What is percentage
The percentage can be referred to as a denotation similar to fractions. Where fractions are referred to with nominators and denominators, the percentage is referred to with the symbol %. As for the similarity, any fraction with the denominator 100 can be termed infractions.
Let’s take an example of 23 apples among a set of 100 apples are rotten, then we can say that 23% of the apples in the lot are rotten.
How does this come to be, the figure 23%? Let’s go ahead and discuss this in detail.
Before we move forward to calculating the percentage part, let’s take a couple of examples on the denotation of percentages.
10/100 can be referred to as 10%
25/100 can be referred to as 25%
63/100 can be referred to as 63%
And so on so forth. As mentioned in the first paragraph, any fraction with the denominator 100 can be called out in terms of percentage.
Moving on, let’s see how the calculation of marks percentage for any given quantity is done.
As we have seen in the simple definition of the percentage that it’s a fraction with the denominator 100. Now, what about the ones that do not have their denominator as 100. How do we calculate the fraction for such numbers or, say, fractions?
Take the first example again with a bit of a twist to help you understand the query better.
Let’s say, this time, the batch of apples has only 80 apples and not 100 and there are 20 apples that are rotten. What would be the percentage now?
The formula for Percentage is often described as:
| Percentage = | Total number of items for which the percentage needs to be found | * 100 |
| Total set |
Let’s try and apply the same to the above-given situation.
So, the total number of items for which we require the percentage is 20 rotten items.
Given total set of items is 80. Replacing the respective values in the formula, we get:
= (20 / 80) * 100
= (1/4) * 100
= 25 percent or 25%
Hence, we can say 25% of the apples are rotten out of the stock of 80 apples.
Now that we have understood how to calculate the percentage for any given quantity let’s understand a few of its usages or use cases where it can be used, specially in the case of marks calculation.
The most common use case of percentage can be found in the comparison of the performance of students.
How you might wonder, well, let’s check it out.
Since we have seen, any entity in the form of fractions can be termed in integral terms via percentage. It makes the percentage a more preferred mode of calculation or comparison or any other use case.
Let’s take an example to understand this better.
Let’s say you have two students, and you have to choose the student who is performing better. Given to you is that student 1 has scored 60 marks and student 2 has scored 80.
Now, do you think the given information is sufficient to make the educated guess of which particular student is better? Well, the answer is no. A fair comparison is not possible unless we know the base quantity, that is, the total marks for each subject.
So, let’s take this query ahead. Student 1 has scored 60 out of 100, whereas student 2 has scored 80 out of 110. Now, here the fraction of student 1 comes out as (60/100), whereas for student 2, it comes out as (80/110).
The fractions of both the student’s marks do not provide us with any indication of whether student 1 is better when compared to student 2 or not. So, to simplify this, let’s calculate the percentage.
Student 1:
Total marks obtained by student 1: 60
Total marks in the test: 100
Percentage = (60/100) * 100 => 60%
Student 2:
Total marks obtained by student 1: 80
Total marks in the test: 110
Percentage = (80/110) * 100 => 72.7%
Now that we have the percentage of marks for both the students, we can see that student 2 has a higher percentage of marks than student 1. Hence student 1 is better when compared.
Now let’s take an example of a mass situation. Suppose there is a class of 50 students, out of which 46 students passed the exam. Now, those, who failed go the following marks: 20, 30, 35, 38 out of 90.
The problem given is to find the percentage of students that failed in the subject and find the percentage of the marks of the failed students.
Let’s first solve the percentage of students that failed in the subject.
Given are the following data:
Total students in the class: 50
Total students that passed the subject: 46
Therefore, the percentage of passing students:
= (46/50) * 100
= 0.92 * 100
= 92%
Hence, the percentage of students that failed in the subject:
100% – 92% = 8%
Hence, we can say that 8% of the students have failed in the subject.
Now, for the second part of the question, let’s assume that the students that failed are A, B, C and D.
Given are the following data for the 4 students:
Marks obtained by A: 20
Marks obtained by B: 30
Marks obtained by C: 35
Marks obtained by D: 38
The percentage of marks obtained by A, B, C, D are as follow:
A = (20/90) * 100 = 22.2 * 100 = 22.2%
B = (30/90) * 100 = 33.3 * 100 = 33.3%
C = (35/90) * 100 = 38.8 * 100 = 38.8%
D = (38/90) * 100 = 42.2 * 100 = 42.2%
Thus, students that scored 22.2%, 33.3%, 38.8% and 42.2% failed the subject of math.
Now, basis our discussion so far there are few points that we can conclude. Primarily being, if we wish to convert any integral value into percentage, then the process would be to first convert the integer into fraction and multiply the obtained figure to 100.
Vice versa, if you have a percentage in your hand and wish to convert it into an integer form, divide the given percentage with 100.
Let’s take an example of the vice versa situation to understand it better.
Let’s say, given to us is 30% of 80.
Then, as discussed in the above para, inorder to change a percentage value to integer, we divide it by 100.
Hence, we get:
= (30/100) * 80
= 3 * 8
= 24
As you can see, for any given percentage amount, just a simple division of the number with 100 and reducing the obtained fraction or expression will give you the required answer.
Another example of the use of percentage is during calculation of increase or decrease of any quantity.
Say for example, a book’s price reduced by 5% in last one year, or a building’s cost increased by 20% in last 10 years.
So, how is this calculated?
Well the formula for the same is quite simple:
For decreasing percentage, we say
Final value = Initial value – Decreased value.
Initial value = Final value Decreased value.
Decreased value = Initial value – Final value.
Now, decreased value = x% of initial value
Quite similarly, for increasing percentage, we say
Final Value = Initial Value Increased Value.
Initial Value = Final Value – Increased Value.
Increased Value = Final Value – Initial Value.
Where,
Increased Value = x% of Initial value
The calculation for the same is exactly how we did in the above examples.
Conclusion
Hope this clears out your doubts on how to calculate the percentage for marks.