6/8 simplified

Simplifying 6/8: A Step-by-Step Guide

Introduction

In this article, we will explore the process of simplifying the fraction 6/8. We will explain what this question means and provide a step-by-step solution to find the simplified form of the fraction. Additionally, we will discuss the concept of finding the Greatest Common Divisor (GCD) or Highest Common Factor (HCF) and provide examples related to simplifying fractions.

What does this question mean?

When we are asked to simplify a fraction, it means we need to express it in its simplest form. This involves reducing the fraction to its lowest terms by dividing both the numerator and denominator by their greatest common divisor.

Answer: 6/8 simplified

Before diving into the method, let's find the answer to the question. The simplified form of 6/8 is 3/4.

Method: Tips

To simplify a fraction, follow these steps:

1. Find the GCD (or HCF) of the numerator and denominator.
2. Divide both the numerator and denominator by the GCD.
3. The resulting fraction is the simplified form.

Step-by-Step Solution

Now, let's go through the step-by-step solution to simplify 6/8:

Step 1: Find the GCD (or HCF) of 6 and 8.

• The factors of 6 are 1, 2, 3, and 6.
• The factors of 8 are 1, 2, 4, and 8.
• The common factors of 6 and 8 are 1 and 2.
• Therefore, the GCD (or HCF) of 6 and 8 is 2.

Step 2: Divide both the numerator and denominator by the GCD.

• Divide 6 by 2: 6/2 = 3.
• Divide 8 by 2: 8/2 = 4.

Step 3: The resulting fraction is 3/4, which is the simplified form of 6/8.

Solved Examples

Let's explore a few examples related to simplifying fractions:

Example 1: Simplify 12/16.

• Step 1: Find the GCD (or HCF) of 12 and 16.
  • The factors of 12 are 1, 2, 3, 4, 6, and 12.
  • The factors of 16 are 1, 2, 4, 8, and 16.
  • The common factors of 12 and 16 are 1, 2, and 4.
  • Therefore, the GCD (or HCF) of 12 and 16 is 4.
• Step 2: Divide both the numerator and denominator by 4.
  • Divide 12 by 4: 12/4 = 3.
  • Divide 16 by 4: 16/4 = 4.
• Step 3: The simplified form of 12/16 is 3/4.

Example 2: Simplify 9/27.

• Step 1: Find the GCD (or HCF) of 9 and 27.
  • The factors of 9 are 1, 3, and 9.
  • The factors of 27 are 1, 3, 9, and 27.
  • The common factors of 9 and 27 are 1, 3, and 9.
  • Therefore, the GCD (or HCF) of 9 and 27 is 9.
• Step 2: Divide both the numerator and denominator by 9.
  • Divide 9 by 9: 9/9 = 1.
  • Divide 27 by 9: 27/9 = 3.
• Step 3: The simplified form of 9/27 is 1/3.

How to find GCD (or HCF)?

To find the GCD (or HCF) of two numbers, follow these steps:

1. List all the factors of both numbers.
2. Identify the common factors.
3. The largest common factor is the GCD (or HCF).

By following these steps, you can determine the GCD (or HCF) of any given numbers.

Conclusion

In conclusion, simplifying a fraction involves expressing it in its simplest form. By finding the GCD (or HCF) of the numerator and denominator and dividing both by this value, we can obtain the simplified fraction. In the case of 6/8, the simplified form is 3/4. By understanding the concept of finding the GCD (or HCF) and following the step-by-step solution, we can simplify any fraction efficiently.