-to-Whole Ratio

A part-to-whole ratio represents a relationship between one part of a whole and the whole. For example, in a recipe that calls for 2 cans of juice concentrate and 3 cans of water, the ratios 2 : 5 and 3 : 5 are part-to-whole ratios, because there are 5 cans in all.

Rate Table

A table that shows the value of a single item in terms of another item. It is used to show equivalent ratios of the two items.

Unit Rate

A unit rate is a rate in which the second number (usually written as the denominator) is 1, or 1 of a quantity. For example, 1.9 children per family, 32 miles per gallon, and 3 flavors of ice cream/1 banana split are unit rates. Unit rates are often found by scaling other rates.

Proportion

An equation stating that two ratios are equal.

Markup

The amount added to the buying price of an item. It is usually a percent of the buying price.

Commission

The amount earned, based on the percent of total sales. For example, a car salesperson who earns 10% on car sales and sells $60,000 worth of cars would earn a commission of $6,000 (10% of $60,000).

Constant of Proportionality

The constant ratio of two proportional quantities, x and y; usually written as y=kx, where k is the constant of proportionality. For example, in the equation y=34x, the constant of proportionality is 34.