Rates, Ratios, and Proportions

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities where one of the quantities is expressed as one unit. For example, if you drive 92 miles using 4 gallons of gas, the unit rate is 23 miles per gallon.

Front

How do you calculate the unit rate?

Back

To calculate the unit rate, divide the total quantity by the number of units. For example, if you have 92 miles and 4 gallons, you divide 92 by 4 to get 23 miles per gallon.

Front

What is a ratio?

Back

A ratio is a relationship between two numbers indicating how many times the first number contains the second. For example, the ratio of dogs to cats can be expressed as 5:3.

Front

How do you write a ratio?

Back

A ratio can be written in three ways: using a colon (5:3), as a fraction (5/3), or with the word 'to' (5 to 3).

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, if the ratio of dogs to cats is 5:3, then the proportion can be written as 5/3 = 25/c.

Front

How do you solve a proportion?

Back

To solve a proportion, cross-multiply and then divide. For example, if 5/3 = 25/c, you would cross-multiply to get 5c = 75, then divide by 5 to find c.

Front

What is the cost per pound?

Back

The cost per pound is calculated by dividing the total cost by the total weight. For example, if a watermelon costs $3.24 for 3 pounds, the cost per pound is $3.24 ÷ 3 = $1.08.

Front

How do you compare prices to find the better buy?

Back

To compare prices, calculate the unit price for each option. For example, for a 12-pack of Pepsi for $3.50, the unit price is $3.50 ÷ 12. For a 6-pack for $1.80, the unit price is $1.80 ÷ 6.

Front

What is the formula for finding the total cost based on unit price?

Back

The total cost can be found by multiplying the unit price by the quantity purchased. For example, if the unit price is $2 per pound and you buy 10 pounds, the total cost is $2 × 10 = $20.

Front

What does it mean if two ratios are equivalent?

Back

If two ratios are equivalent, it means they represent the same relationship between quantities. For example, 1:2 is equivalent to 2:4.