Percent of a Number Formula

The Formula

\text{Part} = \frac{\text{Percent}}{100} \times \text{Whole}

When to use: 25\% of 80 means 'one quarter of 80.' Convert 25\% to 0.25 and multiply: 0.25 \times 80 = 20.

Quick Example

15\% \text{ of } 200 = 0.15 \times 200 = 30; and 50\% of 60 = 0.5 \times 60 = 30.

Notation

p\% of n means \frac{p}{100} \times n

What This Formula Means

Calculating a given percentage of a quantity by converting the percent to a decimal (or fraction) and multiplying.

25\% of 80 means 'one quarter of 80.' Convert 25\% to 0.25 and multiply: 0.25 \times 80 = 20.

Formal View

\text{Part} = \frac{p}{100} \cdot W where p is the percent and W is the whole; equivalently p = \frac{\text{Part}}{W} \times 100

Worked Examples

Example 1

easy
Find 35\% of 140.

Solution

  1. 1
    Convert the percentage to a decimal: 35\% = 0.35.
  2. 2
    Multiply: 0.35 \times 140 = 49.
  3. 3
    Alternatively: \frac{35}{100} \times 140 = \frac{35 \times 140}{100} = \frac{4900}{100} = 49.

Answer

49
Percent of a number follows the pattern: Part = (Percent ÷ 100) × Whole. Converting the percent to a decimal first is the most direct calculation method.

Example 2

medium
A store offers a 40\% discount on a jacket priced at \85$. What is the sale price?

Common Mistakes

  • Forgetting to divide the percent by 100 before multiplying
  • Moving the decimal point the wrong direction
  • Confusing 'percent of' with 'percent change'

Why This Formula Matters

Used for tips, taxes, discounts, statistics, and probability in everyday life.

Frequently Asked Questions

What is the Percent of a Number formula?

Calculating a given percentage of a quantity by converting the percent to a decimal (or fraction) and multiplying.

How do you use the Percent of a Number formula?

25\% of 80 means 'one quarter of 80.' Convert 25\% to 0.25 and multiply: 0.25 \times 80 = 20.

What do the symbols mean in the Percent of a Number formula?

p\% of n means \frac{p}{100} \times n

Why is the Percent of a Number formula important in Math?

Used for tips, taxes, discounts, statistics, and probability in everyday life.

What do students get wrong about Percent of a Number?

Students confuse 'percent of' with 'percent is'—15% of 200 is 30, but 30 is what percent of 200?

What should I learn before the Percent of a Number formula?

Before studying the Percent of a Number formula, you should understand: percentages, decimal fraction conversion.

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