Converting percentages to fractions might seem daunting, but it's a straightforward process once you understand the underlying concept. This guide breaks down the steps into simple, easy-to-follow instructions, ensuring you master this essential skill.
Understanding the Basics: Percentage and Fractions
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. For example, 25% means 25 out of 100.
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Fraction: A fraction represents a part of a whole, expressed as a ratio of two numbers (numerator/denominator). For example, 1/4 represents one part out of four equal parts.
The core idea behind converting a percentage to a fraction is to express the percentage as a fraction with a denominator of 100, and then simplify the fraction to its lowest terms.
Step-by-Step Guide: Percentage to Fraction Conversion
Follow these simple steps to convert any percentage to a fraction:
Step 1: Write the Percentage as a Fraction with a Denominator of 100
This is the easiest part. Simply take the percentage value and place it over 100.
Example: Convert 75% to a fraction.
75% becomes 75/100
Step 2: Simplify the Fraction
This step involves finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it. The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder.
Example (continued): Simplify 75/100
The GCD of 75 and 100 is 25. Divide both the numerator and the denominator by 25:
75 ÷ 25 = 3 100 ÷ 25 = 4
Therefore, 75/100 simplifies to 3/4.
Step 3: Express the Fraction in its Lowest Terms
Once you've simplified the fraction, ensure it's in its simplest form, meaning no further simplification is possible. This is your final answer.
Example (continued): 3/4 is already in its simplest form.
Practice Examples: Mastering the Conversion
Let's work through a few more examples to solidify your understanding:
Example 1: Convert 20% to a fraction.
- 20% = 20/100
- Simplify: GCD of 20 and 100 is 20. 20/100 ÷ 20/20 = 1/5
- Answer: 1/5
Example 2: Convert 60% to a fraction.
- 60% = 60/100
- Simplify: GCD of 60 and 100 is 20. 60/100 ÷ 20/20 = 3/5
- Answer: 3/5
Example 3: Convert 12.5% to a fraction.
- 12.5% = 12.5/100 (Dealing with decimals? Multiply the numerator and denominator by 10 to remove the decimal: 125/1000)
- Simplify: GCD of 125 and 1000 is 125. 125/1000 ÷ 125/125 = 1/8
- Answer: 1/8
Tips for Success: Become a Percentage to Fraction Pro
- Practice regularly: The more you practice, the faster and more accurate you'll become.
- Use online calculators (for verification only): Use online calculators to check your answers, but focus on understanding the process.
- Master finding the GCD: Understanding how to find the greatest common divisor is crucial for simplifying fractions effectively.
By following these steps and practicing regularly, you'll quickly master the art of converting percentages to fractions. Remember, the key is to understand the relationship between percentages and fractions – that a percentage is simply a fraction out of 100.
