Questions: Unit Rates

Question 1

A car travels 240 miles on 8 gallons of gas. What is the unit rate?

• A. 8 miles per gallon
• B. 30 miles per gallon
• C. 240 miles per gallon
• D. 32 miles per gallon

Answer: (B)

Divide the total distance by the total gallons: 240 ÷ 8 = 30 miles per gallon. 'Per gallon' means 'per one gallon,' which is what we get when we divide to find the amount for a single unit.

Question 2

A unit rate and a ratio are the same thing.

• T. True
• F. False

Answer: False

All unit rates are ratios, but not all ratios are unit rates (or even rates). A ratio can compare any two quantities with the same units (like 3 red marbles to 5 blue marbles). A rate compares quantities with different units (like miles and hours). A unit rate is specifically a rate where the second quantity equals 1 (like 60 miles per 1 hour).

Question 3

How is a unit rate connected to the concept of slope in algebra?

Model answer: Slope measures the unit rate of change — how much y changes per one unit increase in x. For example, a slope of 3 means the output increases by 3 for every 1-unit increase in the input, which is a unit rate.

Slope is defined as rise/run, or the change in y per change in x. When run = 1, rise equals the slope — exactly a unit rate. This is why understanding unit rates as 'per one unit' directly prepares students for slope, where we always ask 'how much change per one step?'