Ratios & Rates

Front

What is a ratio?

Back

A ratio is a comparison of two quantities that shows the relative size of one quantity to another, expressed as a fraction or with a colon (e.g., 3:2).

Front

How do you simplify a ratio?

Back

To simplify a ratio, divide both terms by their greatest common factor (GCF). For example, the ratio 8:4 simplifies to 2:1.

Front

What is a rate?

Back

A rate is a specific kind of ratio that compares two different units, such as speed (miles per hour) or price per item.

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 3:4 becomes the fraction 3/4.

Front

If a recipe calls for a ratio of 2:1 for flour to sugar, how much sugar is needed for 4 cups of flour?

Back

2 cups of sugar are needed (4 cups flour ÷ 2 = 2 cups sugar).

Front

What is the unit rate?

Back

The unit rate is a rate in which the second quantity is 1. For example, if a car travels 60 miles in 1 hour, the unit rate is 60 miles per hour.

Front

How do you find the total amount when given a unit rate?

Back

Multiply the unit rate by the number of units. For example, if the unit rate is $5 per item and you buy 3 items, the total cost is $5 x 3 = $15.

Front

What is the relationship between ratios and proportions?

Back

A proportion states that two ratios are equal. For example, if 1/2 = 2/4, then 1:2 is proportional to 2:4.

Front

If the ratio of boys to girls in a class is 3:5 and there are 15 boys, how many girls are there?

Back

There are 25 girls (15 boys x 5/3 = 25 girls).

Front

How do you compare two rates to determine which is better?

Back

To compare two rates, convert them to unit rates and see which one has the higher value. The higher value is the better deal.