What is Percentage?

Percentages are a way of showing a part of a whole as a fraction of 100. The % sign is used to represent percentage. For example, if you have 50 out of 100 marbles, that can be written as 50%.

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Percentage means, a part per hundred.

Examples of Percentage

  • 15% = 15/100 ( = 3/20 (or) 0.15)
  • 33.33% = 33.33/100 ( = 1/3 (or) 0.3333)
  • 80% is equivalent to 4/5 fraction
  • 5% = 5/100 ( = 1/20 (or) 0.05)
  • 70% is equivalent to 7/10 fraction
  • 16.67% = 16.67/100 ( = 1/6 (or) 0.1667)
  • 95% is equivalent to 19/20 fraction
  • 2.5% = 2.5/100 ( = 1/40 (or) 0.025)
  • 60% is equivalent to 3/5 fraction
  • 87.5% = 87.5/100 ( = 7/8 (or) 0.875)

How to calculate Percentage?

Percentages are a way of showing a part of a whole as a fraction of 100. It's often used to describe how much of something is present or how much something has changed.

Formula : Percentage formula = (Value/Total value) × 100

For example, if you have 50 out of 100 marbles, that can be written as,

Percentage = (50/100)* 100 = 50%

We can write percentages as decimals or fractions, like 0.6% or 0.25%. In school, teachers use percentages to tell us how well we did on a test or exam. For example, if Raj got 78% in his final exam, it means he got 78 out of 100 marks. This percentage is calculated by adding up all of Raj's marks in all his subjects, then dividing by the total possible marks.

Parts of Percentage in Maths

Percentage problems have three possible unknowns or variables :

  • Percentage
  • Part
  • Base

Look at the following examples. All three variables are known:

Example 1: 70% of 90 is 63

70 is the percentage.

90 is the base.

63 is the part.

Example 2: 25% of 300 is 75

25 is the percent.

300 is the base.

75 is the part.

Example 3: If a shirt originally cost $40 and is now on sale for 20% off, what is the new price? 20 is the percent. $40 is the original price (or base). The sale price, or part, can be found by multiplying the base by (100% - 20%) or 0.8. So the new price is $32.

Example 4: A pizza is cut into 8 equal slices. If you eat 3 slices, what percentage of the pizza have you eaten? The slices you ate are the part. 8 is the base. To find the percent, you can divide the part by the base and multiply by 100. So 3/8 x 100 = 37.5%. You have eaten 37.5% of the pizza.

Example 5: If there are 20 students in a class and 60% of them are girls, how many girls are in the class? 60 is the percentage. 20 is the base. To find the part, you can multiply the base by the percentage in decimal form (60% = 0.6). So 20 x 0.6 = 12. There are 12 girls in the class.

Commodity in Percentage

A commodity is something that people can buy and sell, like coffee or copper. Sometimes, people buy and sell them in the future instead of right away.

Formula and Example

To calculate the percentage change in the price of a commodity, you can use the following formula: Percentage change = (new price - old price) / old price x 100 For example, if the price of a commodity increases from $50 to $60, the percentage change can be calculated as: Percentage change = (60 - 50) / 50 x 100 = 20%

Population in Percentage

Population is the number of people in a group or area, like a city or country. If we want to know what percentage of the group is in a specific category, we divide the number of people in that category by the total population and multiply it by 100.

Formula and Example

To calculate the percentage of a population in a particular group, you can use the following formula: Percentage = (number of individuals in group / total population) x 100

For example, if a city has a population of 100,000 and 10,000 of those individuals are students, the percentage of students in the city can be calculated as: Percentage = (10,000 / 100,000) x 100 = 10%

Depreciation in Percentage

Depreciation is when something becomes less valuable over time because of things like wear and tear or becoming outdated. To find the percentage of depreciation of something, we divide the decrease in value by the original value and multiply it by 100.

Formula and Example

To calculate the percentage of depreciation of an asset, you can use the following formula: Percentage of depreciation = (depreciation amount / original value of asset) x 100

For example, if a car was purchased for $20,000 and is now worth $12,000 due to depreciation, the percentage of depreciation can be calculated as: Percentage of depreciation = ((20,000 - 12,000) / 20,000) x 100 = 40%

Percentage Problems and Solutions

  1. Which one of the following is equal to 49%?

A. 49 / 25 

B. 49 / 50

C. 49 / 100

D. 49 / 1000

  1. What percent of a rupee is 4 paise?

A. 8%

B. 40%

C. 4%

D. 20%

  1. There are 500 students in a school in which 36% are girls. The difference between the numbers of boys and the girls is :

A. 140

B. 120

C. 180

D. 320

  1. Complete the following using   >,< or == 32.05%   ____________32.5%

A. >

B. <

C. =

D. NONE