4/8 simplified

Simplifying 4/8: A Step-by-Step Solution

Introduction

In this article, we will explore the process of simplifying the fraction 4/8. 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 by dividing both the numerator and denominator by their greatest common divisor (GCD) or highest common factor (HCF). The simplified fraction will have the smallest possible numerator and denominator.

Answer: 4/8 simplified

To find the simplified form of 4/8, we need to determine the GCD of the numerator (4) and the denominator (8) and divide both by this value. The simplified form of 4/8 is 1/2.

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 4/8:

Step 1: Find the GCD (or HCF) of 4 and 8. The factors of 4 are 1, 2, and 4. The factors of 8 are 1, 2, 4, and 8. The GCD of 4 and 8 is 4.

Step 2: Divide both the numerator and denominator by the GCD. 4 ÷ 4 = 1 8 ÷ 4 = 2

Step 3: The simplified fraction is 1/2.

Therefore, 4/8 simplified is equal to 1/2.

Solved Examples

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

Example 1: Simplify 6/12. Step 1: Find the GCD of 6 and 12. The factors of 6 are 1, 2, 3, and 6. The factors of 12 are 1, 2, 3, 4, 6, and 12. The GCD of 6 and 12 is 6.

Step 2: Divide both the numerator and denominator by the GCD. 6 ÷ 6 = 1 12 ÷ 6 = 2

Step 3: The simplified fraction is 1/2.

Therefore, 6/12 simplified is equal to 1/2.

Example 2: Simplify 9/15. Step 1: Find the GCD of 9 and 15. The factors of 9 are 1, 3, and 9. The factors of 15 are 1, 3, 5, and 15. The GCD of 9 and 15 is 3.

Step 2: Divide both the numerator and denominator by the GCD. 9 ÷ 3 = 3 15 ÷ 3 = 5

Step 3: The simplified fraction is 3/5.

Therefore, 9/15 simplified is equal to 3/5.

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).

For example, to find the GCD of 12 and 18: The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. The common factors are 1, 2, 3, and 6. The largest common factor is 6.

Therefore, the GCD of 12 and 18 is 6.

Conclusion

Simplifying fractions involves finding the GCD (or HCF) of the numerator and denominator and dividing both by this value. By following the step-by-step solution, we can easily simplify fractions like 4/8. Remember to always express fractions in their simplest form to make calculations and comparisons easier.