Step by step
The question
Question: find the percent change from 16 to 36.
1 Find the change
First: how much did it change?
It went up from 16 to 36.
36 minus 16 is 20.
It went up, so it is an increase.
2 Compare with the start
Now we compare the change with where we started.
The change, 20, goes on top.
The old number, 16, goes on the bottom.
Careful: we divide by the number we started with, 16.
Not by the new number.
3 Simplify
20 and 16 can both be divided by 4.
That keeps the numbers small.
20 divided by 4 is 5.
16 divided by 4 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.
5 times 25 is 125.
4 times 25 is 100.
125 out of 100 is 125%.
So it is a 125% increase.
5 Check
Let's check: 125% of 16 should be the change, 20.
125% is 125/100.
Of means times.
To keep the numbers small, we divide the top and the bottom by 25.
That is 5/4.
16 divided by 4 is 4.
So it is 5 times 4, that is 20.
And 16 plus 20 is 36, 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.