Percentages Cheat Sheet

Definition

A percentage is a ratio that compares a number to 100. It represents a part out of a whole, where the whole is considered to be 100.

Example: 25% means 25 out of 100.

Percent Symbol

The symbol for percent is %.

Example: 50%

Converting Percent to Decimal

To convert a percent to a decimal, divide by 100.

Example: 50% = 50/100 = 0.50

Converting Decimal to Percent

To convert a decimal to a percent, multiply by 100.

Example: 0.75 = 0.75 * 100 = 75%

Converting Percent to Fraction

Write the percent as a fraction with a denominator of 100. Simplify if possible.

Example: 80% = 80/100 = 4/5

Converting Fraction to Percent

Divide the numerator by the denominator, then multiply by 100.

Example: 1/4 = 0.25 = 0.25 * 100 = 25%

Finding a Percentage of a Number

Multiply the number by the percentage (as a decimal).

Example: What is 20% of 50? 0.20 * 50 = 10

Finding What Percentage One Number Is of Another

Divide the part by the whole, then multiply by 100.

Example: What percentage is 15 of 75? (15/75) * 100 = 20%

Finding the Whole When Given a Percentage and a Part

Divide the part by the percentage (as a decimal).

Example: 25% of what number is 20? 20 / 0.25 = 80

Percent Increase

((New Value - Original Value) / Original Value) * 100

Example: Price increased from $20 to $25. (($25 - $20) / $20) * 100 = 25%

Percent Decrease

((Original Value - New Value) / Original Value) * 100

Example: Price decreased from $20 to $15. (($20 - $15) / $20) * 100 = 25%

Sales Tax

Multiply the price of the item by the sales tax percentage (as a decimal) to find the amount of tax. Add the tax to the original price.

Example: Item costs $50, sales tax is 6%. Tax = $50 * 0.06 = $3. Total cost = $50 + $3 = $53

Discounts

Multiply the original price by the discount percentage (as a decimal) to find the amount of the discount. Subtract the discount from the original price.

Example: Item costs $80, discount is 20%. Discount = $80 * 0.20 = $16. Sale price = $80 - $16 = $64

Simple Interest

Interest = Principal * Rate * Time, where Rate is the interest rate (as a decimal) and Time is in years.

Example: Principal = $1000, Rate = 5% (0.05), Time = 2 years. Interest = $1000 * 0.05 * 2 = $100