3/9 simplified

Simplifying 3/9: A Step-by-Step Solution

Introduction

In this article, we will explore the process of simplifying the fraction 3/9. 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?

The question "What is the answer to 3/9 simplified?" is asking for the simplified form of the fraction 3/9. Simplifying a fraction involves reducing it to its simplest form by dividing both the numerator and denominator by their greatest common divisor.

Answer: 3/9 simplified

To find the simplified form of 3/9, we need to determine the GCD of the numerator (3) and the denominator (9) and divide both by this common factor. The simplified form of 3/9 is 1/3.

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

Let's apply the method mentioned above to simplify 3/9:

Step 1: Find the GCD of 3 and 9.

• The factors of 3 are 1 and 3.
• The factors of 9 are 1, 3, and 9.
• The GCD of 3 and 9 is 3.

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

• 3 ÷ 3 = 1
• 9 ÷ 3 = 3

Step 3: The simplified fraction is 1/3.

Therefore, the simplified form of 3/9 is 1/3.

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, the simplified form of 6/12 is 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, the simplified form of 9/15 is 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 of the numerator and denominator and dividing both by this common factor. In the case of 3/9, the simplified form is 1/3. By following the step-by-step solution provided in this article, you can easily simplify fractions and express them in their simplest form.