# 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

### Example

### 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

### Example

### 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

### Example

### 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.