Unit Rates and Proportionality Problems

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together. It is expressed as a quantity of one unit, such as miles per hour or price per item.

Front

How do you find the constant of proportionality?

Back

The constant of proportionality can be found by dividing one quantity by the other in a proportional relationship. For example, if y is proportional to x, then the constant of proportionality k = y/x.

Front

What is the formula to calculate percentage?

Back

Percentage = (Part/Whole) x 100.

Front

If 225 out of 250 seats are sold, how do you calculate the percent of empty seats?

Back

Empty seats = Total seats - Sold seats = 250 - 225 = 25. Percent of empty seats = (25/250) x 100 = 10%.

Front

What does it mean if two quantities are proportional?

Back

Two quantities are proportional if they maintain a constant ratio or rate. This means that as one quantity increases or decreases, the other does so in a consistent manner.

Front

How do you solve for x in a proportionality equation?

Back

To solve for x, set up the equation based on the proportional relationship and isolate x by performing inverse operations.

Front

What is the relationship between unit rates and proportionality?

Back

Unit rates are a specific type of proportional relationship where one of the quantities is normalized to one unit.

Front

If Ben earns $41 for 4 hours, what is his hourly rate?

Back

Hourly rate = Total earnings / Total hours = $41 / 4 = $10.25.

Front

How do you convert a fraction to a percentage?

Back

To convert a fraction to a percentage, divide the numerator by the denominator and then multiply by 100.

Front

What is the constant of proportionality in the equation y = kx?

Back

In the equation y = kx, k represents the constant of proportionality, which indicates how much y changes for a unit change in x.