Knowing how to calculate percentages is an essential skill that can be used in various situations. In this quick answer guide, we will focus on calculating **20% of 90**. By understanding the basic **percentage formula**, you can easily find the answer.

### Key Takeaways:

- To calculate
**20% of 90**, use the**percentage formula**:**Percentage**= (Value/Total**Value**) x 100 **20% of 90**can be calculated by multiplying 90 by 0.2 or by dividing 90 by 5- Percentages represent parts of a
**whole**out of 100 - Understanding the
**history**and different expressions of percentages adds depth to the**calculation process** **Practice**solving**percentage**problems to reinforce your skills

## Understanding Percentages

Before diving into the calculation, it is important to understand the concept of percentages. Percentages are a way of expressing parts of a **whole** out of 100. For example, if you have *87 percent*, it means you have 87 parts out of 100. Percentages can also be represented as **fractions** or **decimals**. It is crucial to remember that percentages, just like **fractions** and **decimals**, represent parts of the **whole**.

## The Percentage Formula

The **percentage formula** is a fundamental tool for calculating the share of a whole in terms of 100. By using this formula, you can determine the **percentage** of a specific **value** within a **total value**.

The formula is as follows:

Percentage = (Value/Total Value) x 100

Let’s take an example to understand how the percentage formula works. Consider a group of 40 cats and dogs, and you want to find the percentage of dogs in the group. If there are 10 dogs, you can apply the formula as follows:

Percentage of dogs = (10/40) x 100 = 25%

So, in this case, the percentage of dogs in the group is 25%. By using the percentage formula, you can calculate percentages in various scenarios.

### Example: Calculating the Percentage of Dogs in a Group

Let’s further illustrate the percentage formula with an example:

Value | Total Value | Percentage |
---|---|---|

10 (number of dogs) | 40 (total number of cats and dogs) | 25% |

In the given example, there are 10 dogs in a group of 40 cats and dogs. Applying the percentage formula, we find that the percentage of dogs is 25%.

Understanding and utilizing the percentage formula allows you to calculate percentages accurately and efficiently in various situations. Whether you need to determine the percentage of a specific **value** or analyze data, the percentage formula is a valuable tool in your mathematical toolkit.

## Converting Decimals and Fractions to Percentages

Converting **decimals** and **fractions** to percentages is an important skill when working with percentages. Whether you are dealing with decimals or fractions, the **conversion** process is straightforward. Let’s explore how to convert each of them to percentages.

### Converting Decimals to Percentages

To convert a **decimal** to a percentage, you need to multiply it by 100. This will move the **decimal** point two places to the right, effectively expressing the **decimal** as a percentage.

Example: Converting 0.87 to a percentage

0.87 × 100 = 87%

### Converting Fractions to Percentages

Converting a **fraction** to a percentage involves dividing the numerator by the denominator and then multiplying by 100. This will give you the equivalent percentage value of the **fraction**.

Example: Converting 13/100 to a percentage

(13 ÷ 100) × 100 = 13%

It’s important to note that percentages are often represented using the **percent sign** (%). This symbol serves as a visual indicator that a value is being expressed as a percentage.

### In Practice

Let’s apply the **conversion** process to a practical example.

Example: Converting a decimal and a

fractionto percentages

Decimal Percentage 0.35 35% 3/8 37.5%

In this example, we convert the decimal 0.35 to the percentage 35%. Similarly, the fraction 3/8 is converted to the percentage 37.5%. Converting decimals and fractions to percentages allows us to express values in a standardized format, making comparisons and calculations easier.

## Calculating Percentages of Specific Numbers

Sometimes, you may need to find the **percentage of a specific number** instead of a whole. In these cases, you can use **reverse calculation** to determine the percentage. Here’s how:

**Convert the percentage to a decimal:**Divide the percentage by 100. This will give you the**decimal version**of the percentage. For example, if you have a percentage of 25%, you would divide 25 by 100 to get 0.25.**Multiply the decimal by the specific number:**Take the**decimal version**of the percentage and multiply it by the specific number to find the percentage. For example, if you need to save 25% of a $1,500 paycheck for an upcoming vacation, you would follow these steps:

25 ÷ 100 = 0.25

0.25 x 1500 = $375

### Example Calculation:

Let’s take another example to solidify the concept. Suppose you want to calculate 15% of the number 80.

**Convert the percentage to a decimal:**Divide 15 by 100 to get 0.15.**Multiply the decimal by the specific number:**Multiply 0.15 by 80 to get the percentage.

0.15 x 80 = 12

So, 15% of 80 is 12.

### Calculation Example

Percentage | Specific Number | Calculation | Result |
---|---|---|---|

25% | $1,500 | (25 ÷ 100) x 1500 | $375 |

15% | 80 | (15 ÷ 100) x 80 | 12 |

As shown in the above table, you can use the **reverse calculation** method to find the **percentage of a specific number**. By converting the percentage to a decimal and multiplying it by the specific number, you can easily determine the percentage.

## Dealing with Percentages Greater than 100%

When it comes to **percentages greater than 100%**, **interpretation** is key. While it may seem impossible to spend more than 100% of your time or money, percentages that represent a larger quantity or increase can be expressed as **percentages greater than 100%**. To understand this concept better, let’s consider an example.

