Calculate Percentages with Ease Worksheet for Students

Calculating Percentages with Ease: A Step-by-Step Guide for Students

Percentages are a fundamental concept in mathematics, and being able to calculate them with ease is a valuable skill for students of all ages. Whether you’re working with fractions, decimals, or real-world applications, understanding percentages can help you solve problems and make informed decisions. In this worksheet, we’ll walk you through the basics of calculating percentages, including how to convert between fractions, decimals, and percentages, and how to calculate percentage increases and decreases.

Converting between Fractions, Decimals, and Percentages

Before we dive into calculating percentages, it’s essential to understand how to convert between fractions, decimals, and percentages. Here are some key conversions to remember:

• To convert a fraction to a decimal, divide the numerator by the denominator.
• To convert a decimal to a percentage, multiply by 100.
• To convert a percentage to a decimal, divide by 100.
• To convert a decimal to a fraction, write the decimal as a fraction with a denominator of 10, 100, or 1000.

Calculating Percentage Increases

To calculate a percentage increase, you need to know the original value and the percentage increase. Here’s the formula:

New value = Original value + (Original value x Percentage increase)

For example, if the original value is $100 and the percentage increase is 20%, the new value would be:

New value = 100 + (100 x 0.20) = 100 + 20 = $120

Calculating Percentage Decreases

To calculate a percentage decrease, you need to know the original value and the percentage decrease. Here’s the formula:

New value = Original value - (Original value x Percentage decrease)

For example, if the original value is $100 and the percentage decrease is 15%, the new value would be:

New value = 100 - (100 x 0.15) = 100 - 15 = $85

Practice Exercises

Now that you’ve learned the basics of calculating percentages, it’s time to practice! Here are some exercises to help you reinforce your understanding:

1. Convert the following fractions to decimals and percentages:
   • ²⁄₃
   • ³⁄₅
   • ¹⁄₄
2. Calculate the percentage increase of the following values:
   • $50 increased by 25%
   • $200 increased by 10%
   • $300 increased by 5%
3. Calculate the percentage decrease of the following values:
   • $100 decreased by 20%
   • $500 decreased by 15%
   • $250 decreased by 10%

Answers

1. • ²⁄₃ = 0.67 = 67%
   • ³⁄₅ = 0.6 = 60%
   • ¹⁄₄ = 0.25 = 25%
2. • 50 increased by 25% = 62.50
   • 200 increased by 10% = 220
   • 300 increased by 5% = 315
3. • 100 decreased by 20% = 80
   • 500 decreased by 15% = 425
   • 250 decreased by 10% = 225

Tips and Tricks

• When converting between fractions, decimals, and percentages, make sure to line up the decimal points and use the correct conversion factors.
• When calculating percentage increases and decreases, make sure to use the correct formula and to convert the percentage to a decimal before multiplying or dividing.
• Practice, practice, practice! The more you practice calculating percentages, the more comfortable you’ll become with the formulas and conversions.

In Real-Life Scenarios

Calculating percentages is an essential skill in real-life scenarios, such as:

• Shopping: When calculating discounts and sales tax
• Cooking: When scaling recipes up or down
• Finance: When calculating interest rates and investment returns

By mastering the art of calculating percentages, you’ll be better equipped to tackle these real-life scenarios with confidence and accuracy.

In summary, calculating percentages is a valuable skill that requires practice and patience. By understanding how to convert between fractions, decimals, and percentages, and how to calculate percentage increases and decreases, you’ll be well on your way to becoming a math whiz. Remember to practice regularly and to apply your knowledge to real-life scenarios to reinforce your understanding.