12 pencils for 3 pounds is a rate. Divided down to one pound, it is 4 pencils per pound.
Unit rate is how much of one quantity goes with exactly one of the other.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Why it is useful
Two deals are hard to compare until both are written per one. Then it is just two numbers.
Two unit rates from one ratio
12 pencils for 3 pounds is 4 pencils per pound, or 0.25 pounds per pencil. Both are true.
Scaling from one is easy
Once you know one pound buys 4 pencils, 7 pounds buys 7 × 4 = 28.
How much for exactly one
A unit rate is a rate where the second quantity is 1: 60 miles per hour, £3 per kilogram, 12 words per line. Fixing the second quantity at one makes rates directly comparable, which is the entire reason the form exists.
Finding one
If 5 kg costs £12, divide: 12 ÷ 5 = £2.40 per kilogram. Divide the first quantity by the second. The division is what produces "per one", and getting it the right way round is decided by which unit you want the answer in.
Every rate has two unit rates
From 5 kg for £12 you can also say 5 ÷ 12 = 0.42 kg per pound. Both are valid; which is useful depends on the question. "How much does 8 kg cost" wants price per kg; "how much can I buy with £20" wants kg per pound.
Rates in the world
Speed, price per unit, fuel consumption, heart rate, exchange rates and typing speed are all unit rates. Reading the word "per" is usually the signal. Once you notice how many everyday numbers are rates, the concept stops feeling like schoolwork.
Step 2: Try It Yourself
Tap and try it out.
| Pounds | Pencils |
|---|---|
| 1 | 4 |
| 2 | 8 |
| 3 | 12 |
Every row is the same ratio. 1 to 4 is the same comparison as 3 to 12.
Step 3: Watch an Example
One step at a time.
Watch Ana Compare Two Deals
6 apples for 3 pounds, or 10 apples for 4 pounds.
- Step 1
She works out the first deal per pound: 6 ÷ 3 = 2 apples.
Step 4: Your Turn
Practice makes it stick.
The Car
Problem 1 of 2
240 miles on 8 gallons. How many miles per gallon?
miles per gallon
The Typing
Problem 2 of 2
180 words in 4 minutes. How many words per minute?
words per minute
Per One
1 of 4
20 pens for 5 pounds. How many pens per pound?
2 of 4
150 km in 3 hours. How many km per hour?
3 of 4
8 pencils per pound. How many for 6 pounds?
4 of 4
90 pages in 6 days. How many pages per day?
Step 5: Quick Check
Show what you know.
Question 1 of 2
84 miles in 2 hours. How many miles per hour?
Question 2 of 2
Why write two deals as unit rates before comparing?
What You Learned
- A unit rate says how much goes with exactly one.
- Divide to find it.
- Two rates can only be compared once both are per one.