Percentage Calculator Notes

Master percentage calculations with practical examples, real-world applications, and expert tips to avoid common mistakes.

💡Understanding Percentages

A percentage is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin "per centum," meaning "by the hundred."

Key Concepts:

25% = 25 out of 100 = 0.25 as a decimal = ¼ as a fraction
50% = 50 out of 100 = 0.50 as a decimal = ½ as a fraction
100% = the whole amount = 1.00 as a decimal

🌍Real-World Applications

💰 Shopping & Discounts

Example: A $80 jacket is 25% off

📊 Statistics & Data

Example: 180 out of 240 students passed

💳 Finance & Interest

Example: Credit card charges 18% annual interest

On a $1,000 balance for one year:

📈 Business & Growth

Example: Sales increased from $50,000 to $65,000

📋Step-by-Step Examples

Example 1: Calculating Tips

Problem: Your restaurant bill is $85. You want to leave a 20% tip.

Step 1: Convert percentage to decimal

Step 2: Multiply bill by decimal

Step 3: Add tip to bill

Example 2: Grade Percentage

Problem: You scored 42 points out of 50 on a test. What's your percentage?

Step 1: Set up the fraction

Step 2: Convert to percentage

Your grade is 84%

⚠️Common Mistakes to Avoid

❌ Mistake 1: Confusing "of" and "more than"

Wrong: "25% of 100" vs "25% more than 100"

Correct:

❌ Mistake 2: Wrong base for percentage change

Problem: Price changes from $80 to $100. What's the percentage change?

Wrong Base (new value):

Correct Base (original value):

❌ Mistake 3: Decimal placement errors

Remember: Moving the decimal point incorrectly

Wrong:

Correct:

💡Pro Tips & Shortcuts

🧮 Mental Math Shortcuts

10%: Move decimal one place left
20%: Find 10%, then double it
25%: Divide by 4
50%: Divide by 2
75%: Find 50% + 25%

🎯 Estimation Techniques

Example: 23% of 89

Round to easier numbers: 25% of 90

✅ Double-Check Methods

Reverse calculation: If 20% of X = 40, then X should be 200
Reasonableness: 150% of 100 should be more than 100
Unit check: Percentage × Number = Same units as number

🔄 Quick Conversions

0.25 = ¼ = 25%

0.5 = ½ = 50%

0.75 = ¾ = 75%

📝Practice Problems

Try These:

1. What is 15% of 240?
2. 45 is what percent of 180?
3. A $150 item is 30% off. What's the sale price?
4. Population grew from 8,000 to 10,400. What's the percentage increase?

Answers:

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