$\[ \frac{8}{6} + \left(-\frac{9}{5}\right) = \square \\]Related Content:Adding Fractions With Different Signs

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Introduction

Adding fractions with different signs can be a challenging task, especially when dealing with negative numbers. However, with a clear understanding of the concept and the right approach, it can be made easier. In this article, we will delve into the world of adding fractions with different signs, exploring the rules and techniques that will help you master this mathematical operation.

What are Fractions?

Fractions are a way to represent a part of a whole. They consist of two parts: the numerator (the top number) and the denominator (the bottom number). For example, the fraction 3/4 represents three equal parts out of a total of four parts. Fractions can be positive or negative, depending on the sign of the numerator.

Adding Fractions with Different Signs

When adding fractions with different signs, we need to follow a specific set of rules. The first rule is to find a common denominator, which is the least common multiple (LCM) of the two denominators. Once we have the common denominator, we can add the numerators while keeping the denominator the same.

Example 1: Adding a Positive and a Negative Fraction

Let's consider the following example:

86+(−95)=□\frac{8}{6} + \left(-\frac{9}{5}\right) = \square

To add these fractions, we need to find a common denominator. The LCM of 6 and 5 is 30. We can rewrite the fractions with the common denominator:

86=8×56×5=4030\frac{8}{6} = \frac{8 \times 5}{6 \times 5} = \frac{40}{30}

(−95)=(−9×65×6)=(−5430)\left(-\frac{9}{5}\right) = \left(-\frac{9 \times 6}{5 \times 6}\right) = \left(-\frac{54}{30}\right)

Now that we have the common denominator, we can add the numerators:

4030+(−5430)=40−5430=−1430\frac{40}{30} + \left(-\frac{54}{30}\right) = \frac{40 - 54}{30} = \frac{-14}{30}

Example 2: Adding Two Negative Fractions

Let's consider another example:

(−34)+(−23)=□\left(-\frac{3}{4}\right) + \left(-\frac{2}{3}\right) = \square

To add these fractions, we need to find a common denominator. The LCM of 4 and 3 is 12. We can rewrite the fractions with the common denominator:

(−34)=(−3×34×3)=(−912)\left(-\frac{3}{4}\right) = \left(-\frac{3 \times 3}{4 \times 3}\right) = \left(-\frac{9}{12}\right)

(−23)=(−2×43×4)=(−812)\left(-\frac{2}{3}\right) = \left(-\frac{2 \times 4}{3 \times 4}\right) = \left(-\frac{8}{12}\right)

Now that we have the common denominator, we can add the numerators:

(−912)+(−812)=(−9−812)=(−112)\left(-\frac{9}{12}\right) + \left(-\frac{8}{12}\right) = \left(-\frac{9 - 8}{12}\right) = \left(-\frac{1}{12}\right)

Tips and Tricks

Adding fractions with different signs can be challenging, but with practice and patience, you can master this mathematical operation. Here are some tips and tricks to help you:

  • Find the common denominator: The common denominator is the key to adding fractions with different signs. Make sure to find the least common multiple (LCM) of the two denominators.
  • Rewrite the fractions: Once you have the common denominator, rewrite the fractions with the common denominator.
  • Add the numerators: With the common denominator, you can add the numerators while keeping the denominator the same.
  • Simplify the fraction: Finally, simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD).

Conclusion

Adding fractions with different signs may seem daunting at first, but with the right approach and practice, it can be made easier. By following the rules and techniques outlined in this article, you can master this mathematical operation and become more confident in your ability to add fractions with different signs.

Frequently Asked Questions

Q: What is the common denominator?

A: The common denominator is the least common multiple (LCM) of the two denominators.

Q: How do I find the common denominator?

A: To find the common denominator, list the multiples of each denominator and find the smallest multiple that is common to both.

Q: What is the difference between adding fractions with different signs and adding fractions with the same sign?

A: When adding fractions with different signs, we need to find a common denominator and add the numerators while keeping the denominator the same. When adding fractions with the same sign, we can simply add the numerators and keep the denominator the same.

Q: Can I add fractions with different signs without finding the common denominator?

A: No, you cannot add fractions with different signs without finding the common denominator. The common denominator is the key to adding fractions with different signs.

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Introduction

Adding fractions with different signs can be a challenging task, especially when dealing with negative numbers. However, with a clear understanding of the concept and the right approach, it can be made easier. In this article, we will delve into the world of adding fractions with different signs, exploring the rules and techniques that will help you master this mathematical operation.

Q&A: Adding Fractions with Different Signs

Q: What is the rule for adding fractions with different signs?

A: The rule for adding fractions with different signs is to find a common denominator, rewrite the fractions with the common denominator, add the numerators while keeping the denominator the same, and simplify the fraction.

Q: How do I find the common denominator?

A: To find the common denominator, list the multiples of each denominator and find the smallest multiple that is common to both.

Q: What is the difference between adding fractions with different signs and adding fractions with the same sign?

A: When adding fractions with different signs, we need to find a common denominator and add the numerators while keeping the denominator the same. When adding fractions with the same sign, we can simply add the numerators and keep the denominator the same.

Q: Can I add fractions with different signs without finding the common denominator?

A: No, you cannot add fractions with different signs without finding the common denominator. The common denominator is the key to adding fractions with different signs.

Q: How do I add fractions with different signs when the denominators are not multiples of each other?

A: When the denominators are not multiples of each other, you can find the least common multiple (LCM) of the two denominators and rewrite the fractions with the LCM as the denominator.

Q: What is the least common multiple (LCM)?

A: The least common multiple (LCM) is the smallest multiple that is common to both numbers.

Q: How do I find the LCM of two numbers?

A: To find the LCM of two numbers, list the multiples of each number and find the smallest multiple that is common to both.

Q: Can I add fractions with different signs when the denominators are the same?

A: Yes, you can add fractions with different signs when the denominators are the same. In this case, you can simply add the numerators and keep the denominator the same.

Q: How do I add fractions with different signs when the numerators are the same?

A: When the numerators are the same, you can subtract the denominators to find the sum.

Q: What is the difference between adding and subtracting fractions with different signs?

A: When adding fractions with different signs, we need to find a common denominator and add the numerators while keeping the denominator the same. When subtracting fractions with different signs, we need to find a common denominator and subtract the numerators while keeping the denominator the same.

Q: Can I add or subtract fractions with different signs without finding the common denominator?

A: No, you cannot add or subtract fractions with different signs without finding the common denominator. The common denominator is the key to adding and subtracting fractions with different signs.

Conclusion

Adding fractions with different signs may seem daunting at first, but with the right approach and practice, it can be made easier. By following the rules and techniques outlined in this article, you can master this mathematical operation and become more confident in your ability to add fractions with different signs.

Frequently Asked Questions

Q: What is the common denominator?

A: The common denominator is the least common multiple (LCM) of the two denominators.

Q: How do I find the common denominator?

A: To find the common denominator, list the multiples of each denominator and find the smallest multiple that is common to both.

Q: What is the difference between adding fractions with different signs and adding fractions with the same sign?

A: When adding fractions with different signs, we need to find a common denominator and add the numerators while keeping the denominator the same. When adding fractions with the same sign, we can simply add the numerators and keep the denominator the same.

Q: Can I add fractions with different signs without finding the common denominator?

A: No, you cannot add fractions with different signs without finding the common denominator. The common denominator is the key to adding fractions with different signs.

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Discussion Category

Related Resources