## I. Introduction

Percentages are a fundamental part of mathematics and play a crucial role in a variety of real-life scenarios, from calculating sales tax to determining discounts on shopping. Often, knowing how to find percentages can be the key to making informed financial decisions, which is why it’s important to understand the formula and how to use it. In this article, we will walk you through how to find percentages step-by-step, including practical examples, calculation shortcuts, and common mistakes to avoid.

## II. Step-by-step guide

Before diving into the specifics of how to find percentages, it’s important to understand key terms. A percent is a ratio that compares a part to a whole expressed as a fraction with a denominator of 100. Percentages, on the other hand, represent that ratio as a number out of 100.

The formula for calculating a percentage is relatively straightforward: percentage = (part / whole) x 100. To find the percentage of a number, follow these steps:

- Identify the part and whole values. For example, if you want to find 20% of 100, the part is 20 and the whole is 100.
- Divide the part by the whole. For our example, 20 ÷ 100 = 0.2.
- Multiply the result by 100 to convert it to a percentage. In this case, 0.2 x 100 = 20%, which is the answer.

Let’s take another example. If you want to find 15% of 80, the part is 15 and the whole is 80. Using the formula, we get:

- 15 ÷ 80 = 0.1875
- 0.1875 x 100 = 18.75%

## III. Real-life scenarios

Understanding how to find percentages is incredibly useful in real-life scenarios. For example, when shopping, it can help you to determine how much of a discount you’re getting or how much tax you’ll need to pay. Let’s look at a few examples.

**Sales tax:** If you live in a state where the sales tax rate is 7% and you’re buying a $200 item, you can use the formula to calculate the tax you’ll need to pay:

- 7% ÷ 100 = 0.07
- $200 x 0.07 = $14

You’ll need to pay an additional $14 in sales tax.

**Discounts:** If an item has a price tag of $50 and is discounted by 25%, you can use the formula to find the discounted price:

- 25% ÷ 100 = 0.25
- $50 x 0.25 = $12.50
- $50 – $12.50 = $37.50

The discounted price is $37.50.

## IV. Infographics and visuals

Visual aids can be incredibly helpful when it comes to understanding how to find percentages. Here are a few examples:

If you want to find: |
Use this formula: |

5% of 100 | (5 ÷ 100) x 100 = 5% |

20% of 75 | (20 ÷ 75) x 100 = 26.67% |

50% of 200 | (50 ÷ 200) x 100 = 25% |

Another way to visualize percentages is by using a pie chart:

## V. Calculation shortcuts

While the formula for finding percentages is easy enough, there are some calculation shortcuts you can use to speed up the process.

**Divide by 2:** To find 50% of a number, you can simply divide it by 2. For example, 50% of 80 is 40, because 80 ÷ 2 = 40.

**Multiply by 10:** To find 10% of a number, you can multiply it by 0.1 or divide it by 10. For example, 10% of 200 is 20, because 200 x 0.1 = 20, or 200 ÷ 10 = 20.

**Mental math:** For some percentages, you can use mental math to quickly calculate the answer. For example, to find 20% of a number, you can simply divide it by 5 and move the decimal point one space to the left. So, 20% of 80 is 16, because 80 ÷ 5 = 16.

## VI. Common mistakes

When it comes to finding percentages, there are a few common mistakes that people often make:

- Confusing percentages and decimals: Remember that a percentage is always out of 100 and is expressed as a whole number with a % symbol.
- Using the wrong formula: The formula for finding percentages is percentage = (part / whole) x 100. If you’re using a different formula, you may not get the correct answer.
- Forgetting the order of operations: When using the formula, remember to divide before you multiply.

If you make a mistake, don’t worry. The best way to avoid errors is to double-check your work. If you’re still having trouble, try using a calculator or asking a friend for help.

## VII. Conclusion

Knowing how to find percentages is an essential skill that can help you to make informed decisions in a variety of settings. By following the formula and using calculation shortcuts, you can quickly and accurately calculate percentages. Although mistakes can happen, there are simple ways to catch and correct them. With practice, you’ll soon be a pro at finding percentages!

So the next time you need to calculate a sales tax or determine a discount, remember this step-by-step guide.