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A topic often overlooked in mathematics is How to Calculate percentages and what percentage as a word means in mathematics. While most students right from high school already have to deal with percentage calculation, the reality is that they only understand it as a computation tool. This article intends to change that by addressing everything you need to know about percentages and their mathematical importance for solving standard deviation and other percentage-related problems.
This article will systematically highlight what percentages mean and how to calculate them. You will also learn how to calculate percentage difference and, finally, percentage increase and percentage difference.
What is a Percentage?
A percentage is a mathematical number or ratio that can be expressed as a fraction with 100 as its denominator.
Generally, a fraction is a number with a numerator and denominator. However, once the denominator is 100, such a fraction becomes a percentage fraction.
The word per cent means per 100 and is expressed with the symbol %. Mathematically, it means a part of the whole number against 100.
For example, the number 4/100 is a percentage expression and can be stated as four percent, which means four per 100 or four/one hundred. It also means 4%
Now type 4/100 and 4% into your calculator. What is the answer? Of course, 0.04
The Percentage Formula
There are two ways to write the formula for a percentage and they will be considered in this section.
Now there are several occasions where you may have been given a value, let’s say 20, and then you were asked what percentage of 5 has in 20. Now, this question is like asking how much stake the value 5 has in the entire number 20. Of course, we already know that 20 is greater than 5, and removing 5 from 20 will leave us with 15. So it is clear that 5 has a percentage or stake in 20
Now the percentage can be determined by dividing 5 by 20 and multiplying it by 100. As such, the formula would be
X1 is always the smaller, which in this case is 5
X2 is the total value which in this case is 20
Now for a situation where it is required to find a particular percentage of a number, the above formula will need to be adjusted. For example, let’s say find 20% of the number 400. The right way to determine this number is by dividing the 20 by 200 and multiplying it by 100.
Therefore for a problem where it is required to find X% of Y, the formula would be
Percentage Difference Formula
If we have two distinct numbers given as X and Y, then we can calculate their respective percentage difference. The formula for calculating the percentage difference is given as
Percentage Increase and Percentage Decrease Formulas
Determining percentage increase and Percentage decrease is strictly based on their different formulas, and you only need to follow them to get an accurate result.
Percentage increase is a percentage calculation achieved by subtracting an originally given number from a new number and dividing the answer by the original number before multiplying the entire answer by 100. That is;
On the other hand, the percentage decrease is achieved by subtracting a new number from an original number and dividing the answer by the original number before multiplying the entire answer by 100. That is;
Are Percentages Valid Numbers?
A Percentage is actually a number. However, it is dependent on another main number. It has no dimension of its own and cannot stand on its own. It is like an adjective to a verb in the English Language. The verb, in this case, will be the main number while it is simply a part of that whole number.
Let us highlight a few percentages in the table below before we go into taking examples.
| Percent | Fraction expression | Decimal Expression |
| 10% | 10 / 100 | 0.10 |
| 20% | 20 /100 | 0.20 |
| 30% | 30 / 100 | 0.30 |
| 75% | 75 / 100 | 0.75 |
| 98% | 98 / 100 | 0.98 |
| 100% | 100 / 100 | 1 |
The above table simply shows how percentages are expressed. Now we will consider a few examples to aid better understanding.
Examples of Calculating Percentages
Example 1
What is the percentage of 7 in 28?
Solution
Clearly, our fml (1) is the best choice for solving this problem. It is given as:
Where X1 is 7 and X2 is 28.
This implies
This means that the percentage of 7 in 28 is 25%
Example 2
A young girl has a total of 90 oranges in a Basket. If she was to give her friend 25% of the oranges, how many oranges would she have left?
Solution
Now the solution to this problem is actually quite easy. We only need to break the questions into several sections to get our answer
Now we know the main number of oranges in the basket = 90
However, the kind girl wants to give 25% of her 90 oranges to a friend.
Clearly, this problem is similar to the problem that our Fml 2 should always solve. You can refer back above.
Since that is the case. The required formula for this problem is
Where X = 25
Y = 90
That leaves us with
The above solution means that the girl will be giving her friend 22 and half oranges from her 90 oranges when she gives her friend 25%.
So the total oranges the girl will have left would be
90 oranges – 22 ½ oranges = 67 ½ oranges.
Example 3
Consider the two values31 and 22 and find the percentage difference
Solution
When solving for percentage difference, it is best to let the bigger number be your XC, and the smaller number be your Y. As such, our formula above becomes
Percentage difference = 33.96%
Conclusion
Calculating Percentages is quite easy, and the bottom line is all about sticking to given instructions. This piece has outlined basically any challenge that students are likely to encounter anytime they solve percentages.
As can be seen, the entire process is easy, and students only need to follow the formulas relevant to whatever questions they have to handle. It is important to note that word problems are sometimes used for percentage problems. This is evident in the second example solved in this piece.
Students do not have to panic when they encounter such questions. They only need to analyze them and break them into bits, and they will definitely arrive at the right answers.
