How to Find Percentage of a Number?
Answer: The percentage of a number is calculated by the formula –
[Tex]\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 [/Tex]
A percentage is defined as the proportion of a certain thing. It can be the proportion of a number, proportion of liquids, proportion of items, etc. In mathematics, it is represented as a fraction of a hundred or 1/100. The method of using percentage is very common in every field, such as tax percentage, discount percentage on products, percentage of humidity in the air, and percentage composition of substances in mixtures. Thus, knowledge of calculating percentages helps in mathematics and also helps in solving the percentage value of products and many items in day-to-day life.
Percentage of a Number
The percentage symbol is ‘%.’ It is also used to represent the average percentage of students in a class, data representation, profit percentage, loss percentage, interest, etc.
The range of percentages lies between 0 and 100. It can be 0.5%, 10%, 40%, 70%, 80%, 92%, 99%, and maximum up to 100%. 100% of a number is the same as the number.
For example,
100 percentages of 10 means
100% of 10
100 × 1/100 × 10
= 10
Hence proved, that 100% of a number is the same as the number itself.
Note: Percentage equal to the number divided by 100
For example,
20%
20 % = 20/100
Thus, 20% is represented as a fraction of 20/100.
Suppose the percentage of a number N is to be calculated, it will be represented as:
P% of N
P/100 × N
Or
(P × N)/100
Where,
P is the percent
N is the number
% is equal to 1/100
For example,
10% of 20
It is equal to 2
Thus, to find the percentage value of a number, we need to simply multiply the number with the percentage value and divide it by 100.
Steps to find the percentage of a number
Let’s consider an example to find 10% of 500.
Step 1: Substitute 1/100 instead of the % symbol
10 × 1/100 of 500
Step 2: Substitute multiply symbol (×) instead of ‘of’
10 × 1/100 × 500
Step 3: Solve the above-formed equation
10 × 500/100
5000/100
= 50
Thus, 10% of 500 is 50.
Increase in the percentage of a number
Let’s consider an example.
10% increase of the number 50
The formula is given by:
Number + percentage of the same number
50 + 10% of 50
= 50 + 10 × 1/100× 50
= 50 + 500/100
= 50 + 5
= 55
Steps to find the increase in the percentage of a number
Example: Find15% increase of 200.
Step 1: Form an equation using the formula
The formula is given by:
Number + percentage of the same number
= 200 + 15% of 200
Step 2: Substitute 1/100 instead of the % symbol
15× 1/100 of 200
Step 3: Substitute multiply symbol (×) instead of ‘of’
15 × 1/100 × 200
Step 4: Solve the above-formed equation
15× 200/100
3000/100
= 30
Step 4: Add the number
200 + 30
= 230
Thus, a 15% increase of 200 is 230.
Direct formula
(100 + increase percentage value)% × number
(100 + 15)% × 200
(115)% × 200
115 × 1/100 × 200
= 230
Decrease in percentage of a number
Let’s consider an example.
10% decrease of the number 50
The formula is given by:
Number – the percentage of the same number
50 – 10% of 50
= 50 – 10 × 1/100 × 50
= 50 – 500/100
= 50 – 5
= 45
Steps to find the increase in the percentage of a number
Example: Find a 45% decrease of 300.
Step 1: Form an equation using the formula
The formula is given by:
Number – the percentage of the same number
= 300 – 45% of 300
Step 2: Substitute 1/100 instead of the % symbol
45× 1/100 of 300
Step 3: Substitute multiply symbol (×) instead of ‘of’
45 × 1/100 × 300
Step 4: Solve the above-formed equation
45× 300/100
135000/100
= 135
Step 5: Subtract the number
300 – 135
= 165
Thus, a 45% decrease of 300 is 165.
Direct formula
(100 – decrease percentage value)% × number
(100 – 45)% × 300
(55)% × 300
55 ×1/100 × 300
= 165
Sample Problems – How to Find Percentage of a Number?
Question 1: Find 20% of 80?
Solution:
20 × 1/100 × 80
= (20 × 80)/100
= 1600/100
16
Thus, 20% of 80 equals to 16.
Question 2: Find 50% of 200?
Solution:
50 × 1/100 × 200
= (50 × 200)/100
= 10000/100
= 100
Or
50/100 × 200
= (1/2) × 200
= 0.5 × 200
= 100
Thus, 50% of 200 equals to 100.
Question 3: Find 10% of 50?
Solution:
10 × 1/100 × 50
= (10 × 50)/100
= 500/100
= 5
Thus, 10% of 50 equals to 5.
Question 4: Find 0.5% of 5?
Solution:
0.5 × 1/100 × 5
= (0.5 × 5)/100
= 2.5/100
= 0.025
Thus, 0.5% of 5 equals to 0.025.
Question 5: Find 80% of 600?
Solution:
80 × 1/100 × 600
= (80 × 600)/100
= 48000/100
= 480
Thus, 80% of 600 equals to 480.
Question 6: Find a 22% increase of 50.
Solution:
The formula to find the percentage increase of a number is given by:
(100 + increase percentage value)% × number
(100 + 22)% × 50
(122)% × 50
122 × 1/100 × 50
= 61
Question 7: Find 70% decrease of 150.
Solution:
The formula to find the percentage decrease of a number is given by:
(100 – decrease percentage value)% × number
(100 – 70)% × 150
(30)% × 150
30 × 1/100 × 150
= 45
Related Articles:
- Percentage
- How to Calculate Percentage?
- Maths Trick to Find Percentage
Contact Us