How to Write 12 1/2 Percent as a Fraction

Understanding how to convert 12 1/2 percent to a fraction is a common requirement in mathematics. This article will guide you step-by-step through the process, and we will also touch on the fundamental concepts involved.

Step-by-Step Conversion

12 1/2 percent can be written as a fraction in a few different ways, but we will follow a straightforward procedure. Let's break it down:

Step 1: Convert the Mixed Number to an Improper Fraction

First, we convert the mixed number 12 1/2 to an improper fraction:

12 1/2 12 1/2 (12 * 2 1) / 2 25/2

Step 2: Convert the Percentage to a Fraction

Next, we need to convert this improper fraction into a fraction representing a percentage. To do this, we divide the fraction by 100:

(25/2) / 100 25/200

Step 3: Simplify the Fraction

Fraction simplification is our final step. 25/200 can be reduced by dividing both the numerator and the denominator by their greatest common divisor, which is 25:

25/200 1/8

Intuitive Approach

Another way to think about it is to recognize that 12 1/2 percent is a decimal, 12.5. This decimal can be directly converted to a fraction by considering 'percent' as 'per 100.' So, 12.5% is equivalent to 12.5/100, which simplifies to 25/200 and further to 1/8.

Or, you can observe that 12.5 is half of 25, and since 25 is 1/4, 12.5 is 1/8.

Understanding the Conversion

Writing 12 1/2 percent as a fraction involves converting between percentages, decimals, and fractions. Here are some key points:

1. Percent to Decimal Conversion

12 1/2 percent can be written as the decimal 12.5. This is because 'percent' means 'per 100,' and 12 1/2 percent is 12.5 per 100.

12.5 12.5 / 100

2. Eliminating Decimals with Multiplicative Identities

To remove the decimal, multiply the fraction by 10/10:

12.5 / 100 * 10/10 125 / 1000

This can be further simplified by dividing both the numerator and the denominator by 25:

125 / 1000 25 / 200 1 / 8

3. Visualizing with Cents

Another helpful way to visualize is to think of 12.5 cents in relation to 100 cents. Since 25 cents is 1/4 of 100 cents (25/100 1/4), and we are dealing with half of that, we end up with 1/8.

25/100 * 1/2 25/200 1/8

Conclusion

So, when you write 12 1/2 percent as a fraction, the answer is 1/8. Understanding this conversion process not only helps in solving mathematical problems but also in real-world applications where percentages and fractions are used interchangeably.

Related Keywords

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Frequently Asked Questions

What is the decimal form of 12 1/2 percent?
12 1/2 percent is equal to 0.125. Why is 12 1/2 percent equal to 1/8 as a fraction?
Because 12 1/2 percent, or 12.5%, is the same as 12.5/100, which simplifies to 25/200, and further to 1/8. Can you provide an intuitive example of 12 1/2 percent?
Yes, 12 1/2 percent is like taking half of 25 cents (1/4 of 100 cents) or 1/8 of 100.