Step by step
The question
Question: find the population when the population density is 250 people/km² and the area is 12 km².
1 Write the rule
The rule: population density is the population divided by the area.
Population density tells us how many people live on 1 km².
So its unit is people per km².
2 Put the numbers in
The population density is 250.
The area is 12.
The population is what we want: we call it p.
Careful!
The population goes on the top.
The unit, people/km², shows it: people on the top.
3 Remove the fraction
The bottom number is 12.
Times 12 will remove it.
We multiply every part by 12.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
12 divided by 12 is 1.
Write what is left.
Do the multiplications.
No more fractions!
Let's swap the two sides, so p is on the left.
So p = 3000!
4 Check
Let's check: put 3000 in place of p.
First the left side.
Now the right side.
Both sides are 250.
So p = 3000 is right!
So the population is 3000 people.
Let's look back.
First: write the rule.
Then: put the numbers in.
Then: remove the fraction.
Last: check.