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August 10, 202239 Insightful Publications

**How To Calculate Percentage: **In Mathematics, a percentage is defined as a number or a ratio expressed as a fraction of 100. Calculating a percentage means dividing the number by the whole and multiplying it by 100. Thus, it can be said that percentage means a part per hundred. The symbol % represents percentage. Students from secondary classes are taught how to calculate percentages in the classroom.

In this article, we will discuss how to calculate percentages easily. It will help students understand how to go at ease with percentage calculation. Learning how to calculate percentages can also come in handy for the students when they’re planning to calculate their marks for school and competitive exams. Read the article further to know more!

“Percent” is a Latin adverb that means “by the hundred.” It was coined in the 16th century. Later, the abbreviation was changed to per cent. The period was dropped later, and the two parts were combined into the one word ‘per cent. The annotation symbol is %, which is used in brief explanations. The marks percentage calculator compares the marks obtained to the total marks. The formula to calculate the percentage is given below:

**OR**

(Actual Value / Total Value) * 100 = Percentage |

**OR**

In the image given above- p is the percentage value,

x is the value,

and y is the total value

Let’s say that students need to convert 2/7 into a percentage. 2/7 in decimal is 0.28. Multiply 0.28 with 100, and that will give 28%.

But students do not need to calculate every time with pen and paper. They can memorise the percentage formula in their mind and insert values to calculate mentally.

Now that students have gone through the following examples stated above, they should know that there are two types of percentage calculation: One is addictive, and the other is subtractive.

- Additive percentage calculation means the value of a number is to be added. This happens in the case of GST filing cases, extra coupon addition cases, or more such examples.
- Subtractive percentage calculation means the value is subtracted from the original number. This happens for discount codes or if there is any application of getting rebates on the original price, or more such examples accordingly.

So before calculating the percentage, students must read through the whole sum and check if there are any instances where value is to be added or subtracted. They should then go on proceeding with the sum or the calculation that they are opting for.

Let us look at some of the solved examples below:

**A person claims that it snowed 13 days in a certain year. What was the percentage of days that it snowed that year?**

- In this example, consider the number of days for a year to be 365 days (if leap year is not mentioned).
- In the next step, divide 13 by 365 days. (remember, percentage calculation should be done in the same consistent unit- we cannot divide 13 days by one year since the units are different)
- Multiply it by 100 since the percentage is always calculated in 100.
- This will give students a tentative score of 3.5%, which is the answer. The image shown above will also help them in the overall process.

**Let us say you have joined a company and your salary is supposed to be 40,000. But you realise later that there will be a deduction of 5% from your salary. So, how much you will be getting?**

- You need to find 5% of 40,000 = (5/100) X 40,000. = 2000.
- So, there will be a deduction of Rs 2000.
- Subtract 2000 from 40,000, and that will give you 38000.
- So, 38000 is the salary that you will be getting in hand.

**Assume that you bought a shirt whose price is 599. But there is a 5% GST on how to know what you need to pay at the bill counter.**

- Find 5% of 599 and that will give = 5% * 599 = (5/100) * 2995 = 29.95
- Therefore, 29.95 is the extra amount that you need to pay at the counter.
- Add 599 and 29.95 = 599 + 29.95 = 628.95.
- So, you need to pay Rs 629 at the counter.

*Assume that you are watching an advertisement and it says that there is a 20% discount on a laptop. The price tag after the discount is Rs 55,000. Figure out how much was the real price.*

Here, we have the following information:

- Discount given: 20%
- Price after discount: Rs 55000

Let us assume that the actual price of the laptop is Rs X.

