What is Percentage?

🎯 Learning Objective

Understand percent as 'per 100' and convert between percentages, fractions and decimals instantly.

💡 Concept

• Percent means 'per 100' — 25% = 25 out of every 100
• x% of N = (x/100) × N
• Fraction ↔ percent family: 1/2=50%, 1/3=33.33%, 1/4=25%, 1/5=20%, 1/8=12.5%, 1/10=10%
• 10% of any number → just move the decimal one place left
• a% of b = b% of a (e.g. 8% of 50 = 50% of 8 = 4)

🧮 Key Formulas

x% of N = (x × N) / 100

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a% of b = b% of a

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1/8 = 12.5%, 1/6 = 16.67%, 1/3 = 33.33%

✏️ Easy Example

Q. Find 30% of 250.

1. 10% of 250 = 25
2. 30% = 3 × 25

Answer: 75

🇮🇳 Real-Life Example

Your phone battery at 40% — if full charge lasts 20 hours, you have 8 hours left. That's 40% of 20.

📝 Exam-Level Example

Q. A student scored 540 marks out of 900. Find the percentage.

1. Percentage = (540/900) × 100
2. 540/900 = 0.6
3. 0.6 × 100 = 60

Answer: 60%

📝 Exam-Level Example

Q. What is 12.5% of 640?

1. 12.5% = 1/8
2. 640 ÷ 8 = 80

Answer: 80

🪄 Memory Trick

Convert % to fractions before calculating: 12.5%→1/8, 16.67%→1/6, 37.5%→3/8. Division beats multiplication.

⚠️ Common Mistakes

• ❌ Dividing by the wrong base (percentage is always OF the total)
• ❌ Writing 1/3 as 30% (it's 33.33%)

🏆 Exam Tips

• ✅ Memorise the fraction–percent table from 1/2 to 1/12
• ✅ Use a% of b = b% of a to flip hard calculations

📌 Summary

• Percent = per 100
• x% of N = xN/100
• Fraction table is your speed weapon
• a% of b = b% of a