Find The Sum. Write Your Answer As A Fraction In Simplest Form.$\[ -4 \frac{5}{9} + \frac{8}{9} = \square \\]

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Introduction

In mathematics, finding the sum of fractions is a fundamental concept that requires a deep understanding of the underlying principles. When dealing with fractions, it's essential to simplify them to their lowest terms before performing operations. In this article, we will explore the concept of finding the sum of fractions, with a focus on the given problem: −459+89=□-4 \frac{5}{9} + \frac{8}{9} = \square. We will break down the solution step by step, using a combination of mathematical techniques and logical reasoning.

Understanding the Problem

The given problem involves adding two fractions: −459-4 \frac{5}{9} and 89\frac{8}{9}. To solve this problem, we need to first convert the mixed number −459-4 \frac{5}{9} to an improper fraction. This can be done by multiplying the whole number part by the denominator and then adding the numerator.

Converting Mixed Numbers to Improper Fractions

A mixed number is a combination of a whole number and a fraction. To convert a mixed number to an improper fraction, we follow these steps:

  1. Multiply the whole number part by the denominator.
  2. Add the numerator to the result.
  3. Write the result as an improper fraction.

Using this technique, we can convert the mixed number −459-4 \frac{5}{9} to an improper fraction:

−459=−(4×9)+59=−36+59=−419-4 \frac{5}{9} = -\frac{(4 \times 9) + 5}{9} = -\frac{36 + 5}{9} = -\frac{41}{9}

Adding Fractions with Different Denominators

Now that we have converted the mixed number to an improper fraction, we can proceed to add the two fractions. However, the fractions have different denominators, which means we need to find a common denominator before adding them.

Finding a Common Denominator

To add fractions with different denominators, we need to find a common denominator. The common denominator is the least common multiple (LCM) of the two denominators. In this case, the denominators are 9 and 9, so the common denominator is also 9.

Adding the Fractions

Now that we have found the common denominator, we can add the fractions:

−419+89=−419+89=−339-\frac{41}{9} + \frac{8}{9} = -\frac{41}{9} + \frac{8}{9} = -\frac{33}{9}

Simplifying the Result

The result is an improper fraction, which can be simplified by dividing the numerator by the denominator:

−339=−113-\frac{33}{9} = -\frac{11}{3}

Conclusion

In this article, we explored the concept of finding the sum of fractions, with a focus on the given problem: −459+89=□-4 \frac{5}{9} + \frac{8}{9} = \square. We broke down the solution step by step, using a combination of mathematical techniques and logical reasoning. By converting the mixed number to an improper fraction, finding a common denominator, and adding the fractions, we arrived at the final result: −113-\frac{11}{3}.

Final Answer

The final answer is: −113-\frac{11}{3}

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Introduction

In our previous article, we explored the concept of finding the sum of fractions, with a focus on the given problem: −459+89=□-4 \frac{5}{9} + \frac{8}{9} = \square. We broke down the solution step by step, using a combination of mathematical techniques and logical reasoning. In this article, we will answer some of the most frequently asked questions related to finding the sum of fractions.

Q&A

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you need to multiply the whole number part by the denominator and then add the numerator. The result is then written as an improper fraction.

Q: What is the common denominator?

A: The common denominator is the least common multiple (LCM) of the two denominators. It is used to add fractions with different denominators.

Q: How do I find the common denominator?

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

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

A: No, you cannot add fractions with different denominators without finding the common denominator. This is because the denominators must be the same in order to add the fractions.

Q: What is the final answer to the given problem?

A: The final answer to the given problem is −113-\frac{11}{3}.

Q: Can I simplify the result further?

A: Yes, the result can be simplified further by dividing the numerator by the denominator. However, in this case, the result is already in its simplest form.

Q: What are some common mistakes to avoid when finding the sum of fractions?

A: Some common mistakes to avoid when finding the sum of fractions include:

  • Not converting mixed numbers to improper fractions
  • Not finding the common denominator
  • Not adding the fractions correctly
  • Not simplifying the result

Conclusion

In this article, we answered some of the most frequently asked questions related to finding the sum of fractions. We covered topics such as converting mixed numbers to improper fractions, finding the common denominator, and adding fractions with different denominators. By understanding these concepts, you will be able to find the sum of fractions with ease.

Final Tips

  • Always convert mixed numbers to improper fractions before adding fractions.
  • Find the common denominator before adding fractions with different denominators.
  • Add fractions correctly by adding the numerators and keeping the common denominator.
  • Simplify the result by dividing the numerator by the denominator.

Final Answer

The final answer is: −113-\frac{11}{3}