Proportional Relationships

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 calculate the unit rate?

Back

To find the unit rate, divide the total quantity by the number of units. For example, if you have 3 pounds of apples for $3.60, the unit rate is $3.60 ÷ 3 = $1.20 per pound.

Front

If Daniel walked 2/5 mile in 1/4 hour, how do you find his speed in miles per hour?

Back

To find speed, use the formula: Speed = Distance ÷ Time. Here, Speed = (2/5) ÷ (1/4) = (2/5) * (4/1) = 1.6 miles per hour.

Front

What is the constant of proportionality?

Back

The constant of proportionality is the ratio y/x in a proportional relationship, where y is the dependent variable and x is the independent variable.

Front

If a machine makes 56 parts in 4 hours, how many parts does it make in 1 hour?

Back

To find the rate per hour, divide the total parts by the total hours: 56 parts ÷ 4 hours = 14 parts per hour.

Front

How do you predict the output of a proportional relationship?

Back

To predict the output, use the constant of proportionality to scale the input. For example, if the machine makes 14 parts per hour, in 9 hours it will make 14 * 9 = 126 parts.

Front

What is the formula for finding the constant of proportionality?

Back

The formula is y = kx, where k is the constant of proportionality.

Front

If you have 624 calories in 3 servings, how do you find the calories per serving?

Back

Divide the total calories by the number of servings: 624 calories ÷ 3 servings = 208 calories per serving.

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

What is an example of a proportional relationship in real life?

Back

An example is the cost of apples: if 3 pounds cost $3.60, then 1 pound costs $1.20, showing a constant ratio.