- Therefore, Rs X – (20% of Rs X) = Rs 55000
- Rs X – Rs (20/100) × X = Rs 55000
- Or, Rs X – Rs (X/5) = Rs 55000
- Or, Rs (4X/5) = Rs 55000
- Therefore, X = Rs (55000 × 5)/4 = 68750

*Assume that you are appearing for the final examination in which you have already scored 567 marks out of the last six papers. Only one paper is left, which is 100 marks. And you have to score in this paper so that your average percentage is at least 95%. How much should you score, at least?*

In the six last papers, your score is 567 marks. Your target is 95%

- 95* of 7 papers in marks will be-
- 95/100 = (Target marks/Total 7 paper marks)
- (95/100) X 700 = 665 marks
- 665 marks – 567 marks =
**98 marks**

Percentage change refers to the variability of change over time. It is used for various purposes. The older and newer values get compared, and the change percentage score is calculated. Comparison usually goes in with the order value. Here is the formula for Percentage Change:

Percentage Change = ((New Value – Old Value ) / Old Value) * 100 |

- While applying the above formula, if the new value is less than the old value, the %age change will be negative. That indicates that there is a percentage decrease.
- If the new value is more than the old value, the result will be a positive value. That indicates that there is a percentage increase.

Let us look at an example of percentage change:

1**) In 2010, the population of India was at 1,234,281,170 people. In 2019, the population was recorded at 1,366,417,754 people. How much is the percentage change after nine years?**

Use the above formula and provide the new value and old value:

- Percentage Change = ((1,366,417,754 – 1,234,281,170 ) / 1,234,281,170) * 100
- Percentage Change = 10.7055%

So there was a 10.7055% increase in the population of India after nine years.

To remove a percentage, two ways can be there.

- One is to remove the percentage sign and divide by 100. This will convert the number into a decimal number. For example, 21.6%= 21.6/100= 0.216
- Using the percentage formula. This can be done by finding X when P% of X is Y. Formula is Y/P%= X. For example, suppose the question is- 25 is 20% of what number?

Converting this to the percentage formula equation, this turns out to be Y/P% = X, which means that 25/20%=X. Taking out the % sign, we can write it down as 20/100 (=0.20). The original equation now becomes 25/0.20= X. Calculating the values, X turns out to be 125 (which is not a percentage). Therefore, 25 is 20% of 125.

The percentage change is used in the form of formulas for various purposes. The most common among these are – Profit, Discount, and Percent Error. The following sections discuss the formulas to calculate Profit, Discount, and Percent Error in detail.

To understand the formula, we must understand what is profit first. Profit is basically the difference between the selling price of a commodity and the cost price. Now, selling price is the cost at which a commodity is sold, and cost price is the cost at which the commodity was bought originally. Profits (and losses) are usually depicted as profit per cent to know how much profit or loss a business/individual gets.

Given below are the formulas to calculate profit:

**Profit** = Selling Price (SP) – Cost Price (CP)

**Profit Percent** = (Profit x 100) / Cost Price

**Gross Profit** = Revenue – Cost of Products Sold

**Profit Margin** = (Total Income / Net Sales) x 100

When the price of a commodity is lower than the par value (stated value or face value), it results in a discount. In simple terms, the discount is the difference between the price paid for a commodity and the face value of that particular commodity.

Discount is generally used in consumer deals, where people buying products are offered discounts on those products. The discount rate is denoted in the form of a percentage.

**Discount** = List Price – Selling Price

**Discount Rate** or **Discount Percentage** = (Discount / List Price) x 100

**List Price** is the price at which the manufacturer of a product recommends that the retailer sell the product. *

To calculate how to take out the percentage of marks secured by a student in an exam, they have to divide the total marks secured by the student (in all subjects) by the maximum marks and then multiply it by 100.

For example, if a student has secured 95 out of 100 in Maths, 85 out of 100 in Physics, and 75 out of 100 in Chemistry, the total marks secured by the student is (95+85+75) = 255 out of (100+100+100) =300.

Therefore, percentage of marks obtained by the student = (255/300) X 100% = 85%. [marks percentage formula].

This formula will always help students how to find the percentage of marks.

Percentage Error is the difference between approximate (or observed) value and exact (or actual value) as a percentage of actual value. It is used to check manufacturing or calibration errors in measuring instruments.

**Percentage Error** = {(Approximate or Observed Value – Exact or Actual Value) / Exact or Actual Value} x 100

Many people might confuse percentage with percentile. However, these two terms are very different. Percentage denotes a number out of 100, but percentile does not denote any number. Percentiles cannot be expressed as ratios or proportions like a percentage.

