The term percentage means per hundred. The concept can be explained by its source, which is the Latin word ‘per centum’ where centum refers to hundreds. Simply speaking, a percentage denotes a part of a whole value, where the whole value is taken as 100.
The mathematical sign for expressing percentage in %. Percentage is a very useful way of making comparisons for 100 and is commonly used in various mathematical calculations in academics as well as in daily life.
What is the Percentage?
Percentage is the way of denoting a fraction or ratio where the denominator is 100. In other words, the percentage denotes the portion in every hundred.
For example, 12% means 12 parts out of every 100, or in fractions, we write 12/100.
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Calculation of Percentage
Percentage calculation involves determining the value when a fraction is expressed with a denominator of 100. We can calculate percentages in two ways as follows:
Making the Denominator of the Fraction to 100
In this method, we need to find the equivalent fraction of a given fraction where the denominator is 100. Then the numerator of that new fraction will be the percentage.
For example
, 3/20 = (3 x 5)/ (20 × 5) = 15/100 = 15%
Using the Unitar
y Method
In this method, we multiply the given fraction by 100 to get the percentage value.
For example, the percentage value of the fraction 3/20 is calculated as:
3/20 × 100 = 3 x 5 = 15%
It should be noted that the first method of percentage calculation is typically not used when the denominator is not a factor of 100. In those cases, the unitary method is applicable.
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Percentage Value with a Total of 100
When two or more numbers add up to make a total of 100, then the percentage value of each of these numbers is the number itself.
For example, if there are 24 apples, 60 oranges, and 16 pears in a fruit basket, then the percentage of apples is 24%, the percentage of oranges is 60%, and the percentage of pears is 16%.
Percentage Value When the Total Is Not 100
When the sum of individual numbers is not 100, then the percentage of each number is calculated using the unitary method.
For example,
if in a class there are 24 boys and 16 girls, then we can find the percentage of boys and girls as follows:
Total number of students = 24 + 16 = 40
Percentage of boys = (24/40) x 100 = 60%
Percentage of girls = (16/40) x 100 = 40%
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Percentage Formula
The formula for the percentage is used to make the calculation procedure uniform, simple, and accurate. The formula is given below.
Percentage = (actual value/total value) x 100
Calculation of Percentage Increase or Decrease
In a mathematical calculation, when any value is increased or decreased to give a new number, we can calculate the percentage increase or decrease of that number.
Percentage Increase
The formula for percentage increase is:
Percentage I
ncrease Formula
= (New Value - Original Value/Original Value) X 100
For example
, if the price of a product increases from Rs. 500 to Rs. 570, the percentage increase in price will be:
Price I
ncrease
= (570-500)/ (500) x 100 = 14%
Percentage Decrease
The formula for percentage
decrease is:
Percentage D
ecrease Formula
= (Original Value – New Value/Original Value) X 100
For example, if the temperature decreases from 40 degrees to 36 degrees, then the percentage decrease in temperature will be:
Temperature D
ecrease
= (40-36)/ (40) x 100 = 10%
Profit and Loss Percentage Calculation
Using the formula for percentage increase or decrease, we can calculate the profit and loss percentage in sell and purchase operations. Profit means the selling price is more than the cost price, and loss means the selling price is less than the cost price. In these calculations, we have to consider the new value as the selling price and the original value as the cost price to find out the profit or loss percentage.
Profit Percentage = (Profit/Cost price) x 100
Loss Percentage = (Loss/Cost price) x 100
Calculation of Value from Percentage
Sometimes, we need to find the value from a given percentage. This is done by the following formula:
Required Value = (
P
ercentage Value/100) x Given Value
For example, how to calculate 25% of 80?
So, the answer will be:
Required Value = (25/100) x 80 = 20
Percentage Table
Some common percentages corresponding to the fraction equivalents are given in the below table.
|
Percentage Table
|
|
Fraction
|
Percentage
|
|
1/1
|
100%
|
|
1/2
|
50%
|
|
1/3
|
33.33%
|
|
1/4
|
25%
|
|
1/5
|
20%
|
|
1/6
|
16.66%
|
|
1/7
|
14.28%
|
|
1/8
|
12.5%
|
|
1/9
|
11.11%
|
|
1/10
|
10%
|
Solved Sums on Percentage
-
Calculate the percentage marks of a student who obtained 48 marks out of 80 in a subject.
Solution:
Here, the total mark is 80 and the obtained mark is 48. Using the percentage formula, we get
Percentage marks = (48/80) x 100 = 60%
Answer: The student obtained 60% marks in the subject.
2. A medicine shop offers a discount of 15% to customers. What will be the cost of medicines after the discount if the original price is Rs.1200?
Solution:
Discount is the amount equivalent to 15% of Rs.1200.
Discount = (15/100) x 1200 = Rs. 180
So, the cost of medicines after the discount will be: (1200 -180) = Rs.1020
Answer: The cost of medicines will be Rs. 1020 after the discount.
Important Points About Percentage
-
To convert percentages into decimals, remove the % sign and divide by 100.
-
To convert decimals into percentages, multiply by 100 and put the % sign.
-
To convert the fractions into percentages, multiply the fraction by 100.
-
To convert percentages into fractions, divide the fraction by 100.
Percentage is a very important concept in mathematics and is used on numerous occasions for simple to complex calculations. A clear understanding of the concept and application of suitable formulas will help you solve mathematical problems quickly and accurately.
