11.75 as a fraction

Daniel Parker

2 min read

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23-02-2025

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The decimal 11.75 might look intimidating as a fraction at first glance, but converting it is straightforward. This guide will show you how to convert 11.75 to a fraction, step-by-step, explaining the process along the way. We'll also explore different ways to represent the fraction and simplify it to its most basic form. Understanding this process will help you tackle similar decimal-to-fraction conversions.

Understanding Decimals and Fractions

Before we begin, let's quickly review the relationship between decimals and fractions. A decimal is a way of writing a fraction where the denominator is a power of 10 (10, 100, 1000, etc.). The decimal point separates the whole number part from the fractional part.

For example:

• 0.1 is the same as 1/10
• 0.01 is the same as 1/100
• 0.75 is the same as 75/100

Converting 11.75 to a Fraction: The Method

Here's how to convert 11.75 into a fraction:

Step 1: Write the decimal as a fraction with a denominator of 1.

11.75/1

Step 2: Multiply the numerator and denominator by 100 to remove the decimal.

This works because we have two digits after the decimal point (75). If there were three digits, we'd multiply by 1000, and so on.

(11.75 x 100) / (1 x 100) = 1175/100

Step 3: Simplify the fraction.

Find the greatest common divisor (GCD) of the numerator (1175) and the denominator (100). The GCD is 25. Divide both the numerator and denominator by the GCD to simplify:

1175 ÷ 25 = 47 100 ÷ 25 = 4

Therefore, the simplified fraction is 47/4.

Representing the Fraction in Different Forms

While 47/4 is the simplest form, we can also represent the fraction in other ways:

• Mixed Number: We can express it as a mixed number, which includes a whole number and a fraction. Since 47 divided by 4 is 11 with a remainder of 3, the mixed number is 11 3/4. This represents 11 whole units and 3/4 of another unit.

• Decimal: As we already know, the decimal representation is 11.75.

Why This Method Works

The core idea behind converting a decimal to a fraction involves understanding place value. Each digit after the decimal point represents a fraction with a denominator that's a power of 10. Multiplying by a power of 10 effectively shifts the decimal point to the right, converting the decimal into a whole number which then becomes the numerator of our fraction.

Practicing Decimal to Fraction Conversions

Try converting other decimals to fractions using this method. Start with simpler decimals and gradually work your way up to more complex ones. This practice will solidify your understanding and make future conversions easier. Remember, the key steps are:

1. Write the decimal over 1.
2. Multiply the numerator and denominator by a power of 10 to remove the decimal.
3. Simplify the resulting fraction.

By mastering this process, you'll gain confidence in handling various mathematical conversions. This skill is invaluable not only in math but also in various fields requiring numerical calculations.