A unit rate is still "how much for one", even when both numbers are fractions.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
The same division as always
Walking ½ mile in ¼ hour is (½) ÷ (¼) miles per hour.
Dividing by a fraction
Multiply by the reciprocal: ½ × 4 = 2. Two miles an hour.
Does the size make sense
A quarter hour is a small part of an hour, so the hourly figure should be larger than ½. It is.
Rates where neither number is whole
If 3/4 of a litre of paint covers 2/3 of a wall, the rate is (2/3) ÷ (3/4) = 8/9 of a wall per litre. Nothing about the method changes when the quantities are fractions — you still divide to reach "per one".
Dividing fractions to find a rate
Multiply by the reciprocal: (2/3) ÷ (3/4) = (2/3) × (4/3) = 8/9. Getting the division the right way round is decided by the unit you want: walls per litre means walls divided by litres.
Check the size makes sense
Three quarters of a litre covered two thirds of a wall, so a full litre should cover a bit more — and 8/9 is a bit more than 2/3. Checking the direction of the change catches an inverted division at once.
Where fractional rates arise
Recipes scaled by 1 1/2, fuel used over 2/3 of a journey, work done in 3/4 of an hour. Real quantities are rarely whole, which is why the fractional case matters more than the tidy examples suggest.
Step 2: Try It Yourself
Tap and try it out.
Before: 6
After: 24
The factor is more than 1, so the bar got longer.
Step 3: Watch an Example
One step at a time.
Watch Leo Find a Rate from Fractions
Leo paints ¾ of a wall in ½ an hour.
- Step 1
He writes the division: (¾) ÷ (½).
Step 4: Your Turn
Practice makes it stick.
The Walk
Problem 1 of 2
½ mile in ¼ hour. How many miles per hour?
The Recipe
Problem 2 of 2
⅔ cup for ⅓ of a batch. How many cups for a whole batch?
How Much for One
1 of 4
¼ mile in ⅛ hour. Miles per hour?
2 of 4
½ litre in ¼ minute. Litres per minute?
3 of 4
3 miles in ½ hour. Miles per hour?
4 of 4
¾ kg for ¼ of a box. Kilograms for a whole box?
Step 5: Quick Check
Show what you know.
Question 1 of 1
⅖ mile in ⅕ hour. Miles per hour?
What You Learned
- A unit rate is still the first quantity divided by the second.
- Dividing by a fraction means multiplying by its reciprocal.
- Check the size: dividing by a number below one makes the answer larger.