Basic Percentage: Formulas, Rules and Solved Examples

Basic Percentage covers the meaning of percent, conversion between percentages, fractions and decimals, and standard calculation methods. Learn how to find a percentage of a number, calculate what percentage one quantity is of another, and handle percentage increase or decrease using direct formulas and simple examples.

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What is Basic Percentage?

A percentage expresses a quantity as a part out of 100. The symbol % means “per hundred”; therefore, x% = x/100.

For example, 25% means 25 out of 100, or 25/100 = 1/4. A percentage can be written as a fraction, decimal or ratio: 40% = 40/100 = 0.4 = 2/5. In percentage calculations, identify the original or total quantity before applying the required formula.

Basic Percentage Formula & Tricks

Important Formulas

Percentage of a quantity
x% of y = (x/100) × y

To find x% of y, convert x% into x/100 and multiply it by y.

Percentage represented by a part
Percentage = (Part/Whole) × 100

Use this formula when a part and the corresponding whole quantity are given.

Percentage increase
Percentage increase = [(New value − Original value)/Original value] × 100

The original value is always the denominator for an increase.

Percentage decrease
Percentage decrease = [(Original value − New value)/Original value] × 100

The original value is always the denominator for a decrease.

New value after a percentage change
New value = Original value × (1 ± r/100)

Use + for an increase of r% and − for a decrease of r%.

Quick Tricks

Use the interchange rule

x% of y is equal to y% of x. This can make mental calculations easier when one number has a simpler percentage.

Example: 16% of 25 = 25% of 16 = 4.
Use common percentage fractions

Convert familiar percentages into fractions before calculating. For example, 50% = 1/2, 25% = 1/4, 20% = 1/5 and 10% = 1/10.

Example: 25% of 240 = 240/4 = 60.
Break difficult percentages into simple parts

Express a percentage as a sum or difference of easier percentages.

Example: 35% of 200 = 30% of 200 + 5% of 200 = 60 + 10 = 70.

Basic Percentage Concepts

Converting Percentages, Fractions and Decimals

To convert a percentage into a decimal, divide it by 100; to convert it into a fraction, write it over 100 and simplify.

Percentage to decimal: x% = x/100. Decimal to percentage: decimal × 100. Percentage to fraction: x% = x/100 in lowest terms. For example, 62.5% = 62.5/100 = 0.625 = 5/8.

Example: 0.72 = 0.72 × 100% = 72%, while 18% = 18/100 = 9/50 = 0.18.

Finding a Percentage of a Number

To find x% of a number y, multiply y by x/100.

Use x% of y = (x/100) × y. Cancel factors before multiplying when possible. If the percentage is greater than 100%, the result is greater than the original number.

Example: 15% of 360 = (15/100) × 360 = 54.

Finding What Percentage One Quantity Is of Another

When a part and a whole are given, divide the part by the whole and multiply by 100.

Percentage = (Part/Whole) × 100. The whole quantity must be used as the denominator. If 45 is obtained out of 60, the percentage is (45/60) × 100 = 75%.

Example: A student scores 72 marks out of 80: percentage = (72/80) × 100 = 90%.

Percentage Increase and Decrease

Percentage change compares the change with the original value, not the new value.

For an increase, subtract the original value from the new value and divide by the original value. For a decrease, subtract the new value from the original value and divide by the original value. A price rising from ₹500 to ₹575 increases by (75/500) × 100 = 15%. A price falling from ₹500 to ₹425 decreases by (75/500) × 100 = 15%.

Example: A number changes from 240 to 300. Percentage increase = (60/240) × 100 = 25%.

Finding the Original Value After a Percentage Change

To recover the original value, divide the final value by the appropriate percentage multiplier.

After an r% increase, Final value = Original value × (1 + r/100), so Original value = Final value ÷ (1 + r/100). After an r% decrease, Final value = Original value × (1 − r/100), so Original value = Final value ÷ (1 − r/100).

Example: After a 20% increase, a value is 360. Original value = 360 ÷ 1.20 = 300.

Basic Percentage Video Lessons

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8 Lessons
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Percentage Basics and Conversions

Understand what percentage means and learn how to convert percentages between fractions, decimals, and related forms using clear foundational methods.

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Practice Basic Percentage Questions

Practise published questions related to this topic.

1If an item is bought for ₹800 and sold for ₹740, what is the loss percentage?→ 2What is the largest 6-digit number that is completely divisible by 96?→ 3A is smallest 3 digit number divisible by both 14 and 20. B is the largest 3 digit number divisible by 14 and 20. What is the value of B - A?→ 41/(6 + √3) + 1/(6 - √3) = ?→ 5If x+6 is the HCF of x² + 10x + 24 and x² + kx + 12 , then the value of k is:→ 6B = 700 - A. When B is divided by 3, 4 and 5 the remainder is 1 in each case. What is the value of A?→ 7A retailer offers the following discount schemes for buyers on an article. Which scheme will fetch the maximum selling price?→ 8A shopkeeper fixes the marked price of an item 150% above its cost price. What percentage of discount on marked price should be allowed to gain 110%?→ 9A trader bought goods for 240 and sold them at a 25% profit. What was the selling price?→ 10In the records, the value is noted as 7/√7 .Simplify.→

Basic Percentage Quick Quiz

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Quick Revision Notes

Basic Percentage Revision Points

Remember these definitions, formulas and calculation rules.

  • x% means x out of 100, so x% = x/100.
  • Percentage = (Part/Whole) × 100.
  • x% of y = (x/100) × y.
  • For percentage increase or decrease, use the original value as the denominator.
  • New value after r% increase = Original value × (1 + r/100).
  • New value after r% decrease = Original value × (1 − r/100).
  • x% of y = y% of x.
  • To convert a percentage to a decimal, divide by 100; to convert a decimal to a percentage, multiply by 100.

Basic Percentage FAQs

What is the basic percentage formula?

The basic percentage formula is Percentage = (Part/Whole) × 100. For example, 30 out of 50 is (30/50) × 100 = 60%.

How do you calculate 12% of 250?

12% of 250 = (12/100) × 250 = 30.

How do you convert 3/8 into a percentage?

Multiply the fraction by 100: (3/8) × 100 = 37.5%.

What is the percentage increase from 80 to 100?

The increase is 20. Percentage increase = (20/80) × 100 = 25%.

What is the percentage decrease from 500 to 425?

The decrease is 75. Percentage decrease = (75/500) × 100 = 15%.

What is 150% expressed as a fraction and decimal?

150% = 150/100 = 3/2 = 1.5.

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