Percentage
The term “percentage” was adapted from the Latin word “per centum”, which means “by the hundred”. Percentages are fractions with 100 as the denominator. In other words, it is the relation between part and whole where the value of “whole” is always taken as 100.
For example, if the marks of a student in math are 15 out of 50 then the corresponding percentage can be calculated by expressing “marks obtained” as a fraction of “total marks” and multiplying the result by 100. i.e., percentage of marks = 15 / 50 x 100 = 30%.
- 10% = 10/100 ( = 1/10 (or) 0.1)
- 25% = 25/100 ( = 1/4 (or) 0.25)
- 12.5% = 12.5/100 ( = 1/8 (or) 0.125)
- 50% = 50/100 ( = 1/2 (or) 0.5)
One percent (1%) means 1 per 100.
1% of this line is shaded green: it is very small isn’t it?
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50% means 50 per 100 (50% of this box is green) |
| 25% means 25 per 100 (25% of this box is green) |
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A Percent can also be expressed as a Decimal or a Fraction
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Percentage Calculation
Calculating a percentage implies determining the proportion of the total in terms of 100. There are two methods for calculating percentages:
By altering the fraction’s denominator to 100:
We simply find the equivalent fraction of a given fraction such that the resultant denominator is 100 using this method. The numerator is then the proportion.
As an example:
4/25 = 4/25 × 4/4 = 16/100 = 16%
Using the unitary method:
To calculate the percentage, simply multiply the fraction by 100. For instance, the percentage corresponding to the fraction 4/25 is:
4/25 × 100 = 400/25 = 16%
Example:
1. Calculate 25% of 80
Solution:
25% = 25/100
And (25/100) × 80 = 20
So 25% of 80 is 20
2. 15% of 200 apples are bad. How many apples are bad?
Solution:
15% = 15/100
| And (15/100) × 200 | = 15 × 200/100 | |
| = 15 × 2 | ||
| = 30 apples |
30 apples are bad.
3. If only 10 of the 200 apples are bad, what percent is that?
Solution:
As a fraction, 10/200 = 0.05
As a percentage it is: (10/200) x 100 = 5%
5% of those apples are bad
4. A Skateboard is reduced 25% in price. The old price was $120. Find the new price.
Solution:
First, find 25% of Rs. 120:
25% = 25/100
And 25/100 × Rs. 120 = Rs. 30
25% of Rs. 120 is Rs. 30
So the reduction is Rs. 30
Take the reduction from the original price
Rs. 120 − Rs. 30 = Rs. 90
The Price of the Skateboard in the sale is Rs. 90
Percent vs Percentage
My Dictionary says “Percentage” is the “result obtained by multiplying a quantity by a percent”. So 10 percent of 50 apples is 5 apples: the 5 apples is the percentage.
But in practice, people use both words the same way.