Worked examples
The question
Question: 1/2 mile in 1/4 hour: how much is that per hour?
12 mile in 14 hour
A unit rate says how much for 1 hour.
Per hour means: divide by the hours.
per hour = ÷ hours
1 Write the rate
Miles divided by hours: 1/2 ÷ 1/4.
= 12 ÷ 14
miles ÷ hours
Careful!
Not the other way round.
That would be hours per mile.
Careful: not 14 ÷ 12 ✗
2 Divide
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.
÷ 14 → × 41
So 1/4 becomes 4, and divide becomes times.
= 12 × 41
Before we multiply, we make the numbers smaller.
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.
4 and 2: ÷ 2 → 2 and 1
So we multiply smaller numbers.
= 11 × 21
1 times 2 is 2.
So the unit rate is 2 miles per hour.
= 2 miles per hour
3 Check
Let's check: 2 miles per hour, for 1/4 hour.
2 times 1/4 is 1/2.
That is the miles we started with.
So the answer is right!
2 × 14 = 12
Let's look back.
First: write the rate.
Then: divide.
Last: check.
Answer = 2 miles per hour
▶ Watch it solved
The question
Question: 2/3 wall in 1/2 hour: how much is that per hour?
23 wall in 12 hour
A unit rate says how much for 1 hour.
Per hour means: divide by the hours.
per hour = ÷ hours
1 Write the rate
Walls divided by hours: 2/3 ÷ 1/2.
= 23 ÷ 12
walls ÷ hours
Careful!
Not the other way round.
That would be hours per wall.
Careful: not 12 ÷ 23 ✗
2 Divide
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.
÷ 12 → × 21
So 1/2 becomes 2, and divide becomes times.
= 23 × 21
To multiply fractions, we do top times top, and bottom times bottom.
A whole number is a fraction over 1.
= 2 × 23 × 1
2 times 2 is 4.
3 times 1 is 3.
So the unit rate is 4/3 walls per hour.
= 43 walls per hour
3 Check
Let's check: 4/3 walls per hour, for 1/2 hour.
4/3 times 1/2 is 2/3.
That is the walls we started with.
So the answer is right!
43 × 12 = 23
Let's look back.
First: write the rate.
Then: divide.
Last: check.
Answer = 43 walls per hour
▶ Watch it solved
The question
Question: 2 and 1/2 miles in 1/2 hour: how much is that per hour?
212 miles in 12 hour
A unit rate says how much for 1 hour.
Per hour means: divide by the hours.
per hour = ÷ hours
1 Write the rate
Miles divided by hours: 2 and 1/2 ÷ 1/2.
= 212 ÷ 12
miles ÷ hours
Careful!
Not the other way round.
That would be hours per mile.
Careful: not 12 ÷ 212 ✗
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 × 2 + 12 ÷ 12
2 times 2 plus 1 is 5.
So it is 5/2.
= 52 ÷ 12
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.
÷ 12 → × 21
So 1/2 becomes 2, and divide becomes times.
= 52 × 21
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.
2 and 2: ÷ 2 → 1 and 1
So we multiply smaller numbers.
= 51 × 11
5 times 1 is 5.
So the unit rate is 5 miles per hour.
= 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!
5 × 12 = 52
Let's look back.
First: write the rate.
Then: divide.
Last: check.
Answer = 5 miles per hour
▶ Watch it solved
