How to Calculate Percentage

How to Calculate Percentage

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Introduction to Percentage

In Mathematics, we use numbers for comparisons.

Percentage is one of the ways to make comparisons.

Jack and Jolly got their report cards from school.

Explaining the meaning of percentage using example: Jack and Jolly compare their scores using percentages

Jack got 320 out of 400 whereas Jolly got 300 out of 360

Jack says that he has done better.

Do you agree with him?

Explaining the meaning of percentage using report card example.

Jack's mother says that they cannot decide this by just comparing the total marks obtained because the maximum marks are different for both of them.

Since Jolly's percentage is higher than Jack's percentage, this shows Jolly has done better.

Do you agree?


How to Calculate Percentage?

What is Percentage?

Percentages are fractions with denominator as 100

The word "percent" is derived from "per centum" which means "per hundred".

It is represented by %

How to get Percentage?

Percent is another name for indicating hundredths.

Thus, 1% is one hundredth.

How to calculate percentage using 1%

Lovina bought tiles of three different colors for her house.

Look at the table below to see the details of this purchase.

Explaining the way of calculating percentage using example: A girl finds the percentage of each colour of tiles she has.

Since the total number of items add up to 100, the percentages can be easily calculated.

What if the total number of items does not add up to 100?

In such cases, we convert fractions to equivalent fractions with denominator as 100

Let's look at the following example to see how this is done.

Emma has a bracelet with 20 beads in two colours.

The table below shows how to calculate the percentages of the red and blue beads.

Explaining the way of calculating percentage when denominator is not 100 using an example. A girl finds the percentage of each colour of beads she has.

Emma's sisters, Nora and Jenny, calculated the percentages as well, but in different ways.

Nora used the unitary method.

Different ways of finding same percentage

Jenny converted the fraction \(\begin{align}\frac{8}{20}\end{align}\) into an equivalent fraction \(\begin{align}\frac{40}{100}\end{align}\) by multiplying the numerator and denominator with \(\begin{align}\frac{5}{5}\end{align}\)

Different ways of finding same percentage

You have now learned three different ways to calculate percentage when the total does not add up to 100

You can use the method you find most suitable to calculate percentages.

Let's experiment with some percentages in the simulation below.

Set a base amount and the percentage of the tip to be given.

You can observe the amount for the tip being calculated.

The percentage of the tip from the total amount is also visually depicted in the figure.


Percentage Formula

Percentage formula is used to find the share of a whole in terms of 100.

Using this formula, you can represent a number as a fraction of 100.

\(\text{Percentage}=\frac{\text{Value}}{\text{Total Value}} \times 100\)

Calculate Percentage Difference

Sometimes we need to know the increase or decrease in some quantity as percentages also referred to as Percentage Change

For example, increase in population, decrease in poverty, and so on.

We have a formula to show the change in quantity as a percentage.

Percentage increase is given by the formula:

\(\begin{align} \text{% Increase } \!\!=\! \frac{\text{Increased Amount}}{\text{Original Base}}\!\! \times\! 100\end{align}\)

Now, you can easily guess the formula for percentage decrease.

Percentage decrease can be calculated by:

\(\begin{align} \text{% Decrease } \!\!=\! \frac{\text{Decreased Amount}}{\text{Original Base}}\!\! \times\! 100\end{align}\)

You can experiment using this formula in the simulation below.

 
Thinking out of the box
Think Tank
 
Amy told her son that a few years ago, the rate of petrol was Rs. 1 per litre. Now, it is Rs. 52 per litre. Her son asks her the percentage by which the rate had gone up. Can you find it?

Practice questions on percentage change: Change in prices of petrol over time.

 

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Percentage: Increase and Decrease with Solved Examples

We often come across information in our daily lives like 25% off on market prices or 8% hike in petrol prices.

This indicates an increase or decrease in the original prices of those items.

Examples of percentage change in daily life: Hike in prices, discounts

Let us go through a few examples to understand this concept better.

Increase in Percentage

Example 1

 

 

Robert is happy because he got promoted.

He also got a 5% hike in his salary.

Example of percentage increase: Hike in salary after promotion.

His current salary is Rs. 24,000

What is his revised salary after his promotion?

Solution:

Robert's salary = Rs. 24,000

1% of Rs. 24,000 is

\(\begin{align}\frac{1}{100}\times(\text{Rs.} \; 24,000)=\text{Rs.} \; 240\end {align}\)

To find 5% of Rs. 24,000, we must find 5 times 1%

Hence, 

\(5 \times (\text{Rs.}\; 240)=\text{Rs.} \; 1200\)

Robert's pay hike is Rs. 1200 annually.

Thus, his new salary will be the sum of his current salary and Rs.1200

\(\therefore\) Robert's salary after his promotion will be Rs. 25,200

Decrease in Percentage

Example 2

 

 

A new model of a mobile was launched in the market.

Neil purchased the model for Rs. 56,000

Example of percentage decrease: Value of mobile depreciates every year.

The value of the mobile decreases by 3% on its original price every year.

Neil wants to know the value of his mobile after 3 years.

Can you help Neil calculate the price of the mobile after 3 years?

Solution:

1% of Rs. 56,000 is

\(\begin{align}\frac{1}{100}\times(\text{Rs.} \; 56,000)=\text{Rs.} \; 560\end{align}\)

To find 3% of Rs. 56,000, we must find 3 times 1%

Hence, 

\(3 \times (\text{Rs.} \; 560)=\text{Rs.}\; 1680\)

The mobile depreciates Rs. 1680 every year.

Thus, the value of the mobile after 3 years will be

\(\begin{align}&= \text{Rs.}56,000-(3\times \text{Rs.}1680) \\ &=\text{Rs.}50,960\end{align}\)

\(\therefore\) The value of the mobile after 3 years will be Rs. 50,960
 
important notes to remember
Important Notes
  1. To find the percentage of a whole, work out the value of 1% and then multiply it by the percent we need to find.
  2. Increase or decrease in any quantity can be expressed as a percentage.
  3. Fractions can be converted into percentages and vice-versa.
  4. Percentages are reversible. For example, 25% of 40 is same as 40% of 25

 

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Practice Questions

Here are few activities for you to practice.

Select/Type your answer and click the "Check Answer" button to see the result.

 
 
 
 
 
 

Maths Olympiad Sample Papers

IMO (International Maths Olympiad) is a competitive exam in Mathematics conducted annually for school students. It encourages children to develop their math solving skills from a competition perspective.

You can download the FREE grade-wise sample papers from below:

To know more about the Maths Olympiad you can click here


Frequently Asked Questions (FAQs)

1. How to calculate the percentage of a number?

To find the percentage of any number, convert the percent into a decimal number and replace "of" with multiplication.

For example, 40% of 50 is 0.4 X 50 = 20

2. How to calculate percentage of marks?

To find the percentage of marks divide the obtained marks by maximum marks and then multiply this ratio by 100

For example, if you scored 24 out of 30, the percentage would be

\(\begin{align} \frac{24}{30} \times 100 = 80 \end{align}\)

3. How do you calculate percentages easily?

The list of easy ways to calculate the percentage very quickly and without a calculator is given below.

  1. To find 50% of any number, simply divide the number by 2
  2. To find 25% of any number, simply divide the number by 4
  3. To find 10% of any number, simply divide the number by 10

These key points will help you to calculate all the percentages in a much simpler way.

4. How do I calculate the percentage of a total?

To find the percentage of a total, convert the percent into decimal number and then multiply this ratio by 100

  
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