Guide to percentage calculations in Mathematics

An introduction to Percentage: Definition, Calculations, and Examples

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 100th. 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.

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