Step by step
The question
Question: find the percent change from 120 to 90.
1 Find the change
First: how much did it change?
It went down from 120 to 90.
120 minus 90 is 30.
It went down, so it is a decrease.
2 Compare with the start
Now we compare the change with where we started.
The change, 30, goes on top.
The old number, 120, goes on the bottom.
Careful: we divide by the number we started with, 120.
Not by the new number.
3 Simplify
30 and 120 can both be divided by 30.
That keeps the numbers small.
30 divided by 30 is 1.
120 divided by 30 is 4.
4 Make the bottom 100
Percent means out of 100.
4 times 25 is 100.
So we multiply the top and the bottom by 25.
25/25 is 1.
Times 1 does not change the size.
1 times 25 is 25.
4 times 25 is 100.
25 out of 100 is 25%.
So it is a 25% decrease.
5 Check
Let's check: 25% of 120 should be the change, 30.
25% is 25/100.
Of means times.
To keep the numbers small, we divide the top and the bottom by 25.
That is 1/4.
120 divided by 4 is 30.
That is 30.
And 120 minus 30 is 90, the new number.
So it is right!
Let's look back.
First: find the change.
Then: compare with the start.
Then: simplify.
Then: make the bottom 100.
Last: check.