Calculate percent increase and percent decrease

Percent increase or decrease measures a change relative to the original amount—the baseline—not the new amount: percent change equals change divided by original amount, multiplied by 100%, with the sign indicating increase or decrease. The learner connects percent, fraction, decimal, and multiplier representations to calculate final amounts for prices, taxes, discounts, and other positive financial quantities, and distinguishes percent change from percentage-point change. The scope is limited to single changes, excluding compound successive changes and more advanced algebraic generalizations.

Detailed Explanation: Calculate percent increase and percent decrease

A percent change compares the change with the original amount, also called the baseline.

\text{Percent change}=\frac{\text{change}}{\text{original amount}}\times 100\%

If the new amount is greater, it is a percent increase.
If the new amount is smaller, it is a percent decrease.

Example

A backpack originally costs 80 $. Its price increases to$ $92$. What is the percent increase?

Step 1: Find the change.

\$92-\$80=\$12

The price increased by 12$.

Step 2: Divide by the original amount.

\frac{12}{80}=0.15

Use 80 $, not$ $92$, because the original amount is the baseline.

Step 3: Convert the decimal to a percent.

0.15\times 100\%=15\%

The price increased by $(15\%)$ .

You can also use a multiplier to find the new price:

1+0.15=1.15

\$80(1.15)=\$92

For a decrease, subtract the decimal from $1$ . For example, a $(15\%)$ decrease uses the multiplier

1-0.15=0.85.

Remember: a percent change is different from a percentage-point change. Percent change compares amounts, while percentage points compare percentages directly.

Learn by doing: Calculate percent increase and percent decrease

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Percent growth of a number (5% multiples)

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