 ## Understanding Percent Equations: A Step-by-Step Guide

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

$\frac{ \text{'is'}}{ \text{'of'}} = \frac{\text{'percent'}} {100}$

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

So if you have $$50%$$ of $$200$$, it translates to

$\frac{\text{'is'}} { 200} = \frac{50} { 100}$

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

$\frac{\text{'is'}} { \text{'of'}} = \frac{\text{'percent'} }{ 100}$

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.

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 $$\frac{'is'} {'of'} = \frac {'percent'} {100}$$, now becomes $$\frac{ 'is'}{150} = 0.2$$.

4. Step 4: Solve the equation

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

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 $$30$$.

### Exercises for Percentage Calculations

1) $$4.2$$ is what percentage of $$12?$$$$\ \Rightarrow \$$

2) $$9.45$$ is what percentage of $$27?$$$$\ \Rightarrow \$$

3) $$0.95$$ is what percentage of $$19?$$$$\ \Rightarrow \$$

4) $$24.6$$ is what percentage of $$41?$$$$\ \Rightarrow \$$

5) $$15.3$$ is what percentage of $$34?$$$$\ \Rightarrow \$$

6) $$16.8$$ is what percentage of $$56?$$$$\ \Rightarrow \$$

7) $$53.55$$ is what percentage of $$63?$$$$\ \Rightarrow \$$

8) $$74.1$$ is what percentage of $$78?$$$$\ \Rightarrow \$$

9) $$63.75$$ is what percentage of $$85?$$$$\ \Rightarrow \$$

10) $$80$$ is what percentage of $$100?$$$$\ \Rightarrow \$$

1) $$4.2$$ is what percentage of $$12?$$$$\ \Rightarrow \ \color{red}{\frac{4.2 \times 100}{12} \ = \ 35}$$
2) $$9.45$$ is what percentage of $$27?$$$$\ \Rightarrow \ \color{red}{\frac{9.45 \times 100}{27} \ = \ 35}$$
3) $$0.95$$ is what percentage of $$19?$$$$\ \Rightarrow \ \color{red}{\frac{0.95 \times 100}{19} \ = \ 5}$$
4) $$24.6$$ is what percentage of $$41?$$$$\ \Rightarrow \ \color{red}{\frac{24.6 \times 100}{41} \ = \ 60}$$
5) $$15.3$$ is what percentage of $$34?$$$$\ \Rightarrow \ \color{red}{\frac{15.3 \times 100}{34} \ = \ 45}$$
6) $$16.8$$ is what percentage of $$56?$$$$\ \Rightarrow \ \color{red}{\frac{16.8 \times 100}{56} \ = \ 30}$$
7) $$53.55$$ is what percentage of $$63?$$$$\ \Rightarrow \ \color{red}{\frac{53.55 \times 100}{63} \ = \ 85}$$
8) $$74.1$$ is what percentage of $$78?$$$$\ \Rightarrow \ \color{red}{\frac{74.1 \times 100}{78} \ = \ 95}$$
9) $$63.75$$ is what percentage of $$85?$$$$\ \Rightarrow \ \color{red}{\frac{63.75 \times 100}{85} \ = \ 75}$$
10) $$80$$ is what percentage of $$100?$$$$\ \Rightarrow \ \color{red}{\frac{80 \times 100}{100} \ = \ 80}$$

## Percentage Calculations Practice Quiz

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