# Percent of Change

How to find the percent of change of the given data: formula, 3 examples, and their solutions.

## Formula

### Formula

(percent of change)
= [(new) - (original)] / (original) × 100%.

100% is multiplied to make the unit % (percent).

The numerator, (new) - (original),
is the amount of change.

So the percent of change
is the ratio of (change)/(original).

## Example 1

### Solution

The original value is 15.
The new value is 21.
So the percent of change is
(21 - 15)/15 ⋅ 100.

21 - 15 = 6

Reduce 100 to, 100/5, 20
and reduce 15 to, 15/5, 3.

So (21 - 15)/15 ⋅ 100 = (6/3)⋅20.

6/3 = 2

So (6/3)⋅20 = 2⋅20.

2⋅20 = 40

The percent of change is 40.
40 is plus.
So [40% increase] is the answer.

## Example 2

### Solution

The original value is 25.
The new value is 22.
So the percent of change is
(22 - 25)/25 ⋅ 100.

22 - 25 = -3

Cancel the denominator 25
and reduce 100 to, 100/25, 4.

So (22 - 25)/25 ⋅ 100 = -3⋅4.

-3⋅4 = -12

The percent of change is -12.
-12 is minus.
So [12% decrease] is the answer.

## Example 3

### Solution

The original value is 8.
The new value is x.
So the percent of change is
(x - 8)/8 ⋅ 100.

And this shows 25% of increase.
So (x - 8)/8 ⋅ 100 = 25.

Solve this linear equation.

Divide both sides by 25.
In the left side, reduce 100 to, 100/25, 4.
And in the right side, reduce 25 to, 25/25, 1.

So (x - 8)/8 ⋅ 4 = 1.

In the left side,
cancel the numerator 4
and reduce the denominator 8 to, 8/4, 2.

So (x - 8)/2 = 1.

Multiply 2 to both sides.
Then x - 8 = 2.

Move -8 to the right side.

Then x = 10.

So x = 10 is the answer.