12.5 as a fraction

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15-01-2025

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Understanding how to convert decimals to fractions is a fundamental skill in mathematics. This guide will walk you through the process of converting the decimal 12.5 into its fractional equivalent. We'll cover the steps involved and offer some helpful tips. By the end, you'll be able to confidently tackle similar decimal-to-fraction conversions.

Understanding Decimals and Fractions

Before we begin, let's quickly review the basics. A decimal represents a part of a whole number, using a decimal point to separate the whole number from its fractional part. A fraction, on the other hand, expresses a part of a whole number as a ratio of two integers (numerator and denominator).

Converting 12.5 to a Fraction: Step-by-Step

Here's how to convert 12.5 into a fraction:

Step 1: Write the decimal as a fraction over 1.

This is the first step in converting any decimal to a fraction. We write 12.5 as:

12.5/1

Step 2: Remove the decimal point.

To remove the decimal point, we multiply both the numerator and the denominator by 10 (since there's one digit after the decimal point). If there were two digits after the decimal, we'd multiply by 100, and so on.

(12.5 x 10) / (1 x 10) = 125/10

Step 3: Simplify the fraction.

Now, we simplify the fraction by finding the greatest common divisor (GCD) of the numerator (125) and the denominator (10). The GCD of 125 and 10 is 5. We divide both the numerator and the denominator by 5:

125 ÷ 5 = 25 10 ÷ 5 = 2

Therefore, the simplified fraction is:

25/2

Step 4: (Optional) Convert to a mixed number.

While 25/2 is a perfectly acceptable answer, we can also express it as a mixed number. A mixed number combines a whole number and a fraction. To do this, we divide the numerator (25) by the denominator (2):

25 ÷ 2 = 12 with a remainder of 1

This means 25/2 is equal to 12 and 1/2, or 12 ½.

Therefore, 12.5 as a fraction is 25/2 or 12 ½.

Other Examples: Converting Decimals to Fractions

Let's look at a few more examples to solidify your understanding:

• 0.75: This is 75/100, which simplifies to 3/4.
• 3.2: This is 32/10, which simplifies to 16/5 or 3 1/5.
• 0.6: This is 6/10, which simplifies to 3/5.

Practice Makes Perfect

The best way to master converting decimals to fractions is through practice. Try converting some decimals on your own, and check your answers using the steps outlined above. You can find plenty of practice exercises online. Remember, the key is to remove the decimal point by multiplying by the appropriate power of 10, then simplify the resulting fraction.

With a little practice, converting decimals like 12.5 to fractions will become second nature!