Percent Equations

Percent Equations

Use multiplication to find the percent of a number when the percent and the original number (a.k.a. "base") are given.

Example:

Find 3% of \$15,000.

Steps:

1. Confirm the percent and the base are given.

2. Convert the percentage to a decimal or fraction with a denominator of 100.

(In most cases, converting the percentage to a decimal makes multiplication easier)

3. Multiply these numbers to find the new amount.

The amount is \$450.

Percent Equations

The basic percent equation is:

Percent  ×  Base Number  =  New Number

Also, certain English words have the following mathematical symbols:

• of is written as "×" (multiplication)
• is is written as "=" (equals)
• what is written as "n" (the unknown number)

Example

What is 5% of 20?

n = 5% × 20

n = 0.05 × 20

n = 1

You can find a percent when the base and amount are given by using the formula:

Example

What percent of 4 is 3?

Percent × base = amount

n × 4  =  3

You can find the base number when the percent and amount are given by using the following formula:

Percent  ×  Base Number  =  New Number

Example

15% of what is \$300?

Percent × base = amount

15% × n  =  300

0.15 × n  =  300

n = \$2000

Using a Proportion

You can also use a proportion to solve a percent problem.  The percent is written as a ratio , and the other ratio is expressed as , or .  Set the ratios equal and solve.

Example

Thanks to a donor, your department's budget for this year's supplies is 160% of last year's budget. If last year's budget was \$2,125.00, what is this year's budget?

Solution

This year's budget is \$3,400.