Step by step
The question
Question: find the percent change from 80 to 92.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Find the change
First: how much did it change?
It went up from 80 to 92.
92 minus 80 is 12.
It went up, so it is an increase.
2 Compare with the start
Now we compare the change with where we started.
The change, 12, goes on top.
The old number, 80, goes on the bottom.
Careful: we divide by the number we started with, 80.
Not by the new number.
3 Simplify
Smaller numbers are easier.
What goes into 12 and 80?
We list the numbers that go into each.
Into 12: 1, 2, 3, 4, 6, 12.
Into 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80.
4 is the biggest one in both lists.
We divide the top and the bottom by 4.
12 divided by 4 is 3.
80 divided by 4 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% increase.
5 Check
Let's check: 15% of 80 should be the change, 12.
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.
80 divided by 20 is 4.
So it is 3 times 4, that is 12.
And 80 plus 12 is 92, the new number.
So it is right!
6 Pick the choice
Our answer is 15%.
That is choice C.
7 Why not the others
A is 12%.
Wrong: 92 − 80 = 12 is the change in dollars, not the percent.
B is 13%.
Wrong: 12 out of 92: we divide by the starting price, 80.
D is 115%.
Wrong: 92 ÷ 80: that is the new price as a percent of the old.
Let's look back.
First: find the change.
Then: compare with the start.
Then: simplify.
Then: make the bottom 100.
Then: check.
Then: pick the choice.
Last: why not the others.