The percentile formula is used to ascertain a person’s performance with respect to others. This formula is often used in exam results and scores to denote the individual performance with reference to others. The percentile formula is also used to calculate income, weight, etc. So, for a value ‘x’, its percentile can be expressed as the ratio of the number of denominations below ‘x’ to the total number of denominations.

**Percentile** = (Number of denominations below ‘x’ / Total number of denominations) x 100

If students want to calculate total marks from the percentage obtained, all they need to do is multiply their percentage divided by 100 to the total marks, which is the total of all subjects.

Suppose they have got 66% in 5 subjects. Thus, the total of 5 subjects is 5*100=500. Therefore, their marks in 5 subjects will be (66/100)* 500= 330. Thus, 330 is scored out of 500 marks.

Given below are some of the questions on percentage calculation. Students can practice these to understand the formulas better.

1. Find the value: 15% of 40. |

2. The price of a box of apples is Rs. 500. After a week, the price changed to Rs. 750. Find the change in percent. Also, state whether the change is positive or negative. |

3. Nicola measures the length of her textbook as 20cm. If the length is 17.6cm, what is the percentage error in Nicola’s calculation? |

4. The length of a textbook is calculated as 45cm. Find the percentage error in the calculation if the book’s length is 32cm. |

5. Ron bought a coin collection. He then sold it for a profit of 25%. Find the cost of the collection if he sold it for Rs. 3,000. |

6. In the year 2020, the number of specimens in an endangered animal species was found to be 5,000. Their number is speculated to decrease by 10% each year. Calculate how many animals will survive at the end of 2025? |

7. A bank offers 5% compound interest which is calculated twice annually. A customer deposits Rs. 2000 on January 1st and July 1st every year. Calculate the amount he would have gained in the form of interest by the end of a year. |

Now let us go through the short tricks that students can use to find the Percentage of any number in a short time:

- Percent implies for each hundred. X% is read out as X percent.
- For calculating x% of y, Formula is (x/100)*y= (x*y)/100. Remember x% of y= y% of x.
- For calculating percentage change, remember, Percentage change = {change/(initial value)} x 100
- Increase N by X% is N( 1+ X/100 )
- Decrease N by X% is N( 1- X/100 )
- Successive Percentage Change Formula is: {(a + b + (ab/100)}% where, a% and b% are the effective percentage values.

Also, Check,

Let us look at some of the fractional numbers as a percentage:

One-third = 1/3 of 100% | 33% |

One-fourth = 1/4 of 100% | 25% |

One-third = 1/5 of 100% | 20% |

One-sixth = 1/6 of 100% | 17.5% (half of 1/3) |

One-sixth = 1/7 of 100% | 14.28% |

One-eight = 1/8 of 100% | 12.5% (half of 1/4) |

One-ninth = 1/9 of 100% | 11.11% |

Calculation of percentages has numerous uses in our everyday lives. Some of them are listed below:

- Used to express fractions in a simple way and comparison of fractions.
- Percentage, in the form of discounts, is used for advertising products.
- It is used to express interest charged for loans or investments.
- Change in percentages like increase and decrease is used to describe profit or losses suffered by companies.
- Expressed as commissions, a percentage of the sales offered to the salesperson.
- The percentage can help in comparing the fractions.
- The percentage formula will help to identify the difference in terms of increase and decrease of the formula.

**Q.1: What is the formula for calculating percentage?Ans:** The formula for calculating the percentage is as follows: (Actual Value / Total Value) * 100 = Percentage

**Q.2: What do you mean by percentage?Ans:**

**Q.3: How to calculate the total percentage of marks?Ans: **To calculate the percentage of marks secured by a student in an exam, you have to divide the total marks secured by the student (in all subjects) by the maximum marks and then multiply it by 100.

**Q.4: How to calculate percentage change?****Ans:*** *Percentage change is either an increase or decrease from the previous value. If the new value is more than the previous value, there is a Percentage Increase. If the new value is less than the previous value, there is a Percentage Decrease. Here is the formula for Percentage change: Percentage Change = {change/(initial value)} x 100

**Q.5: How to calculate the percentage of marks?Ans:**