Percent of a Number Formula

Percent of a number is calculating a given percentage of a quantity by converting the percent to a decimal (or fraction) and multiplying.

The Formula

Part=Percent100×Whole\text{Part} = \frac{\text{Percent}}{100} \times \text{Whole}

When to use: 25%25\% of 80 means 'one quarter of 80.' Convert 25%25\% to 0.250.25 and multiply: 0.25×80=200.25 \times 80 = 20.

Quick Example

15% of 200=0.15×200=3015\% \text{ of } 200 = 0.15 \times 200 = 30; and 50%50\% of 60=0.5×60=3060 = 0.5 \times 60 = 30.

Notation

p%p\% of nn means p100×n\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%25\% of 80 means 'one quarter of 80.' Convert 25%25\% to 0.250.25 and multiply: 0.25×80=200.25 \times 80 = 20.

Formal View

Part=p100⋅W\text{Part} = \frac{p}{100} \cdot W where pp is the percent and WW is the whole; equivalently p=PartW×100p = \frac{\text{Part}}{W} \times 100

Worked Examples

Example 1

easy
Find 35%35\% of 140140.

Answer

4949

First step

1
Convert the percentage to a decimal: 35%=0.3535\% = 0.35.

Full solution

  1. 2
    Multiply: 0.35×140=490.35 \times 140 = 49.
  2. 3
    Alternatively: 35100×140=35×140100=4900100=49\frac{35}{100} \times 140 = \frac{35 \times 140}{100} = \frac{4900}{100} = 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%40\% discount on a jacket priced at $85\$85. What is the sale price?

Example 3

easy
What is 75%75\% of 8080?

Common Mistakes

  • Multiplying by the percent without dividing by 100 first - 25%25\% means 0.250.25, so 0.25×n0.25\times n.
  • Confusing the part with the whole - 25%25\% of 80 gives the part (20), not the leftover (60).
  • Forgetting to subtract for a discount - a 25% discount on $80 means pay 80−20=$6080-20=\$60, not $20.

Why This Formula Matters

This is the workhorse of everyday money math — tips, sales tax, discounts — and the base for percent change and interest. Forget to divide the percent by 100 and you multiply by the raw number, getting an answer 100 times too big. Recognizing it by "Am I taking a stated percent of a given quantity?" — rather than by familiar numbers — is what lets a student tell it apart from fraction of a number and percent change and percentages in a mixed problem set.

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%25\% of 80 means 'one quarter of 80.' Convert 25%25\% to 0.250.25 and multiply: 0.25×80=200.25 \times 80 = 20.

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

p%p\% of nn means p100×n\frac{p}{100} \times n

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

This is the workhorse of everyday money math — tips, sales tax, discounts — and the base for percent change and interest. Forget to divide the percent by 100 and you multiply by the raw number, getting an answer 100 times too big. Recognizing it by "Am I taking a stated percent of a given quantity?" — rather than by familiar numbers — is what lets a student tell it apart from fraction of a number and percent change and percentages in a mixed problem set.

What do students get wrong about Percent of a Number?

The procedure for percent of a number is the easy part; the trap is multiplying by the percent without dividing by 100 first. Asking "Am I taking a stated percent of a given quantity?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

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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