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 /1/4 miles per hour, equivalently 2 miles per hour.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
How far does someone walk in one whole hour if they cover 3/4 mile in 20 minutes? Questions like that ask for a unit rate, the amount of one quantity that goes with exactly 1 of another: miles per hour, dollars per pound, cups of flour per cup of milk. Sixth graders found unit rates from whole-number ratios like 120 miles in 3 hours. Seventh graders meet the harder and more realistic case where both quantities are fractions, such as walking 3/4 mile in 1/3 hour.
The answer comes from dividing: (3/4) ÷ (1/3) = 9/4, or 2 1/4 miles per hour. Written as a single fraction with fractions in the numerator and denominator, this is called a complex fraction, and students learn to simplify it by dividing. The quantities can be lengths, areas, volumes, time or money, measured in the same unit or in different units. What matters is keeping track of which quantity is 'per 1' so the rate answers the question asked.
Students often divide the larger-looking number by the smaller one. Ask which quantity should be 'per 1'. Miles per hour means miles divided by hours, whatever the sizes of the fractions.
Seeing two fractions, some students multiply 3/4 × 1/3 and get 1/4 mile per hour, which is slower than the walk itself. A quick reasonableness check (less than an hour of walking already covered 3/4 mile) catches this.
A fraction bar with fractions above and below means one division. Rewriting it as numerator ÷ denominator before computing removes the confusion.
A rate of 9/4 without units cannot be checked. Insisting on 'miles per hour' or 'cups per batch' shows whether the division was set up the right way round.
A hiker covers 3/4 mile every 1/3 hour. What is the hiker's speed in miles per hour?
Answer: The hiker's speed is 9/4 = 2.25 miles per hour.
Double number lines and tape diagrams help students see why dividing works: mark 3/4 mile against 1/3 hour, then extend the line to 3/3 hour by repeating the jump. After a few drawn examples, connect the picture to the division of fractions they learned in 6.NS.A.1 so the complex fraction feels like a shortcut, not a new rule.
Assessment items often hide the unit rate inside a comparison: which pump fills a tank faster, or which paint covers more area per gallon. Students who find each unit rate first and then compare usually avoid the traps in these questions.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 3 (also accepted: 3 chapters)
Chapters per hour means chapters ÷ hours: (1/2) ÷ (1/6) = (1/2) × 6 = 3 chapters per hour.
Answer: C) 4/5
Divide the fraction of the tank by the time: (2/5) ÷ (1/2) = (2/5) × 2 = 4/5 of the tank per hour.
Answer: 1.5 (also accepted: 1 1/2, 3/2)
Flour per cup of milk is (3/4) ÷ (1/2) = (3/4) × 2 = 3/2, which is 1 1/2 cups of flour per cup of milk.
Answer: A) (5/6) ÷ (1/3)
Miles per hour is miles divided by hours, so the miles (5/6) go first and are divided by the hours (1/3). The answer is 5/2 = 2 1/2 miles per hour.
Answer: 4 (also accepted: 4 gallons)
Gallons per whole fence is (1/3) ÷ (1/12) = (1/3) × 12 = 4 gallons.
Answer: C) 2 buckets per minute
Buckets per minute is (3/2) ÷ (3/4) = (3/2) × (4/3) = 2. Multiplying the fractions instead gives 1 1/8, which is a common slip.
A full lesson with slides, activities and an exit ticket on unit rates with fractions, pitched to grade 7 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 7.RP.A.1 with an answer key, ready in about a minute.
Make a worksheet →Turn unit rates with fractions into a quiz students answer online that marks itself, with a class summary for you.
Build a test →It is a fraction whose numerator, denominator or both are fractions, such as (1/2)/(1/4). In this standard it records a rate, and you simplify it by dividing the top fraction by the bottom one.
In sixth grade (6.RP.A.2) the quantities are usually whole numbers. Seventh grade extends unit rates to fractional quantities, so students must divide fractions to find the rate.