Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for unit rates with fractions 7th grade? Then this Grade 7 lesson on Finding Unit Rates When Quantities Are Fractions explains each idea step by step, with worked examples.
Quick answer: A unit rate with fractions tells how much of one quantity matches exactly 1 unit of another when the measurements are fractions. Divide the first quantity by the second, multiply by the reciprocal of the divisor, and simplify. For example, 1/2 mile in 1/4 hour is 2 miles per hour.
Standards: 7.RP.A.1 · Level: Grade 7
What is a unit rate when the measurements are fractions?
A unit rate says how much of one quantity matches exactly 1 unit of another quantity. When the measurements themselves are fractions, the rate is written as a complex fraction, a fraction whose top and bottom are fractions.
A unit rate compares two quantities so that the second quantity equals 1. Examples: miles per hour, dollars per pound, cups per batch, square feet per minute.
How do you simplify a complex fraction?
A fraction bar means division. So a complex fraction is a division of two fractions, and dividing by a fraction means multiplying by its reciprocal.
abcd = ab ÷ cd = ab × dc
The quantity on top of the fraction bar is the one being measured; the quantity on the bottom is the one that becomes 1.
- Decide which quantity is measured and which one should become 1 (the word after "per").
- Write the quantities as a division, first quantity ÷ second quantity.
- Change any mixed numbers to improper fractions.
- Multiply by the reciprocal of the second fraction.
- Simplify and write the answer with its unit.
A kayaker paddles 56 mile in 38 hour. Find the speed in miles per hour.
56 ÷ 38 = 56 × 83 = 4018 = 209 = 2 29. The unit rate is 2 29 miles per hour.
What if the two quantities use different units?
Compute the rate in the units you are given, then convert. A rate in miles per minute becomes miles per hour when multiplied by 60, because 1 hour has 60 minutes.
Dividing in the wrong order. For 14 mile in 3 minutes, 14 ÷ 3 gives miles per minute, but 3 ÷ 14 gives minutes per mile. Say the rate aloud, "miles per minute", to pick the order.
Check your answer by multiplying it back: unit rate × second quantity should return the first quantity. If 2 29 × 38 gives 56, you are right.
- A unit rate has 1 in the denominator: miles per 1 hour, dollars per 1 pound.
- A complex fraction is just a division of two fractions.
- Dividing by a fraction means multiplying by its reciprocal.
- When units differ, convert after finding the rate (for example, multiply by 60 to go from minutes to hours).
- Multiplying the unit rate by the second quantity must give back the first quantity.
Finding Unit Rates When Quantities Are Fractions: frequently asked questions
What is a complex fraction?
A complex fraction has a fraction in its numerator, its denominator, or both. It is read as a division: the top fraction divided by the bottom fraction.
Why do we multiply by the reciprocal?
Dividing by a fraction asks how many of that fraction fit into the amount. Multiplying by the reciprocal gives the same result and is faster, because the reciprocal of 3/8 is 8/3.
How do I know which quantity to divide by?
Look at the word after per. In miles per hour, hours is the quantity that becomes 1, so divide miles by hours.
Can a unit rate be a fraction or a mixed number?
Yes. A unit rate can be any positive rational number, such as 2 2/9 miles per hour or 3/4 cup per batch.
How do I find a unit rate when the units are different?
Divide the quantities as given, then convert with a conversion factor such as 60 minutes per hour or 3 feet per yard. Check that the final unit matches the question.
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