In mathematics, a percentage is a number or ratio expressed as a fraction of 100. A percentage is used to express the proportionate part of a total. A percentage is basically a notation used to express the accuracy out of 100 if any work or any payment is 100% or fewer marks are also awarded in percentage. A percentage is used to reduce the large amount in a simpler form.

In this post, we will learn all the basics of the percentage that are required.

## What is the percentage?

A percentage is a part of a whole expressed in 100^{th}. In mathematics, a percentage is a number or ratio expressed as a fraction of a hundred.

To understand the percentage, let take a pizza that is cut into 8 parts. Now if you pick up one slice, you are holding some percentage of pizza in your hand. It means that percentage is actually a part of a whole amount of something.

If you are interpreting % as something between 0 and 100%, then more than half is equivalent to greater than 50%.

## Notation

Percentage is denoted by **%** sign e.g., 20%, 30%, 100%, etc.

## Methods of Percentage

We have two methods of percentage. Let us discuss them briefly.

### Number to percentage

When we have to calculate the percentage, we use a general formula to convert a number to a percentage. In which we divide the number by total numbers multiply by 100 and then put the percentage sign,

**Percentage = number / total number x 100%**

Let us take some examples.

**Example 1**

Find the percentage, **if a college student has obtained 800 marks out of 1100 in exams.**

**Solution**

**Step 1: **Identify and write down the values.

**Obtained marks = 800**

** Total marks = 1100**

**Step 2: **Write down the percentage formula.

**Percentage = number / total number x 100%**

**Step 3: **Substitute the values in the percentage equation.

**Percentage = 800/1100 x 100**

**Step 4: **Calculate the percentage by solving the equation.

**Percentage = 80000/1100**

**Percentage = 800/11**

**Percentage = 72.73% **

So, a student with 800 marks out of 1100 got **72.73% **in exams.

**Example 2**

Find the percentage, **if a shopkeeper sold a book at the profit of 120 and the cost price of that book is 360.**

**Solution**

**Step 1: **Identify and write down the values.

**Profit = 120**

**Cost price = 360**

**Step 2: **Write down the percentage formula.

**Percentage = number / total number x 100%**

**Step 3: **Substitute the values in the percentage equation.

**Percentage = 120/360 x 100**

**Step 4: **Calculate the percentage by solving the equation.

**Percentage = 12000/360**

**Percentage = 1200/36**

**Percentage = 33.33% **

So, a shopkeeper with a profit of 120 out of 360 got **33.33% **profit. You can also find the percentage by using an online percentage calculator.

**Example 3**

Find the percentage, **if a wholesaler sold some items at the profit of 12230 and the cost price of those items is 36000.**

**Solution**

**Step 1: **Identify and write down the values.

**Profit = 12230**

**Cost price = 36000**

**Step 2: **Write down the percentage formula.

**Percentage = number / total number x 100%**

**Step 3: **Substitute the values in the percentage equation.

**Percentage = 12230/36000 x 100**

**Step 4: **Calculate the percentage by solving the equation.

**Percentage = 1223000/36000**

**Percentage = 1223/36**

**Percentage = 33.97% **

So, a wholesaler with a profit of 12230 out of 36000 got **33.97% **profit.

**Example 4**

Find the percentage, **if a wholesaler sold some items at the profit of 16230 and the cost price of those items is 26000.**

**Solution**

**Step 1: **Identify and write down the values.

**Profit = 16230**

**Cost price = 26000**

**Step 2: **Write down the percentage formula.

**Percentage = number / total number x 100%**

**Step 3: **Substitute the values in the percentage equation.

**Percentage = 16230/26000 x 100**

**Step 4: **Calculate the percentage by solving the equation.

**Percentage = 1623000/26000**

**Percentage = 1623/26**

**Percentage = 62.42% **

So, a wholesaler with a profit of 16230 out of 26000 got **62.42% **profit.

### Percentage to number

When the percentage is given, we use this method. In this method, we find the number or total number by rearranging the percentage formula.

**Percentage/100 x total number = number **

**Or**

**Total number = number/percentage x 100**

Let us take some examples to understand this method.

**Example 1**

**What is 30% of 1800?**

**Solution**

**Step 1:** Identify and write down the values.

**Percentage = 30%**

**Total number = 1800**

**Step 2:** Write down the formula.

**Percentage/100 x total number = number **

**Step 3:** Substitute the values in the percentage equation.

**30/100 x 1800 = number**

**Step 4:** Calculate the equation.

**Number = 54000/100**

**Number = 540**

So, 30% of 1800 is **540**.

**Example 2**

**What is 70% of 10800?**

**Solution**

**Step 1:** Identify and write down the values.

**Percentage = 70%**

**Total number = 10800**

**Step 2:** Write down the formula.

**Percentage/100 x total number = number **

**Step 3:** Substitute the values in the percentage equation.

**70/100 x 10800 = number**

**Step 4:** Calculate the equation.

**Number = 756000/100**

**Number = 7560**

So, 70% of 10800 is **7560**.

**Example 3 **

**1000 is 30% of what?**

**Solution**

**Step 1:** Identify and write down the values.

**Percentage = 30%**

** Number = 1000**

**Step 2:** Write down the percentage formula.

**Total number = number/percentage x 100**

**Step 3:** Substitute the values in the percentage equation.

**Total number = 1000/30 x 100**

**Step 4:** Calculate the percentage by solving the equation.

**Total number = 100000/30**

**Total number = 10000/3 = 3333.33**

So, 1000 is 30% of **3333**.33.

**Example 4**

**10 is 30% of what?**

**Solution**

**Step 1:** Identify and write down the values.

**Percentage = 30%**

** Number = 10**

**Step 2:** Write down the percentage formula.

**Total number = number/percentage x 100**

**Step 3:** Substitute the values in the percentage equation.

**Total number = 10/30 x 100**

**Step 4:** Calculate the percentage by solving the equation.

**Total number = 1000/30**

**Total number = 100/3 = 33.33**

So, 10 is 30% of **33.33**

**Summary **

In this article, we discuss all the basics of the percentage. Now you are witnessed that this topic is not difficult. Once you grab the knowledge of this topic you can easily perform the problems related to percentage.