7.RP.A.1 7th Grade Ratios & Proportional Relationships

Unit Rates

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.

How to explain it

The anchor students hold onto: Divide the first quantity by the second so the second becomes 1, then label the unit. To divide by a fraction, multiply by its reciprocal. To compare, find each unit rate.

A unit rate is the slope of a proportional relationship: the amount per one unit is exactly the constant of proportionality k in y = kx, which leads directly into 7.RP.A.2.

Worked examples

Example 1 Whole-Number Rate

180 miles in 4 hours: mph?

Step 1Set up the rate: 180 miles over 4 hours.

Step 2Divide: 180 ÷ 4 = 45.

Answer45 miles per hour

Example 2 Fraction Ratio

1/2 mile in 1/4 hour: mph?

Step 1Divide the fractions: 1/2 ÷ 1/4.

Step 2Multiply by the reciprocal: 1/2 × 4 = 2.

Answer2 miles per hour

Example 3 Compare Rates

60 mi/3 hr vs 80 mi/5 hr?

Step 1First rate: 60 ÷ 3 = 20.

Step 2Second rate: 80 ÷ 5 = 16.

AnswerFirst is faster (20 > 16)

Common mistakes

What students write Divides the second quantity by the first, inverting the rate.

The fix Divide first ÷ second: 180 miles ÷ 4 hours = 45 mph, not 4 ÷ 180.

What students write Stops at the ratio without simplifying to a per-ONE rate.

The fix Divide all the way: 180:4 becomes 45:1, so the unit rate is 45.

Teacher tip

Head off the two predictable errors before they happen. First: Divide first ÷ second: 180 miles ÷ 4 hours = 45 mph, not 4 ÷ 180. Second: Divide all the way: 180:4 becomes 45:1, so the unit rate is 45.