Step by step
The question
Question: find the area when the population density is 400 people/km² and the population is 6000 people.
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 400.
The population is 6000.
The area is what we want: we call it x.
3 Move x to the top
x is at the bottom.
Times x moves it up.
We do it on both sides, so they stay equal.
x divided by x is 1.
So just 6000 is left on the right.
Now we have 400x = 6000.
4 Remove the 400
400x means 400 times x.
We want just x.
To remove times 400, we divide by 400.
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.
400 divided by 400 is 1.
So just x is left.
6000 divided by 400 is 15.
So x = 15!
5 Check
Let's check: put 15 in place of x.
We get 6000, the same as the right side.
So x = 15 is right!
So the area is 15 km².
Let's look back.
First: write the rule.
Then: put the numbers in.
Then: move x to the top.
Then: remove the 400.
Last: check.