Using the Percent Equation

Our Pre-Algebra tutorial software program contains over 60 topic areas. One of them is Using the Percent Equation, and this page summarizes the main ideas of this topic. This page is intended for review, and is not a substitute for the interactive, self-paced tutorials of the MathTutor pre-algebra software program.

General Explanation

In this lesson we will practice solving problems involving percent. Here are some examples of the problems we will learn to solve:
What is 8% of 200?
2 is what percent of 135?
16 is 5% of what amount?
All of these problems can be solved using the percent equation.
The PERCENT EQUATION can be expressed as follows:
PERCENT (as a decimal) x BASE = AMOUNT
Whenever we solve problems using the percent equation, we must identify the PERCENT, the BASE, and the AMOUNT in the problem.
The percent part is indicated by the % sign or the word "percent". The base part usually follows the word "of". The amount is the part that is related to the base by the percent.
Sample Problem 1

What is 30% of 82?


We are given the PERCENT (30%) and the BASE (82). We are asked to find the AMOUNT.
Let's use the percent equation to find the amount.
PERCENT (as a decimal) x BASE = AMOUNT
0.30 x 82 = AMOUNT
AMOUNT = 24.6
Our final answer is 24.6.

Sample Problem 2

90 is what percent of 360?


PERCENT is the unknown value. 360 follows the word "of", and is the BASE. 90 must be the AMOUNT.
Let's use the variable "n" to represent percent as a decimal number, and solve for "n" using the percent equation:
PERCENT (as a decimal) x BASE = AMOUNT
n x 360 = 90
n = 90/360
n = 0.25
We have found the value of n in decimal form. To convert it to a percent move the decimal two places to the right.