How to Solve Percent Equations

Understanding Percent Equations: A Step-by-Step Guide

 Read,3 minutes

When working with percentages, it is common to encounter equations where you have to calculate a missing value. These are known as percent equations. In this article, we will learn step by step how to solve percent equations. Let's get started.

Step 1: Understand the Percent Equation
The first step is to understand the structure of a percent equation. A percent equation is usually represented as

'is''of'='percent'100

where 'is' represents the part, 'of' stands for the whole, 'percent' is the percentage.

So if you have 50 of 200, it translates to

'is'200=50100

where 'is' is what you're trying to find.

Step 2: Convert the Percentage to a Decimal
To make calculations easier, convert the given percentage into a decimal. This is done by dividing the percentage by 100 So, if you have 50, you would convert it to 0.5.

Step 3: Set Up the Equation
Now, you need to set up your equation. You will replace 'is', 'of', 'percent' in the equation

'is''of'='percent'100

with the values you have and the variable you are trying to find.

Step 4: Solve the Equation
Now that your equation is set up, you can solve it. Use your knowledge of algebra to solve for the variable. This may involve cross-multiplying or using equivalent fractions to find the missing value.

Step 5: Check Your Answer
Lastly, always remember to check your answer. You can do this by plugging your solution back into the original problem to make sure it makes sense.

Understanding and solving percent equations is a valuable skill that's widely used in various fields, such as finance, data analysis, and shopping discounts. Keep practicing to become more proficient at it. Happy learning!

Example

Let's solve a percentage problem:

Problem: What is 20% of 150?

Here are the steps to solve the problem:

  1. Step 1: Understand the problem

    We're asked to find 20% of 150. In terms of the equation, we're looking for the 'is' value. 'Of' is 150, and 'percent' is 20.

  2. Step 2: Convert the percentage to a decimal

    20 divided by 100 gives us 0.2.

  3. Step 3: Set up the equation

    Our equation, based on isof=percent100, now becomes is150=0.2.

  4. Step 4: Solve the equation

    We can solve for 'is' by multiplying both sides of the equation by 150. This gives us 'is' = 150×0.2.

  5. Step 5: Solve and check the answer

    Doing the multiplication, we find that 'is' equals 30. We can check this answer by observing that 30 is indeed 20% of 150.

So, 20% of 150 is 30.

Free printable Worksheets

Exercises for Percentage Calculations

1) 4.2 is what percentage of 12?  

2) 9.45 is what percentage of 27?  

3) 0.95 is what percentage of 19?  

4) 24.6 is what percentage of 41?  

5) 15.3 is what percentage of 34?  

6) 16.8 is what percentage of 56?  

7) 53.55 is what percentage of 63?  

8) 74.1 is what percentage of 78?  

9) 63.75 is what percentage of 85?  

10) 80 is what percentage of 100?  

 
1) 4.2 is what percentage of 12?  4.2×10012 = 35
2) 9.45 is what percentage of 27?  9.45×10027 = 35
3) 0.95 is what percentage of 19?  0.95×10019 = 5
4) 24.6 is what percentage of 41?  24.6×10041 = 60
5) 15.3 is what percentage of 34?  15.3×10034 = 45
6) 16.8 is what percentage of 56?  16.8×10056 = 30
7) 53.55 is what percentage of 63?  53.55×10063 = 85
8) 74.1 is what percentage of 78?  74.1×10078 = 95
9) 63.75 is what percentage of 85?  63.75×10085 = 75
10) 80 is what percentage of 100?  80×100100 = 80

Percentage Calculations Practice Quiz