Unit Rate Word Problems: 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 a quantity of one. For example, if a car travels 300 miles in 5 hours, the unit rate is 60 miles per hour.

Front

How do you find the unit rate from a word problem?

Back

To find the unit rate, divide the total quantity of one item by the total quantity of the other item. For example, if 3 pounds of hamburger costs $6, the unit rate is $6 ÷ 3 pounds = $2 per pound.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, if a recipe calls for 2 cups of milk for every 3 cups of flour, the proportion can be written as 2/3 = x/8, where x is the amount of flour needed.

Front

How do you solve a proportion?

Back

To solve a proportion, cross-multiply the two ratios and set them equal to each other. For example, if 2/3 = x/8, then 2 * 8 = 3 * x, leading to x = 16/3.

Front

What is the formula for direct variation?

Back

The formula for direct variation is y = kx, where k is the constant of variation. This means that as x increases, y increases proportionally.

Front

If a car travels 280 miles in 7 hours, how far will it travel in 12 hours?

Back

The car travels 480 miles in 12 hours.

Front

What is the ratio of total students to boys in a class of 12 girls and 16 boys?

Back

The ratio of total students to boys is 7/4.

Front

How do you calculate the cost for a different quantity using unit rates?

Back

To calculate the cost for a different quantity, multiply the unit rate by the new quantity. For example, if the unit rate is $2 per pound and you want 10 pounds, the cost is $2 * 10 = $20.

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 the ratio of girls to boys is 12:16, the proportion can be set up as 12/16 = x/y.

Front

How do you convert a ratio to simplest form?

Back

To convert a ratio to simplest form, divide both terms of the ratio by their greatest common divisor (GCD). For example, the ratio 12:16 can be simplified to 3:4.