Important Formulas: Percentage | Mathematics for JAMB PDF Download

The word “Percentage” was coined from the Latin word “Percentum” which means “by hundred”, therefore, it is said that percentages are the fractions with 100 in the denominator. Whenever we want to estimate something based on some pre-defined data which are already present, the best tool we can use is the percentage. In mathematics, a percentage is a number or ratio that represents a fractional part of a percent, i.e., per 100. It is often denoted by the sign % or percent or pct. Examples of percentages are,

• 10% is 10/100, that is, 1/10 of the number.
• 20% is 20/100, that is, 1/5 of the number.
• 30% is 30/100, that is, 3/10 of the number.
• 40% is 40/100, that is, 2/5 of the number.
• 50% is 50/100, that is, 1/2 of the number.

Percentage Formula

Percentage formula is a formula that is used to find the amount or share of a quantity in terms of a hundred. So, for calculating the percentage, we basically need three variables. First, the total value V₁, the present value V₂, and the percentage value P. The algebraic equation for this will be:
V₁ × P = V₂
Or
Percentage (P%) = (Parts (V₂) / Whole (V₁)) × 100

How to Calculate Percentage?

The formula for the percentage is shown above. However, for solving this equation, two variable is required. For example, let’s see the 20 parts of 30 whole,
P × 30 = 20
P = 20/30
P = 2/3 or
P = 0.6666667
Here, P% = 0.6666667 × P/100 = 66.6666667%.

Percentage Difference Formula

The percentage difference or the percentage change formula is calculated when the difference between two values is divided by the average of the same values. We can say that the percentage difference is used to calculate the change in the value over the given period. Mathematically, we can be written as:
Percentage Difference = (Absolute difference / Average) × 100
It is expressed as a ratio and is a unitless number. We can calculate the differences in two cases:

Percentage Increase Formula

We can use the percentage difference formula to find the change in the value when it increases over a time period. The percentage increase formula is given below:
Percentage difference = (Increase value – Original value / Average) × 100

Percentage Decrease Formula

We can use the percentage difference formula to find the change in the value when it decreases over a time period. The percentage decrease formula is given below:
Percentage difference = (Original value – Decrease value / Average) × 100

Note

• If the value obtained is negative while calculating percentage increase formula, then it is actually percentage decrease.
• If the value obtained is negative while calculating percentage decrease formula, then it is actually percentage increase.
• Percentage change is also used to find the percentage errors in maths, physics and chemistry.

Converting Percentage to Fraction

In some cases, we are provided with the percentage and need to convert it to a fraction number. For converting percentage to fraction, some calculations are required. We can use the formula,
Fraction = Percentage/100

After getting it to reduce it further. For example, 

• Fraction of 25% = 25/100 = 1/4.
• Fraction of 50% = 50/100 = 1/2. 
• Fraction of 75% = 75/100 = 3/4. 
• Fraction of 90% = 90/100 = 9/10.

Converting Fraction to Percentage 

For converting fraction to percentage, let’s assume the fraction is represented by a/b, where “a” is the part of the whole “b”. Multiplying numerator and denominator by 100.

a/b x 100/100 = (a/b x 100) x 1/100
We know that 1/100 = 1%
Therefore, the equation can be written as,
a/b × 100%.
Hence, to convert fraction to percentage, multiply the fraction by 100.

Percentage Chart

Let’s see the percentage chart of fractions converted into percentages,

Difference between Percentage and Percent

The words percentage and percent are related to each other, but there is a difference between both of them. Percent is always accompanied by a number, for example, 25%. While percentage does not need a number to be accompanied by the term. For example, the percentage of the people who participated in the voting in 2022 is more than the percentage of people who participated in 2021. Fractions, decimals, ratios and percentages are also related to each other. Below is the chart that shows the relationship among these terms.

Percentage in Maths

In mathematics, the percentage is written with three possible unknowns and variables. The three terms are known as:

• Percentage
• Part
• Base

For instance, the 50% of 400 is 200. Here, 50 is the percentage, 400 is the base, and 200 is the part.
Example: If 25% of 200 is 50, explain the different terms in the calculation.
Answer:
25% of 400 is 50. Here 25 is the percentage, 200 is the base, and 50 is the part.
In fraction, it can be written as,
Part/Base = 25/200 = 1/4
1/4 is the fraction obtained. However, we have learned how to convert fractions into percentages. Therefore, multiply 1/4 by 100,
1/4 × 100 = 25%.

Percentage Tricks

There are percentage tricks that can be used while calculating the percentage of numbers. Below given trick is the most used, % x of y = % y of x
Example: Solve 300% of 50.
Solution: Here, solving 300% of 50 can be a little lengthy and tricky. However, using the trick it can be easily solved,
%x of y = %y of x
300% of 50 = 50% of 300
Now, solving 50% of 300 is relatively is. 50% of 300 is just half of 300. Therefore, 50% of 300 is 150.
Therefore, 300% of 50 is 150.

Marks Percentage 

The percentage is mostly used when marks are calculated for students. The marks of students are with respect to the total marks. That fraction is converted into a percentage by multiplying it by 100. In this way, we can calculate the marks in percentage. Let’s see some examples of marks obtained in percentage,