Solved Problems: Finding a Percent of a Quantity for 6th Graders

📚 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 "out of one hundred." So, when we say 25%, we mean 25 out of every 100.

📜 A Brief History

The concept of percentages has been around for centuries. Ancient Romans used fractions similar to percentages when calculating taxes and interest rates. However, the modern percentage symbol (%) didn't appear until much later, evolving from abbreviations used in 15th-century mercantile arithmetic.

🔑 Key Principles for Finding a Percent of a Quantity

• 🔢 Convert the percentage to a decimal: Divide the percentage by 100. For example, 20% becomes $20 \div 100 = 0.20$.
• ✖️ Multiply the decimal by the quantity: Multiply the decimal you just found by the total quantity. For example, to find 20% of 50, multiply $0.20 \times 50$.
• ✅ The result is the percentage of the quantity: The answer you get after multiplying is the percentage of the original quantity. In our example, $0.20 \times 50 = 10$, so 20% of 50 is 10.

🌍 Real-World Examples

• 🛍️ Discounts: If a shirt costs $25 and is 30% off, you can calculate the discount by finding 30% of $25. $0.30 \times 25 = $7.50$ off.
• 🍕 Splitting a bill: If your share of a restaurant bill is $15 and you want to leave a 15% tip, calculate 15% of $15. $0.15 \times 15 = $2.25$ tip.
• 📊 Test scores: If you get 80 out of 100 questions right on a test, you can say you scored 80%.

💡 Tips and Tricks

• ➗ Dividing by 100: To quickly convert a percentage to a decimal, move the decimal point two places to the left (e.g., 50% becomes 0.50).
• 🧮 Estimating: To estimate a percentage, round the numbers to make the calculation easier (e.g., to find approximately 26% of 82, round to 25% of 80, which is $0.25 \times 80 = 20$).
• 📝 Practice: The more you practice, the easier it will become to find percentages!

✍️ Practice Quiz

Let's test your knowledge! Solve the following problems:

1. ❓ What is 10% of 80?
2. ❓ What is 25% of 40?
3. ❓ What is 50% of 60?
4. ❓ What is 75% of 20?
5. ❓ What is 20% of 150?
6. ❓ What is 5% of 100?
7. ❓ What is 1% of 200?

Answers:

1. 8
2. 10
3. 30
4. 15
5. 30
6. 5
7. 2

✅ Conclusion

Finding a percent of a quantity is a fundamental skill with many practical applications. By understanding the basic principles and practicing regularly, you'll master this concept in no time!