The lesson
Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
A unit rate is 'per one'
A unit rate tells you how much of one quantity goes with exactly one of another - like miles per hour or cost per pound.
When the numbers are fractions
The denominator tells you how many equal parts the whole is split into. The numerator tells you how many of those parts you have.
Always ask: "What is the whole?" In 3/4 of a pizza, the whole is one pizza. In 3/4 of 20 students, the whole is 20 students.
- 1Write the rate as a fraction (a complex fraction).
- 2Divide the top by the bottom - multiply by the reciprocal.
- 3Simplify to get the rate per one.
A person walks 1/2 mile in 1/4 hour. What is the speed in miles per hour?
- 1Set up the rate: (1/2) ÷ (1/4).
- 2Multiply by the reciprocal: 1/2 × 4/1 = 4/2 = 2.
- 3The unit rate is 2 miles per hour.
Why this matters
Find a per-one rate even when the quantities are fractions.
These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.
Common mistakes to avoid
Adding numerators and denominators separately (2/3 + 1/4 is not 3/7). Match denominators first, or use a clear model.
Forgetting to simplify the final answer when a smaller equivalent fraction is possible.
Key ideas from this lesson
- A unit rate is 'per one'
- When the numbers are fractions
- Write the rate as a fraction (a complex fraction).
- Divide the top by the bottom - multiply by the reciprocal.
- Simplify to get the rate per one.
Video walkthroughs
Determining Rates with Fractions
Turn a ratio of fractions into a clean unit rate.
Watch on YouTube
Rates and Unit Rates
Turn a rate into a per-one unit rate with fractions.
Watch on YouTube
Practice
For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.
Exercise 1
Try it yourselfA jogger runs 3/4 mile in 1/2 hour. Find the speed in miles per hour.
Step-by-step solution
- 1Rate = (3/4) ÷ (1/2).
- 2Multiply by reciprocal: 3/4 × 2/1 = 6/4 = 3/2.
- 3The unit rate is 1.5 miles per hour.
Exercise 2
Try it yourselfYou type 2/5 page in 1/10 minute. How many pages per minute?
Step-by-step solution
- 1(2/5) ÷ (1/10) = 2/5 × 10/1 = 20/5 = 4 pages per minute.
Exercise 3
Try it yourselfA hose fills 5/6 of a tank in 2/3 hour. How much of the tank is filled per hour?
Step-by-step solution
- 1(5/6) ÷ (2/3) = 5/6 × 3/2 = 15/12 = 5/4.
- 2The tank fills at 5/4 (or 1.25) tanks per hour.
Exercise 4
Try it yourselfApples cost $4.50 for 3/4 lb. What is the cost per pound?
Step-by-step solution
- 1Unit rate = 4.50 ÷ (3/4) = 4.50 × (4/3) = 18/3 = 6.
- 2The cost is $6 per pound.
Exercise 5
Try it yourselfA cyclist travels 7/8 km in 1/4 hour. Find the speed in km/h.
Step-by-step solution
- 1(7/8) ÷ (1/4) = 7/8 × 4/1 = 28/8 = 7/2.
- 2The speed is 3.5 km/h.
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Unit Rates with Fractions
Question 1 of 4
You read 1/3 page in 1/6 minute. What is your rate in pages per minute?