Imagine you own a hot dog stand and you sell 30 hot dogs in the afternoon compared to 10 in the morning. The percentage increase in sales can be calculated by dividing the difference by the original amount and multiplying by 100:

Percentage increase = ((Afternoon sales – Morning sales) / Morning sales) x 100

Substituting the values from our example:

Percentage increase = ((30 – 10) / 10) x 100

Percentage increase = 3 x 100

Percentage increase = 300%

So, the afternoon sales are three times higher than the morning sales, resulting in a 300% increase.

Sales | Morning | Afternoon | Percentage Increase |
---|---|---|---|

Hot Dogs | 10 | 30 | 300% |

This example demonstrates that **percentages greater than 100%** can represent substantial increases or larger quantities. It is important to consider the context and **interpretation** when dealing with such percentages.

## Solving Percent Problems

Solving **percent problems** can sometimes be challenging, but with the right **tricks** and **shortcuts**, it can become much easier. One key aspect to understand is the **connection between percentages and fractions**. By leveraging this connection, you can quickly solve many **percent problems**.

Let’s explore some useful **tricks** and **shortcuts**:

### Finding 100% and 50%

Finding 100% of a number is the same as the number itself. This means that if you’re looking to calculate the number that represents the whole, the answer is simply the number itself.

Similarly, finding 50% of a number is equivalent to dividing the number by 2. This shortcut can be handy when you need to calculate half of a value quickly.

### Converting Percentages to Fractions

To convert a percentage to a fraction, simply divide it by 100 and simplify the resulting fraction if necessary. For example, 25% is equal to 25/100, which simplifies to 1/4.

By understanding these **shortcuts** and the **connection between percentages and fractions**, you can approach **percent problems** with confidence and efficiency. Take a look at the example below to see how the shortcuts can be applied:

Example:You want to calculate 15% of 80.

To find 15% of 80, you can use the shortcut of converting the percentage to a fraction. 15% becomes 15/100, which simplifies to 3/20. Now, all you need to do is multiply 3/20 by 80:

15% of 80 = (3/20) * 80 = 12

Therefore, 15% of 80 is 12.

By utilizing these **tricks** and shortcuts, you can solve **percent** problems more efficiently and accurately, saving time and effort in the process.

Example | Numerator | Denominator | Equivalent Fraction | Percentage |
---|---|---|---|---|

Example 1 | 3 | 4 | 75/100 | 75% |

Example 2 | 20 | 25 | 80/100 | 80% |

Example 3 | 5 | 8 | 62.5/100 | 62.5% |

## Practice Problems

Now that you have learned the fundamentals of calculating percentages, it’s time to put your skills into **practice**. In this section, we have prepared three practice problems along with their **solutions** to help reinforce your understanding of percentage calculations.

The first problem involves finding the percentage of correct answers on a test. Let’s say Mark answered 35 out of 50 questions correctly. To calculate the percentage, you would use the formula (35/50) x 100, which gives us 70%. Therefore, Mark scored 70% on the test.

The second problem revolves around determining the percentage of time spent on an activity. For instance, if Sarah spends 2 hours out of a total of 8 hours studying, the calculation would be (2/8) x 100, resulting in 25%. Therefore, Sarah spends 25% of her time studying.

The final problem involves calculating the tax percentage on a purchase. Let’s say David purchased a laptop for $1,500, and the tax rate is 7%. To find the tax amount, we multiply $1,500 by 7/100, which gives us $105. Therefore, the tax percentage on David’s purchase is 7%.

By solving these practice problems, you can gain confidence in your ability to apply percentage calculations in different real-life scenarios. Remember to use the percentage formula, convert decimals or fractions when necessary, and pay attention to the context of the problem. With enough practice, you’ll become a pro at calculating percentages!

## FAQ

### What is the basic concept of percentages?

Percentages are a way of expressing parts of a whole out of 100. They can also be represented as fractions or decimals.

### What is the formula for calculating percentages?

The formula is: Percentage = (Value/Total Value) x 100.

### How do you convert decimals and fractions to percentages?

To convert a decimal to a percentage, multiply it by 100. To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100.

### How can you find the percentage of a specific number?

Reverse the **calculation process** by converting the percentage to a decimal and then multiply it by the specific number.

### How are percentages greater than 100% interpreted?

Percentages greater than 100% can represent a larger quantity or increase, depending on the context.

### Are there any shortcuts for solving percent problems?

Yes, understanding the **connection between percentages and fractions** can help solve percent problems more easily.

### What is the historical background of percentages?

Percentages have a long **history**, dating back to Ancient Rome. The **percent sign** (%) evolved from the Italian phrase “per cento,” meaning “for a hundred.”

### Are there other ways to express proportions besides percentages?

Yes, **parts-per notation**, such as **parts-per-million (PPM)**, is used to measure the **concentration** of substances in **solutions** or mixtures.

### What is the step-by-step process for calculating percentages?

The process involves identifying the numerator and denominator, determining whether the denominator is a factor of 100, finding **equivalent fractions**, and expressing the fraction as a percentage.

### Can you provide practice problems to reinforce the understanding of percentage calculations?

Yes, we have provided three practice problems with solutions to help you practice calculating percentages in different scenarios.