# Percent of Change

How to solve percent of change problems (increase, decrease): formula, examples, and their solutions.

## 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).

Ratio

## Example 1: Percent of Increase

First write

the original value ($15) and the new value ($21).

Put the written numbers (15, 21)

into the (% of change) formula.

Reduce 6 to 2.

(6 ÷ 3 = 2)

And reduce 15 to 5.

(15 ÷ 3 = 5)

Reduce 100 to 20.

(100 ÷ 5 = 20)

And cancel the denominator 5.

(5 ÷ 5 = 1)

You got 40%, which is (+).

So [40% of increase] is the answer.

If the calculated result is (+),

the it shows the percent of increase.

## Example 2: Percent of Decrease

First write

the original value ($25) and the new value ($22).

Put the written numbers (25, 22)

into the (% of change) formula.

Reduce 100 to 4.

(100 ÷ 25 = 4)

And cancel the denominator 25.

(25 ÷ 25 = 1)

You got -12%, which is (-).

So [12% of decrease] is the answer.

If the calculated result is (-),

the it shows the percent of decrease.

## Example 3

First write

the original value (8) and the new value (*x*).

Put the written numbers (8, *x*)

into the (% of change) formula.

Then it's time to solve this equation.

Linear equations (one variable)

Divide both sided by 25.

Reduce 8 to 2.

(8 ÷ 4 = 2)

And cancel 4.

(4 ÷ 4 = 1)

Multiply both sides by 2.

Move -8 to the right side.

Then *x* = 2 + 8

= 10.

## Example 4

First write

the original value (*x*) and the new value (14).

Put the written numbers (*x*, 14)

into the (% of change) formula.

Then solve this equation.

Linear equations (one variable)

Divide both sided by 10.

Multiply both sides by *x*.

Solve the left side's parentheses.

First multiply 14 and 10: 140.

Then multiply -*x* and 10: -10*x*.

Linear equations (one variable) - Example 6

Move 140 to the right side.

And move -3*x* to the left side.

Then the left side is, +3*x* - 10*x*, -7*x*.

And the right side is -140.

Divide both sides by -7.

Then *x* = -140/(-7) = 20.