Unit Rate and Proportions Flashcard

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 a quantity of one. For example, if you travel 150 miles in 5 hours, the unit rate is 30 miles per hour.

Front

How do you calculate a unit rate?

Back

To calculate a unit rate, divide the first quantity by the second quantity. For example, if you have 150 miles and 5 gallons, the unit rate is 150 miles ÷ 5 gallons = 30 miles per gallon.

Front

What is a proportion?

Back

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

Front

How can you use proportions to solve problems?

Back

You can set up a proportion to find an unknown value by cross-multiplying and solving for the variable. For example, if 5/20 = x/100, then cross-multiplying gives 5*100 = 20*x.

Front

What does it mean to compare prices using unit rates?

Back

Comparing prices using unit rates allows you to determine which option offers the best value. For example, if one item costs $2 for 1 pound and another costs $3 for 2 pounds, you can find the unit rate to see which is cheaper per pound.

Front

If a car travels 240 miles on 8 gallons of gas, what is the unit rate in miles per gallon?

Back

30 miles per gallon (240 miles ÷ 8 gallons = 30 miles/gallon).

Front

If a recipe calls for 3 cups of flour for every 4 cups of sugar, what is the ratio of flour to sugar?

Back

The ratio of flour to sugar is 3:4.

Front

How do you find the total number of items based on a unit rate?

Back

Multiply the unit rate by the total number of units. For example, if the unit rate is 5 wins per 7 games, and there are 28 games, then the expected wins are (5/7) * 28 = 20 wins.

Front

What is the relationship between ratios and proportions?

Back

Ratios are comparisons of two quantities, while proportions state that two ratios are equal. For example, if the ratio of dogs to cats is 1:5, then the proportion can be expressed as 1/5 = 2/10.

Front

If you buy 4 notebooks for $8, what is the cost per notebook?

Back

$2 per notebook ($8 ÷ 4 notebooks = $2/notebook).