Comparing Rates

Front

What is a rate?

Back

A rate is a ratio that compares two different quantities, often expressed as a fraction. For example, speed is a rate that compares distance to time.

Front

How do you calculate the unit rate?

Back

To find the unit rate, divide the quantity by the number of units. For example, if 20 tickets cost $250, the unit rate is $250 ÷ 20 = $12.50 per ticket.

Front

What is the formula for finding the cost per item?

Back

Cost per item = Total cost ÷ Number of items.

Front

If a recipe has a ratio of 7:3 for sugar to flour, how do you find the amount of flour needed if you have 63 ounces of sugar?

Back

Set up a proportion: 7/3 = 63/x. Cross-multiply and solve for x to find that you need 27 ounces of flour.

Front

How do you find the speed of an object?

Back

Speed = Distance ÷ Time. For example, if Ernie travels 195 miles in 3 hours, his speed is 195 ÷ 3 = 65 miles per hour.

Front

What is a proportional relationship?

Back

A proportional relationship is one where two quantities maintain a constant ratio or rate. For example, if you double one quantity, the other also doubles.

Front

How do you compare two rates?

Back

To compare two rates, convert them to the same unit or find the unit rate for each and then compare the results.

Front

What is the unit rate of a cheetah that runs 60 feet in 4 seconds?

Back

Unit rate = 60 feet ÷ 4 seconds = 15 feet per second.

Front

What is the unit rate of a gazelle that runs 100 feet in 8 seconds?

Back

Unit rate = 100 feet ÷ 8 seconds = 12.5 feet per second.

Front

How do you solve for an unknown in a ratio?

Back

Use cross-multiplication to set up an equation based on the ratio and solve for the unknown.