How To Convert 6.75 Into Fraction Form: A Step-By-Step Guide

Converting decimal numbers into fraction form can seem daunting at first, but it's actually a straightforward process once you get the hang of it! In this guide, we will walk you through the steps to convert the decimal 6.75 into a fraction. We’ll also share some helpful tips and common mistakes to avoid. So, let’s dive in! 😊

Understanding the Basics

Before we start, it’s important to understand what a fraction is. A fraction consists of two parts: the numerator (the top number) and the denominator (the bottom number). In the case of converting a decimal to a fraction, our goal is to express the decimal in this fraction format.

Step 1: Separate the Whole Number and Decimal Part

The first step in converting 6.75 into a fraction is to break it down into its whole number and decimal components.

• Whole Number: The whole part of 6.75 is 6.
• Decimal Part: The decimal part is 0.75.

At this point, we can represent 6.75 as:

[ 6.75 = 6 + 0.75 ]

Step 2: Convert the Decimal to a Fraction

Next, we need to convert the decimal part (0.75) into a fraction.

0.75 can be written as:

[ 0.75 = \frac{75}{100} ]

Step 3: Simplify the Fraction

Now, let’s simplify (\frac{75}{100}). To do this, we need to find the greatest common divisor (GCD) of 75 and 100.

Both numbers can be divided by 25:

[ \frac{75 \div 25}{100 \div 25} = \frac{3}{4} ]

Step 4: Combine the Whole Number and Fraction

Now that we have converted 0.75 into the fraction (\frac{3}{4}), we can combine this with the whole number part.

Thus, we can express 6.75 as:

[ 6.75 = 6 + \frac{3}{4} ]

Step 5: Write as an Improper Fraction

To convert this into an improper fraction, we will use the following formula:

[ \text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator}\right) + \text{Numerator} ]

For our example, that looks like this:

[ 6 + \frac{3}{4} = \frac{6 \times 4 + 3}{4} = \frac{24 + 3}{4} = \frac{27}{4} ]

And there you have it! The decimal 6.75 is equivalent to the fraction (\frac{27}{4}).

Quick Summary Table

To summarize, here’s a quick table detailing the steps taken to convert 6.75 into fraction form:

<table> <tr> <th>Step</th> <th>Description</th> <th>Result</th> </tr> <tr> <td>1</td> <td>Separate whole number and decimal</td> <td>6 and 0.75</td> </tr> <tr> <td>2</td> <td>Convert decimal to fraction</td> <td>(\frac{75}{100})</td> </tr> <tr> <td>3</td> <td>Simplify the fraction</td> <td>(\frac{3}{4})</td> </tr> <tr> <td>4</td> <td>Combine whole number and fraction</td> <td>6 + (\frac{3}{4})</td> </tr> <tr> <td>5</td> <td>Convert to improper fraction</td> <td>(\frac{27}{4})</td> </tr> </table>

Common Mistakes to Avoid

When converting decimals to fractions, here are some pitfalls to avoid:

1. Forgetting to Simplify: Always remember to simplify the fraction when you can!
2. Incorrectly Separating the Whole Number: Ensure you properly identify the whole number and decimal components.
3. Rounding Off: Be careful not to round the decimal prematurely; use the exact value instead.

Troubleshooting Issues

If you find yourself stuck or your fraction doesn't look right, consider these tips:

• Recheck your division while simplifying.
• Make sure you correctly identified the decimal as a fraction.
• If you’re having trouble with simplification, use a GCD calculator or list out the factors.

<div class="faq-section"> <div class="faq-container"> <h2>Frequently Asked Questions</h2> <div class="faq-item"> <div class="faq-question"> <h3>What is the fraction form of 0.5?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>0.5 can be converted to the fraction 1/2.</p> </div> </div> <div class="faq-item"> <div class="faq-question"> <h3>How do you simplify a fraction?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>Find the GCD of the numerator and denominator and divide both by that number.</p> </div> </div> <div class="faq-item"> <div class="faq-question"> <h3>Can all decimals be converted to fractions?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>Yes, all decimal numbers can be expressed as a fraction.</p> </div> </div> <div class="faq-item"> <div class="faq-question"> <h3>Is 6.75 a rational number?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>Yes, 6.75 is a rational number because it can be expressed as a fraction.</p> </div> </div> </div> </div>

Recap of what we've learned today: We started by separating the whole number from the decimal, converting the decimal to a fraction, simplifying that fraction, and finally combining it back with the whole number to get the improper fraction (\frac{27}{4}). Remember to practice this process, as it will make converting other decimals much easier!

Feel free to explore more tutorials on fractions and decimals in this blog. The more you practice, the more confident you’ll become!

<p class="pro-note">✨Pro Tip: Always double-check your work and don’t hesitate to ask for help if you're stuck!</p>