Step by step
The question
Question: find the percent change from 8000 to 6800.
1 Find the change
First: how much did it change?
It went down from 8000 to 6800.
8000 minus 6800 is 1200.
It went down, so it is a decrease.
2 Compare with the start
Now we compare the change with where we started.
The change, 1200, goes on top.
The old number, 8000, goes on the bottom.
Careful: we divide by the number we started with, 8000.
Not by the new number.
3 Simplify
Smaller numbers are easier.
We divide by small numbers that go into both, until none is left.
We used 2, 2, 2, 2, 5 and 5.
Together: 2 times 2 times 2 times 2 times 5 times 5 is 400.
We divide the top and the bottom by 400.
1200 divided by 400 is 3.
8000 divided by 400 is 20.
4 Make the bottom 100
Percent means out of 100.
So we want 100 at the bottom.
100 divided by 20 is 5.
So 20 times 5 is 100.
We multiply the top and the bottom by 5.
So the fraction keeps its size.
3 times 5 is 15.
20 times 5 is 100.
15 out of 100 is 15%.
So it is a 15% decrease.
5 Check
Let's check: 15% of 8000 should be the change, 1200.
15% is 15/100.
Of means times.
To keep the numbers small, we divide the top and the bottom by 5.
What goes into 15 and 100?
We list the numbers that go into each.
Into 15: 1, 3, 5, 15.
Into 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
5 is the biggest one in both lists.
That is 3/20.
8000 divided by 20 is 400.
So it is 3 times 400, that is 1200.
And 8000 minus 1200 is 6800, 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.