Comparing Quantities

Uses of Percentage

What if you are asked to choose a bigger fraction from \( \frac{3}{4} \) and \( \frac{7}{8}\)? It becomes a little tricky while calculating the result; on the other hand, if you are asked to choose a bigger value from 75% and 87.5%, it becomes simple and easy. Clearly, percentage values are easier than fractions to interpret. In this module, we will study regarding different uses of percentages but, before we go forward, let us discuss what exactly the percentage means.

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Interpreting Percentages

A percentage is a number without a unit or dimension denoting a fraction of 100. The root word of percentage is a Latin word per centum, where centum means hundred. Therefore, percentage means per hundred. It implies that a percentage value is the numerator value of a fraction with the denominator as 100.


(Source: Pixabay)

A percentage is a number without having any unit or dimension. It is denoted by % symbol. So, 20 % is nothing but 20 parts per 100 which can also be written as \frac{20}{100} = \frac{1}{5}. Therefore, the percentage value can be interpreted as a fraction by dividing the value by 100.

Similarly, to convert a fraction into a percentage, we multiply and divide the fraction by 100 to make it into an equivalent fraction with the denominator as 100. This denominator value takes the form of %. Note that the sum of percentages of different possibilities within a given problem/case can never be more than 100.

Example: Convert the fraction \( \frac{3}{5} \) into a percentage.

Solution: \( \frac{3}{5} \) × \( \frac{100}{100} \) = \( \frac{3}{5} \) × 100 % = 60%

Applying Percentages in Real Life

Using and interpreting percentages has many real-life applications which we will study in this module.

1. Knowing “how much” or “how many” using Percentage

A percentage value helps in calculating exactly what’s the amount or figure one is talking about. For instance, let’s say that Ravi is spending 60% of his salary; it implies that Ravi is spending Rs 60 for every Rs 100 he has been earning. So, how much Ravi is actually spending if salary is Rs 60000 per month?

We know that Ravi spends 60% of his salary. Replacing 60% by \( \frac{60}{100} \) for calculating the amount, therefore, the amount Ravi is spending = \( \frac{60}{100} \) × 60000 = Rs 36,000

2. Comparing Fractions

Fractions can be converted into percentages to create a simple picture for the comparison. This is particularly useful when the denominator values of two fractions are not the same. For instance, Amar ate 3/5th of a pizza and Dinesh ate 5/8th of the other pizza of similar size. So, if we have to find who ate more, we need to compare by simply converting fractions into the percentage.

  • Amar ate \( \frac{3}{5} \) × 100 = 60% of the pizza.
  • And Dinesh ate \( \frac{5}{8} \) × 100 = 62.5% of the pizza

As we convert the ratios into percentages, it becomes instantly clear that Dinesh ate more pizza than Amar.

3. Finding Percentage Increase or Decrease

This application of using percentage is particularly important in analyzing or comparing performances and progress. The application particularly becomes even more useful when the base criterion of comparison is different. For instance, let’s say that in the mid-term exam, Rohit scored a total of 310 out of 500.

In the finals, he scored 430 out of 500. Clearly, the marks scored in the finals are higher than that scored in the mid-term exams. Therefore, there is an increment in the performance with the base value of 500.

\( \frac{Change in the performance}{The base value} \) × 100 ⇐ denotes the percentage change

Here, the increment in the performance = 430 – 310 = 120.

∴ Percentage increment = \( \frac{120}{500} \) × 100 = 24%

Solved Examples for You

Question 1: In a survey of 50 students, 80% of students liked Science, and 20% of students liked Arts. How many numbers of students liked Science?

Answer: We know that 80% of students liked science in the survey of 50 students

∴ Number of students who liked Science = \( \frac{80}{100} \) × 50 = 40

Question 2: In Yashoda hospital 35 old-aged patients died out of 210 admitted in 2016. In 2017, 10 old-aged patients died out of 150. What’s the increase or decrease of the death rate in the hospital?

Answer :Here, the base value is different for both the cases. Therefore, converting both the data into a percentage:

  • Death rate (%) in 2016 = \( \frac{35}{210} \) × 100 = 16.66%
  • Death rate (%) in 2017 = \( \frac{10}{150} \) × 100 = 6.66%

Clearly, there is a decrease in death rate in the hospital in 2017 when compared to that in 2016.

∴ Decrease in death rate (%) = \( \frac{16.66 − 6.66}{100} \) × 100 = 10%

Question 3: What do you mean by percentage?

Answer: A percentage refers to a number that does not have a unit or dimension which denotes a fraction of 100. The term percentage is derived from the Latin word per centum, where centum’s meaning is hundred. Thus, the percentage means per hundred. Similarly, it means that a percentage value is the numerator value of a fraction with the denominator as 100.

Question 4: How do I calculate a percentage?

Answer: In order to calculate the percentage of a certain number, you need to first convert the percentage number to a decimal. Thus, you must divide your percentage by 100. So, 60% would be 60 divided by 100.

Question 5: Why do we use percentages?

Answer: Percentages are quite an essential part of our daily lives. It comes in handy when we are writing fractions. Moreover, you can compare percentages more easily than fractions. Similarly, financial institutions quote interest they charge to the client on loans, or interest paid for money invested, as a percentage.

Question 6: What percent is 3% of 5%?

Answer: 60 % is percent of 3% of 5%. You get that by solving it:

To convert 3/5 to a percentage, we need to turn the denominator from a 5 to a 100. Thus, we need to multiply 5 by 20 and we get 100. Thus, you multiply the top and bottom of the fraction by 20 and the answer you get is 60%.

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