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We are very familiar with the word ' percentage' as it is regularly used in the media to describe anything from interest rate changes to the number of people taking holidays abroad, to the success rate of the latest medical procedures or examination results. Percentages are a helpful way to compare, apart from calculating the many taxes we pay such as income tax, VAT, insurance tax, and fuel tax, to name but a few.

Therefore, percentages are a great part of our life. But what does it actually mean?

Now, "percentage" in mathematical language means “out of 100" and “out of” means “divide by”. So, if you get 85% scores in test out of 100% that means you have scored 85 marks out of 100 marks.

So, \(85\% = \dfrac{85}{100}\)

Let's look at some other general percentage amounts, as well as their decimal and fractional equivalents.

\(75\% = \dfrac{75}{100} = \dfrac{3}{4} = 0.75\) 

\(50\% = \dfrac{50}{100} = \dfrac{1}{2} = 0.5\)

\(25\% = \dfrac{25}{100} = \dfrac{1}{4} = 0.25\)

\(10\% = \dfrac{10}{100} = \dfrac{1}{10} = 0.1\) 

\(5\% = \dfrac{5}{100} = \dfrac{1}{20} = 0.05\)

It should be noted that dividing by 2, 50% can be found and by dividing 10, 10% can be found easily.

Now let's look at writing fractions as a percentage. For example, you get 18 values from 20 in the test. What’s the percentage?

First, as a fraction, write the information. You get 18 out of 20 values, so it's 18/20 faction. Because the percentage requires a denominator of 100, by multiplying the numerator and denominator by 5 we can turn 18/20 into a fraction out of 100:

\(\dfrac{18}{20} = \dfrac{18 \times 5}{20 \times 5} = \dfrac{90}{100} = 90\%\)                                                                                                                    Because we multiply the numerator and denominator by 5, we don't change the fraction value, only finding the equivalent fraction.

In the example it's easy to see that, to make the denominator 100, we need to multiply 20 by 5. But if it's not easy to see this, like with a score, say, 53 out of 68, we just write the number as a fraction and then multiply by 100/100:

\(\dfrac{53}{68} \times \dfrac{100}{100} = \dfrac{53}{68} \times 100\% = 77.94\%\)

Which is \(78\%\) to the closest whole number. You can use a percentage calculator for finding percentages of such calculations.

Key Facts about (%) Percentages

1.The percent is another name for one hundred so that percentages are hundreds and similar to fractions and decimals, they are another way to write fractions.

2.They are different from fractions and decimals because they always give a number of parts out of 100.

3.In simple terms, the percentage is the ratio of the denominator 100/10. So one way to think about percentages is to use them for comparison, for example, to ensure a discount that you will get in sales compared to the full original price. As a result of the need to compare this, the percentage of having a denominator is 100. Therefore, it is important to know what 100% refers to at each time.

4.Another way to look at percentages is to think of them as operators, that is, percentages tell us to take certain actions. If we need to find VAT for an object or discount on an item, we will use the numerator and denominator in the percentage to complete the operation. Or simply you can use VAT calculator for VAT calculation.

Other uses of Percentage

In sport statistics, when the referenced number is expressed as a decimal proportion, not a percentage, the word "percentage" is often a misnomer. "Shaquille O'Neal of the Phoenix Suns led the NBA in the 2008–09 season with a 0.609 field goal percentage (FG %)." That simply means in term of percentage O'Neal made 60.9% of his shots, not 0.609%.

Similarly, a team's winning percentage and the fraction of matches the club has won is usually expressed as a decimal proportion; a team with a winning percentage of 0.500 has won 50% of their matches. The practice is likely to be related to the batting averages being quoted similarly.

It is also used to describe the steepness of a road or railway slope, for which the formula is \(= 100 \times \dfrac{rise}{run}\)

That could also be expressed as the inclination angle tangent 100 times. This is the distance ratio that a vehicle would move vertically and horizontally, respectively, expressed in percentage when going up or down. The percentage is also used to express mass percentage and mole percentage of composition of a mixture.

How Percentage Shapes Our Daily Life?

"I will never need math again!" Everyone says this as soon as he does graduation. With a little distance from our school years, everyone claims to do so, unfortunately, this is not true. We are faced with basic mathematical problems, including percentages, almost every day. If you are trying to calculate your margin as a retailer or know how much VAT you are paying, we must manage the percentages every day!
Calculating percentages is an important task for everyday mathematics, just like calculating the discounted percentage in the shopping mall on "Sale Days".

How does Percentage Work?

The percentage indicates the quantitative relationship and performs the same function as the fractions. For example, half means 50% and 25% quarterly. Percentages can also reveal better proportions. For example, 63% means 63/100 of the original value.
The percentage rate, the new value, and the original value are the central numbers of the percentage equation. 

  • The percentage rate is calculated by dividing the new value by the original value and multiplying by 100%.
  • The percentage value or the new value is calculated by multiplying the original value by the percentage level and dividing by 100%.
  • The original value is calculated by dividing the amount already paid by the percentage and multiplying the result by 100.

Where does the idea of "percentage" come from?

Initially, the term "percentage" came from merchants of ancient Babylon. Interest rates are described in particular using fractions and percentages. This term appeared for the first time in Germany in the fifteenth century, although in Italian the "cento" ("percent"). The % symbol only appears later. In the 19th century, the line in the % symbol was not diagonal.

Basic knowledge of calculation of percentages

The percentage indicates the quantitative relationship and fulfills the same function as the fraction, such as half or quarter. Half means 50% and one quarter, 25%. Percentages can also reveal finer relationships, for example, 53% means 53/100 of the original value.

  • The meaning of the terms "by" and "to" must be distinguished:
  • "My salary increases by 5%" means that "My salary went from 105% to its original level".
  • "My income has dropped by 3%" means the same as "My income has dropped to 97% from the original level".
  • If we say "the consumption falls in a quarter", it is equivalent to saying "the consumption falls to three-quarters of the previous level".
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