📊 How to Calculate Percentage: A Complete Guide

📊 How to Calculate Percentage: A Complete Guide

Percentage is a fundamental concept used in mathematics, finance, statistics, and everyday life. Whether you're calculating exam scores, discounts, profit margins, or interest rates, understanding how to calculate percentages is essential.

This guide will explain all possible ways to calculate percentages with formulas, examples, and practical applications.

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📌 Table of Contents

1. What is a Percentage?
2. Basic Percentage Formula
3. How to Find a Percentage of a Number
4. How to Convert Fractions & Decimals to Percentages
5. How to Calculate Percentage Increase & Decrease
6. How to Find What Percentage One Number is of Another
7. How to Reverse a Percentage Calculation
8. Percentage Applications in Real Life
9. Frequently Asked Questions (FAQs)

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🔢 What is a Percentage? <a name="what-is-percentage"></a>

A percentage (%) represents a part of 100. It tells us how much out of 100 something is.

🔹 Example: 50% means 50 out of 100.
🔹 1% means 1 out of 100.
🔹 100% means the whole (1).

A percentage can also be represented as:

• A fraction (e.g., 50% = 50/100 = 1/2)
• A decimal (e.g., 50% = 0.50)

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📏 Basic Percentage Formula <a name="basic-formula"></a>

The fundamental formula for percentage is:

$$\text{Percentage} = \left( \frac{\text{Part}}{\text{Total}} \right) \times 100$$

🔹 Example: If you scored 40 marks out of 50, the percentage is:

$$\left( \frac{40}{50} \right) \times 100 = 80\%$$

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🧮 How to Find a Percentage of a Number <a name="percentage-of-number"></a>

✅ Formula:

$$\left( \frac{\text{Percentage}}{100} \right) \times \text{Total Number}$$

🔹 Example 1: Find 20% of 150.

$$\left( \frac{20}{100} \right) \times 150 = 30$$

Answer: 30

🔹 Example 2: Find 75% of 200.

$$\left( \frac{75}{100} \right) \times 200 = 150$$

Answer: 150

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🔄 How to Convert Fractions & Decimals to Percentages <a name="convert-fractions"></a>

✅ Convert Fractions to Percentages

$$\text{Percentage} = \left( \frac{\text{Numerator}}{\text{Denominator}} \right) \times 100$$

🔹 Example: Convert 3/5 to percentage.

$$\left( \frac{3}{5} \right) \times 100 = 60\%$$

✅ Convert Decimals to Percentages

Multiply the decimal by 100.

🔹 Example: Convert 0.75 to percentage.

$$0.75 \times 100 = 75\%$$

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📈 How to Calculate Percentage Increase & Decrease <a name="percentage-change"></a>

✅ Formula for Percentage Increase:

$$\left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100$$

🔹 Example: If a product's price increases from ₹500 to ₹650, the percentage increase is:

$$\left( \frac{650 - 500}{500} \right) \times 100 = 30\%$$

✅ Formula for Percentage Decrease:

$$\left( \frac{\text{Old Value} - \text{New Value}}{\text{Old Value}} \right) \times 100$$

🔹 Example: If a phone's price drops from ₹40,000 to ₹35,000, the percentage decrease is:

$$\left( \frac{40,000 - 35,000}{40,000} \right) \times 100 = 12.5\%$$

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🔢 How to Find What Percentage One Number is of Another <a name="percentage-of-another"></a>

✅ Formula:

$$\left( \frac{\text{Part}}{\text{Total}} \right) \times 100$$

🔹 Example: What percentage is 30 out of 80?

$$\left( \frac{30}{80} \right) \times 100 = 37.5\%$$

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🔄 How to Reverse a Percentage Calculation <a name="reverse-percentage"></a>

Sometimes, we need to find the original value before a percentage change.

✅ Formula to Find the Original Value:

$$\text{Original Value} = \frac{\text{New Value}}{(1 + \frac{\text{Percentage Increase}}{100})}$$

🔹 Example: A phone is now ₹12,000 after a 20% increase. What was the original price?

$$\text{Original Value} = \frac{12,000}{1.20} = 10,000$$

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🌍 Percentage Applications in Real Life <a name="real-life-applications"></a>

✅ Bank Interest Rates – Calculate interest on savings, loans, and EMIs.
✅ Discounts & Shopping – Find sale prices and final amounts.
✅ Profit & Loss – Used in business calculations.
✅ Health & Fitness – Calculate body fat percentage, calorie intake, etc.
✅ Exams & Grades – Convert marks into percentages for results.

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❓ Frequently Asked Questions (FAQs) <a name="faqs"></a>

🔹 What is 1% of a number?
✅ Formula:

$$\frac{1}{100} \times \text{Total}$$

🔹 How do I increase a number by a percentage?
✅ Formula:

$$\text{New Value} = \text{Original Value} + \left( \frac{\text{Percentage Increase}}{100} \times \text{Original Value} \right)$$

🔹 How do I decrease a number by a percentage?
✅ Formula:

$$\text{New Value} = \text{Original Value} - \left( \frac{\text{Percentage Decrease}}{100} \times \text{Original Value} \right)$$

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🎯 Final Thoughts

Percentages are an essential part of daily life, from finance and shopping to health and business. Knowing how to calculate percentages in different ways helps in making better financial and personal decisions.

💡 Tip: Practice with real-life examples like shopping discounts, bank interest, and exam scores to master percentages!

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