Percentage Calculator

Percentage Increase Calculation:

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A percentage is a fraction with the denominator as 100. When we express some fraction as a percentage, we express how many parts of the 100, the fraction denotes. In other words, a percentage indicates the quantity of something in terms of 100. The word ‘percent’ essentially means ‘per hundred’. Percentages are extremely useful in mathematical calculations, and for finding and comparing ratios. The symbol for percentage is %. For example, the ratio 15/16 as a percentage is 93.75%.

The simplest way of expressing a fraction (or ratio) as a percentage is A/B = P × 100, where ‘A’ is the numerator of the fraction, ‘B’ is the denominator and ‘P’ is the percentage. In a percentage calculation, the denominator denotes the total value of a quantity, and the numerator denotes some part of the total value. The percentage simply expresses this ratio in terms of 100.

There are basic percentage calculations. If A and B are the numbers involved and P is the percentage, then

     i) Finding P percent of A.

     ii) Finding what percent of A is B.

     iii) Find A if B is P percent of A.

If A is a given number, and we need to find B, which is P percent of A, then the formula is $$ P\% \; of \; A \; = \; B $$

Consider this example, we need to find 10% of 200. The steps for this are as follows.

     1) This problem can be written in the form of an equation as 𝑃% 𝑜𝑓 𝐴 = 𝐵.

     2) Here, A = 200 and P = 10. Plugging these in the equation gives 10% 𝑜𝑓 200 = 𝐵

     3) Now convert the percentage to a decimal by removing the percentage sign, and dividing P by 100. Here, 10/100 = 0.01.

     4) In the equation, replace the 10% by 0.01 and perform the multiplication. $$ 10\% \, of \, 200 = B \\ 0.01 \, of 200 = B \\ 0.01 * 200 = 20 $$

     5) This gives B = 20. Hence, 10% of 200 is 20.

If A and B are two given numbers, and we need to find what percent of A is B, then the formula used is $$ {B\over A} = P\% $$

For this method, we consider the problem, what percent of 50 is 18? The steps are

     1) This problem can be written in the form of an equation as B/A = 𝑃%.

     2) Here, A = 50 and B = 18. Plugging these in the equation gives 18/50 = 𝑃%.

     3) Carry out the division of A by B. 18 divided by 50 gives 0.36. We express the final answer of the division process in decimal form.

     4) To obtain the corresponding percentage, multiply this decimal answer by 100. Therefore, 0.36 × 100 = 36%.

     5) This gives P = 36%. Hence, 36% of 50 (which is A) is 18 (which is B).

If B is known to be some percentage of the number A, the number A can be found using the formula $$ {B \over P\%} = A $$

We consider the problem, 48 is 80% of what number? The steps are

     1) This problem can be written in the form of an equation as $$ {B \over P\%} = A $$

     2) Here, B = 48 and P = 80. Substituting these in the equation gives 48/80% = 𝐴

     3) Now, convert the percentage to a decimal number by dividing P by 100. Thus, 80/100 = 0.8

     4) Replace the P% in the equation in step 2 by the equivalent decimal number. This gives 48/0.8 = 𝐴

     5) Perform long division of the resulting fraction. 48 divided by 0.8 gives 60.

     6) Hence, A = 60. So, 80% of 60 is 48.

Percentages are used in all walks of life. Bank interest rates, discounts in shops, statistical data, grades of examinations, rates of inflation, and taxes are expressed using percentages. When a consumer buys goods, they are charged 18% GST of the total price. Percentages are used extensively in finance. They are also useful for comparing different fractions because 100 as a denominator is easier to comprehend. For example, 4/7 of the students in a classroom are boys can be expressed as 57% of the students in the classroom are boys. The percentage is easier to understand than a fraction (4/7 ≈ 57%). Consider the following problem making use of percentages.

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