Step by step
The question
Question: 7 and 1/2 miles in 1 and 1/4 hours: 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: 7 and 1/2 ÷ 1 and 1/4.
Careful!
Not the other way round.
That would be hours per mile.
2 Divide
7 and 1/2 is a mixed number.
Each whole one is 2/2.
So we do 7 times 2, plus 1.
The bottom stays 2.
7 times 2 plus 1 is 15.
So it is 15/2.
1 and 1/4 is a mixed number.
Each whole one is 4/4.
So we do 1 times 4, plus 1.
The bottom stays 4.
1 times 4 plus 1 is 5.
So it is 5/4.
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 5/4 becomes 4/5, and divide becomes times.
Before we multiply, we make the numbers smaller.
15 on top and 5 at the bottom both divide by 5.
4 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.
3 times 2 is 6.
So the unit rate is 6 miles per hour.
3 Check
Let's check: 6 miles per hour, for 1 and 1/4 hours.
6 times 5/4 is 15/2.
That is the miles we started with.
So the answer is right!
Let's look back.
First: write the rate.
Then: divide.
Last: check.