Converting percentages to fractions might seem daunting at first, but with the right approach, it becomes a simple process. This guide provides easy-to-follow steps and examples to help you master this essential skill. Whether you're a student tackling math problems or someone needing this skill for everyday calculations, this guide is for you.
Understanding the Basics: Percentage and Fraction
Before diving into the conversion process, let's refresh our understanding of percentages and fractions.
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Percentage: A percentage represents a fraction of 100. The symbol "%" signifies "per hundred". For example, 25% means 25 out of 100.
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Fraction: A fraction represents a part of a whole. It's expressed as a ratio of two numbers: the numerator (top number) and the denominator (bottom number). For instance, 1/4 represents one part out of four equal parts.
Step-by-Step Guide: Converting Percentage to Fraction
Here's a breakdown of the process:
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Write the percentage as a fraction with a denominator of 100: This is the simplest step. Just place the percentage number over 100.
- Example: Convert 75% to a fraction. This becomes 75/100.
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Simplify the fraction (Reduce to the lowest terms): Find the greatest common divisor (GCD) of the numerator and denominator, and divide both by that number. This simplifies the fraction to its simplest form.
- Example: To simplify 75/100, find the GCD of 75 and 100. The GCD is 25. Divide both numerator and denominator by 25: 75 ÷ 25 = 3 and 100 ÷ 25 = 4. Therefore, 75/100 simplifies to 3/4.
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Check your answer: Ensure the fraction is in its lowest terms; no common factors other than 1 should exist between the numerator and denominator.
Examples to Practice
Let's work through a few more examples:
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Convert 20% to a fraction:
- Write as a fraction: 20/100
- Simplify: Both 20 and 100 are divisible by 20. 20 ÷ 20 = 1 and 100 ÷ 20 = 5.
- Simplified fraction: 1/5
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Convert 30% to a fraction:
- Write as a fraction: 30/100
- Simplify: Both 30 and 100 are divisible by 10. 30 ÷ 10 = 3 and 100 ÷ 10 = 10.
- Simplified fraction: 3/10
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Convert 12.5% to a fraction:
- Write as a fraction: 12.5/100 (Dealing with decimals is easy. Multiply the top and bottom by 10 to get rid of the decimal)
- This becomes: 125/1000
- Simplify: The GCD of 125 and 1000 is 125. 125 ÷ 125 = 1 and 1000 ÷ 125 = 8.
- Simplified fraction: 1/8
Tips and Tricks for Success
- Memorize common conversions: Familiarize yourself with common percentage-to-fraction conversions (e.g., 25% = 1/4, 50% = 1/2, 75% = 3/4) to speed up the process.
- Practice regularly: Consistent practice is key to mastering this skill. Work through various examples to build confidence and improve your speed.
- Use online calculators (for verification only): While calculators can help check your answers, actively working through the steps is crucial for understanding the concept.
By following these steps and practicing regularly, you'll quickly become proficient in converting percentages to fractions. This fundamental skill will prove invaluable in various mathematical and real-world applications.
