Scale Factor and Proportions

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, some quantity. It is used to determine how much larger or smaller a figure is compared to another figure.

Front

How do you find a unit rate?

Back

To find a unit rate, divide the total amount by the number of items. For example, if $12 is for 5 boxes of cereal, the unit rate is $12 ÷ 5 = $2.40 per box.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, if the ratio of boys to girls is 4:6, it can be expressed as 4/6 = x/y.

Front

If the ratio of Marvel fans to DC fans is 5:4 and there are 85 Marvel fans, how many DC fans are there?

Back

68 DC fans.

Front

What is the formula to find the actual distance using a scale?

Back

Actual Distance = (Distance on Map) × (Scale Factor). For example, if the scale is 2 inches = 40 miles, and the distance on the map is 4.125 inches, the actual distance is 4.125 × (40/2) = 82.5 miles.

Front

What does it mean to simplify a ratio?

Back

To simplify a ratio means to reduce it to its smallest form by dividing both terms by their greatest common divisor.

Front

How do you convert a ratio to a fraction?

Back

To convert a ratio to a fraction, write the first term as the numerator and the second term as the denominator. For example, the ratio 5:4 can be written as 5/4.

Front

What is the relationship between ratios and proportions?

Back

Ratios compare two quantities, while proportions state that two ratios are equal. For example, if 5:4 = x:y, then x and y are in proportion.

Front

If a map has a scale of 1 inch = 20 miles, how far apart are two cities that are 3 inches apart on the map?

Back

60 miles apart (3 inches × 20 miles/inch).

Front

What is the scale factor from a smaller shape to a larger shape if the smaller shape's dimensions are multiplied by 3?

Back

The scale factor is 3.