7.RP.1: Unit Rates with Fractions
Also written as 7.RP.A.1 and CCSS.MATH.CONTENT.7.RP.A.1 · Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems.
The Official Wording
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour.
Common Core State Standards, Grade 7, Ratios & Proportional Relationships · Read it at the source · Checked October 14, 2026
What 7.RP.1 Means in Plain English
Seventh graders find a rate when both numbers are fractions. A recipe uses 3/4 cup of flour for 1/2 batch, so the unit rate is (3/4) ÷ (1/2) = 1 1/2 cups per batch. Dividing fractions, learned in 6th grade, now turns any ratio into a per-one amount.
The units can differ, like miles per hour, or match, like one length compared with another. The unit rate found here becomes the constant of proportionality in 7.RP.2 and the slope of a line in 8th grade (8.EE.5), so the per-one habit is worth building carefully.
7.RP.1 I Can Statements
- I can divide two fractions to find a unit rate.
- I can find a rate like miles per hour from fractional amounts.
- I can explain what a unit rate means in the situation.
7.RP.1 Worked Example
Ten minutes of jogging, measured as a fraction of an hour: the complex fraction looks worse than it is.
Jordan jogs 3/4 mile in 1/6 hour (10 minutes). What is Jordan’s speed in miles per hour?
- Speed means miles for 1 hour, so the unit rate is miles divided by hours. Write it as a complex fraction.(3/4) ÷ (1/6) miles per hour
- Dividing by a fraction is multiplying by its reciprocal. Flip 1/6 to 6/1.3/4 × 6/1 = 18/4
- Simplify 18/4. Divide top and bottom by 2, then write it as a mixed number.18/4 = 9/2 = 4 1/2
- Attach the units. The 1 hidden in the rate is 1 hour.4 1/2 miles per hour
Check it: Six 10-minute stretches make an hour, and six lots of 3/4 mile is 18/4 = 4 1/2 miles. Or multiply back: 4 1/2 × 1/6 = 9/12 = 3/4 mile.
Common Mistakes with 7.RP.1
Dividing in the wrong order
(1/6) ÷ (3/4) = 2/9 miles per hour
Try this: Say the rate in words first: miles per hour means miles divided by hours, so the distance goes on top of the fraction.
Flipping the wrong fraction
3/4 ÷ 1/6 = 4/3 × 1/6 = 4/18
Try this: Write the division as a multiplication before touching anything, then flip only the second fraction: 3/4 × 6/1.
Dropping the units
The answer is 4 1/2
Try this: Ask “4 1/2 what, per what?” every time. A unit rate without units cannot be compared to another rate or checked for sense.
Where 7.RP.1 Fits
Practice 7.RP.1
Quick Check
- A recipe uses 2/3 cup of sugar for 1/2 batch. How much sugar is that per full batch?
- A snail crawls 3/8 meter in 1/4 hour. What is its speed in meters per hour?
- A rectangle is 2 1/2 inches long and 1 1/4 inches wide. How many times as long as it is wide?