Step by step
The question
Question: 2 and 1/2 miles in 1/2 hour: how much is that per hour?
A unit rate says how much for 1 hour.
Per hour means: divide by the hours.
1 Write the rate
Miles divided by hours: 2 and 1/2 ÷ 1/2.
Careful!
Not the other way round.
That would be hours per mile.
2 Divide
2 and 1/2 is a mixed number.
Each whole one is 2/2.
So we do 2 times 2, plus 1.
The bottom stays 2.
2 times 2 plus 1 is 5.
So it is 5/2.
Dividing by a fraction is the same as times its flip.
Keep the first number.
Change divide to times.
Turn the second fraction upside down.
So 1/2 becomes 2, and divide becomes times.
Before we multiply, we make the numbers smaller.
2 on top and 2 at the bottom both divide by 2.
A top and a bottom divided by the same number: the answer stays the same.
So we multiply smaller numbers.
5 times 1 is 5.
So the unit rate is 5 miles per hour.
3 Check
Let's check: 5 miles per hour, for 1/2 hour.
5 times 1/2 is 5/2.
That is the miles we started with.
So the answer is right!
Let's look back.
First: write the rate.
Then: divide.
Last: check.