6/9+4/5+3/8 How Much Is It

Feb 28, 2025 by ADMIN 27 views

6/9 + 4/5 + 3/8: A Step-by-Step Guide to Simplifying Fractions

Introduction

When it comes to adding fractions, it can be a daunting task, especially when dealing with different denominators. However, with a clear understanding of the concept and a step-by-step approach, you can simplify fractions and arrive at the correct answer. In this article, we will explore the process of adding fractions, using the example 6/9 + 4/5 + 3/8.

Understanding Fractions

Before we dive into the example, let's take a moment to understand what fractions are. A fraction is a way to represent a part of a whole. It consists of two parts: the numerator (the top number) and the denominator (the bottom number). The numerator tells us how many equal parts we have, while the denominator tells us how many parts the whole is divided into.

For example, in the fraction 1/2, the numerator is 1 and the denominator is 2. This means we have 1 equal part out of a total of 2 parts.

Adding Fractions with Different Denominators

When adding fractions with different denominators, we need to find a common denominator. The common denominator is the smallest multiple that both denominators can divide into evenly.

Let's take the example 6/9 + 4/5 + 3/8. To add these fractions, we need to find a common denominator.

Finding the Least Common Multiple (LCM)

To find the common denominator, we need to find the least common multiple (LCM) of the denominators 9, 5, and 8.

The LCM of 9, 5, and 8 is 360.

Converting Fractions to Have the Same Denominator

Now that we have the common denominator, we need to convert each fraction to have the same denominator.

6/9 = (6 x 40) / (9 x 40) = 240/360
4/5 = (4 x 72) / (5 x 72) = 288/360
3/8 = (3 x 45) / (8 x 45) = 135/360

Adding the Fractions

Now that we have all the fractions with the same denominator, we can add them together.

240/360 + 288/360 + 135/360 = 663/360

Simplifying the Fraction

The fraction 663/360 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD).

The GCD of 663 and 360 is 3.

663 ÷ 3 = 221 360 ÷ 3 = 120

So, the simplified fraction is 221/120.

Conclusion

Adding fractions with different denominators requires finding a common denominator and converting each fraction to have the same denominator. In this article, we used the example 6/9 + 4/5 + 3/8 to demonstrate the process of adding fractions and simplifying the result. By following these steps, you can simplify fractions and arrive at the correct answer.

Frequently Asked Questions

What is the least common multiple (LCM) of 9, 5, and 8? The LCM of 9, 5, and 8 is 360.
How do I convert a fraction to have a different denominator? To convert a fraction to have a different denominator, multiply the numerator and the denominator by the same number.
How do I simplify a fraction? To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD).

Additional Resources

Mathway: A math problem solver that can help you with fractions and other math concepts.
Khan Academy: A free online resource that offers video lessons and practice exercises on fractions and other math topics.
Wolfram Alpha: A computational knowledge engine that can help you with fractions and other math concepts.

Final Answer

The final answer to the problem 6/9 + 4/5 + 3/8 is 221/120.

Introduction

In our previous article, we explored the process of adding fractions with different denominators, using the example 6/9 + 4/5 + 3/8. We found the least common multiple (LCM) of the denominators, converted each fraction to have the same denominator, and simplified the result. In this article, we will answer some frequently asked questions related to the topic.

Q&A

Q: What is the least common multiple (LCM) of 9, 5, and 8?

A: The LCM of 9, 5, and 8 is 360.

Q: How do I convert a fraction to have a different denominator?

A: To convert a fraction to have a different denominator, multiply the numerator and the denominator by the same number. For example, to convert 1/2 to have a denominator of 4, multiply the numerator and the denominator by 2: (1 x 2) / (2 x 2) = 2/4.

Q: How do I simplify a fraction?

A: To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD). For example, to simplify 6/8, find the GCD of 6 and 8, which is 2. Then, divide both the numerator and the denominator by 2: (6 ÷ 2) / (8 ÷ 2) = 3/4.

Q: What is the difference between a numerator and a denominator?

A: The numerator is the top number in a fraction, and it tells us how many equal parts we have. The denominator is the bottom number in a fraction, and it tells us how many parts the whole is divided into.

Q: Can I add fractions with different signs?

A: Yes, you can add fractions with different signs. When adding fractions with different signs, you need to find a common denominator and then add the numerators. For example, to add 2/3 and -1/4, find the LCM of 3 and 4, which is 12. Then, convert each fraction to have a denominator of 12: (2 x 4) / (3 x 4) = 8/12 and (-1 x 3) / (4 x 3) = -3/12. Finally, add the numerators: 8/12 + (-3/12) = 5/12.

Q: Can I subtract fractions with different signs?

A: Yes, you can subtract fractions with different signs. When subtracting fractions with different signs, you need to find a common denominator and then subtract the numerators. For example, to subtract 2/3 and -1/4, find the LCM of 3 and 4, which is 12. Then, convert each fraction to have a denominator of 12: (2 x 4) / (3 x 4) = 8/12 and (-1 x 3) / (4 x 3) = -3/12. Finally, subtract the numerators: 8/12 - (-3/12) = 11/12.

Q: Can I multiply fractions with different signs?

A: Yes, you can multiply fractions with different signs. When multiplying fractions with different signs, you need to multiply the numerators and the denominators separately. For example, to multiply 2/3 and -1/4, multiply the numerators and the denominators: (2 x -1) / (3 x 4) = -2/12.

Q: Can I divide fractions with different signs?

A: Yes, you can divide fractions with different signs. When dividing fractions with different signs, you need to invert the second fraction (i.e., flip the numerator and the denominator) and then multiply the fractions. For example, to divide 2/3 by -1/4, invert the second fraction: -1/4 becomes 4/-1. Then, multiply the fractions: (2 x 4) / (3 x -1) = 8/-3.