Step by step
The question
Question: find the percent change from 350 to 315.
1 Find the change
First: how much did it change?
It went down from 350 to 315.
350 minus 315 is 35.
It went down, so it is a decrease.
2 Compare with the start
Now we compare the change with where we started.
The change, 35, goes on top.
The old number, 350, goes on the bottom.
Careful: we divide by the number we started with, 350.
Not by the new number.
3 Simplify
Smaller numbers are easier.
35 goes into 350: 35 × 10 = 350.
So 35 goes into both.
We divide the top and the bottom by 35.
35 divided by 35 is 1.
350 divided by 35 is 10.
4 Make the bottom 100
Percent means out of 100.
So we want 100 at the bottom.
100 divided by 10 is 10.
So 10 times 10 is 100.
We multiply the top and the bottom by 10.
So the fraction keeps its size.
1 times 10 is 10.
10 times 10 is 100.
10 out of 100 is 10%.
So it is a 10% decrease.
5 Check
Let's check: 10% of 350 should be the change, 35.
10% is 10/100.
Of means times.
To keep the numbers small, we divide the top and the bottom by 10.
10 goes into 100: 10 × 10 = 100.
So 10 goes into both.
That is 1/10.
350 divided by 10 is 35.
That is 35.
And 350 minus 35 is 315, 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.