Percentages Formula

The Formula

p\% = \frac{p}{100} (to convert a percent to a fraction or decimal, divide by 100)

When to use: Percent means 'per hundred.' 25\% means 25 out of every 100.

Quick Example

25\% = \frac{25}{100} = 0.25 = \frac{1}{4} and 50\% = \frac{50}{100} = 0.5 = \frac{1}{2}

Notation

p\% means p per hundred; equivalently \frac{p}{100} or 0.0p (for single/double-digit p)

What This Formula Means

A way of expressing a quantity as a fraction of 100, written with the symbol % to mean 'per hundred.'

Percent means 'per hundred.' 25\% means 25 out of every 100.

Formal View

p\% = \frac{p}{100}, so p\% of x is \frac{p}{100} \cdot x

Worked Examples

Example 1

easy
What is 25\% of \80$?

Solution

  1. 1
    Recall that "percent" means per hundred, so 25\% = \frac{25}{100} = 0.25 as a decimal.
  2. 2
    Multiply the decimal by the whole amount: 0.25 \times 80.
  3. 3
    Calculate: 0.25 \times 80 = 20

Answer

\$20
Finding a percentage of a number means multiplying the number by the percentage expressed as a decimal (or fraction). 25\% is the same as \frac{1}{4}.

Example 2

medium
A student scored 42 out of 60 on a test. What is the percentage score?

Common Mistakes

  • Forgetting to convert between forms
  • Calculating percent of vs percent change

Why This Formula Matters

Universal language for discounts, interest, probability, and statistics.

Frequently Asked Questions

What is the Percentages formula?

A way of expressing a quantity as a fraction of 100, written with the symbol % to mean 'per hundred.'

How do you use the Percentages formula?

Percent means 'per hundred.' 25\% means 25 out of every 100.

What do the symbols mean in the Percentages formula?

p\% means p per hundred; equivalently \frac{p}{100} or 0.0p (for single/double-digit p)

Why is the Percentages formula important in Math?

Universal language for discounts, interest, probability, and statistics.

What do students get wrong about Percentages?

Converting between percent, decimal, and fraction forms fluently — especially remembering to divide by 100 to convert percent to decimal.

What should I learn before the Percentages formula?

Before studying the Percentages formula, you should understand: fractions, decimals.

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