Proportional Relationships 2/8/25

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other quantity is constant.

Front

How do you find the unit rate from a proportional relationship?

Back

To find the unit rate, divide the total amount by the number of units. For example, if it costs $38 for 4 people, the unit rate is $38 ÷ 4 = $9.50 per person.

Front

What is the unit rate if 10 apples cost $5?

Back

The unit rate is $5 ÷ 10 apples = $0.50 per apple.

Front

If a car travels 300 miles on 10 gallons of gas, what is the unit rate of miles per gallon?

Back

The unit rate is 300 miles ÷ 10 gallons = 30 miles per gallon.

Front

What does it mean if two quantities are directly proportional?

Back

If two quantities are directly proportional, as one quantity increases, the other quantity increases at a constant rate.

Front

If a recipe requires 2 cups of flour for 4 servings, how much flour is needed for 10 servings?

Back

To find the amount needed for 10 servings, set up a proportion: 2 cups/4 servings = x cups/10 servings. Solving gives x = 5 cups.

Front

What is the constant of proportionality?

Back

The constant of proportionality is the ratio between two proportional quantities, often represented as 'k' in the equation y = kx.

Front

If a bike travels 15 miles in 1 hour, how far will it travel in 3 hours?

Back

Using the unit rate, the bike will travel 15 miles/hour × 3 hours = 45 miles.

Front

What is the formula for finding the constant of proportionality?

Back

The formula is k = y/x, where y is the dependent variable and x is the independent variable.

Front

If 5 pounds of apples cost $10, what is the cost per pound?

Back

The cost per pound is $10 ÷ 5 pounds = $2 per pound.