Step by step
The question
Question: find the percent change from 200 to 50.
1 Find the change
First: how much did it change?
It went down from 200 to 50.
200 minus 50 is 150.
It went down, so it is a decrease.
2 Compare with the start
Now we compare the change with where we started.
The change, 150, goes on top.
The old number, 200, goes on the bottom.
Careful: we divide by the number we started with, 200.
Not by the new number.
3 Simplify
150 and 200 can both be divided by 50.
That keeps the numbers small.
150 divided by 50 is 3.
200 divided by 50 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.
3 times 25 is 75.
4 times 25 is 100.
75 out of 100 is 75%.
So it is a 75% decrease.
5 Check
Let's check: 75% of 200 should be the change, 150.
75% is 75/100.
Of means times.
To keep the numbers small, we divide the top and the bottom by 25.
That is 3/4.
200 divided by 4 is 50.
So it is 3 times 50, that is 150.
And 200 minus 150 is 50, 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.