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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.
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?
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.
Lovina bought tiles of three different colors for her house.
Look at the table below to see the details of this purchase.
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.
Emma's sisters, Nora and Jenny, calculated the percentages as well, but in different ways.
Nora used the unitary method.
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 \(\begin{align}\frac{5}{5}\end{align}\)
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.
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? 

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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.
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.
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
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 
 To find the percentage of a whole, work out the value of 1% and then multiply it by the percent we need to find.
 Increase or decrease in any quantity can be expressed as a percentage.
 Fractions can be converted into percentages and viceversa.
 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 gradewise sample papers from below:
 IMO Sample Paper Class 1
 IMO Sample Paper Class 2
 IMO Sample Paper Class 3
 IMO Sample Paper Class 4
 IMO Sample Paper Class 5
 IMO Sample Paper Class 6
 IMO Sample Paper Class 7
 IMO Sample Paper Class 8
 IMO Sample Paper Class 9
 IMO Sample Paper Class 10
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.
 To find 50% of any number, simply divide the number by 2
 To find 25% of any number, simply divide the number by 4
 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