Mathematics.

numerical relationships

Percentages

Pre-Algebra20 minDifficulty2 out of 10

You should know: ratios and proportions

Overview

A percentage is a ratio expressed as a fraction of 100, denoted with the % symbol — 'percent' literally means 'per hundred.' Percentages give a standard scale for comparing proportions (a 25% discount means the same relative reduction whether applied to $4 or $4,000), which is why they're used everywhere from sales tax to test scores to statistics.

Formal Definition

Definition

A quantity of p percent equals the ratio p/100. To convert a percentage to a decimal, divide by 100; to find p% of a number N, multiply N by p/100.

p%=p100p\% = \frac{p}{100}
Definition
p% of N=p100×Np\% \text{ of } N = \frac{p}{100} \times N
Percentage of a quantity

Properties

Percent to decimal

p%=p100p\% = \frac{p}{100}

Percent change

% change=new−oldold×100%\text{\% change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100\%

Worked Examples

  1. Convert 20% to a decimal and multiply.

    0.20×50=100.20 \times 50 = 10

Answer: 10

Practice Problems

Difficulty 2/10

A shirt priced at $40 is discounted by 15%. What is the sale price?

Common Mistakes

Common Mistake

Forgetting to convert a percentage to a decimal (or fraction) before multiplying, e.g. computing '20% of 50' as 20 × 50.

Always divide the percent by 100 first: 20% of 50 = (20/100) × 50 = 10, not 20 × 50 = 1000.

Summary

  • A percentage p% means the ratio p/100.
  • To find p% of N, compute (p/100) × N.
  • Percent change compares the difference between new and old values to the original value.

References

  1. WebsiteWikipedia — Percentage