Find The Sum.${ \begin{array}{r} 3 \frac{5}{6} = 3 \frac{?}{24} \ +5 \frac{3}{8} = 5 \frac{?}{24} \ \hline \end{array} }$

Introduction

In mathematics, finding the sum of fractions can be a daunting task, especially when dealing with mixed numbers. However, with the right approach and techniques, it can be a straightforward process. In this article, we will explore how to find the sum of two mixed numbers, specifically $3 \frac{5}{6}$ and $5 \frac{3}{8}$, and express the result in the form of a mixed number with a denominator of 24.

Understanding Mixed Numbers

Before we dive into the problem, let's take a moment to understand what mixed numbers are. A mixed number is a combination of a whole number and a fraction. It is written in the form of $a \frac{b}{c}$, where $a$ is the whole number, $b$ is the numerator of the fraction, and $c$ is the denominator of the fraction. For example, $3 \frac{5}{6}$ is a mixed number where 3 is the whole number and $\frac{5}{6}$ is the fraction.

Converting Mixed Numbers to Improper Fractions

To find the sum of two mixed numbers, we need to convert them into improper fractions first. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator. The result is then written as the numerator over the denominator.

For example, let's convert $3 \frac{5}{6}$ to an improper fraction:

$$3 \frac{5}{6} = \frac{(3 \times 6) + 5}{6} = \frac{18 + 5}{6} = \frac{23}{6}$$

Similarly, let's convert $5 \frac{3}{8}$ to an improper fraction:

$$5 \frac{3}{8} = \frac{(5 \times 8) + 3}{8} = \frac{40 + 3}{8} = \frac{43}{8}$$

Finding the Least Common Multiple (LCM)

To add two fractions, we need to have the same denominator. The least common multiple (LCM) of the denominators is the smallest number that both denominators can divide into evenly. In this case, the denominators are 6 and 8, so we need to find the LCM of 6 and 8.

The multiples of 6 are: 6, 12, 18, 24, 30, ... The multiples of 8 are: 8, 16, 24, 32, 40, ...

As we can see, the first number that appears in both lists is 24, so the LCM of 6 and 8 is 24.

Adding the Fractions

Now that we have the LCM, we can add the fractions. We need to convert both fractions to have a denominator of 24.

$$\frac{23}{6} = \frac{23 \times 4}{6 \times 4} = \frac{92}{24}$$

$$\frac{43}{8} = \frac{43 \times 3}{8 \times 3} = \frac{129}{24}$$

Now we can add the fractions:

$$\frac{92}{24} + \frac{129}{24} = \frac{221}{24}$$

Converting the Result to a Mixed Number

Finally, we need to convert the result to a mixed number. To do this, we divide the numerator by the denominator and write the remainder as the numerator of the fraction.

$$\frac{221}{24} = 9 \frac{5}{24}$$

Therefore, the sum of $3 \frac{5}{6}$ and $5 \frac{3}{8}$ is $9 \frac{5}{24}$.

Conclusion

Finding the sum of two mixed numbers can be a challenging task, but with the right techniques and approach, it can be a straightforward process. By converting the mixed numbers to improper fractions, finding the LCM, adding the fractions, and converting the result to a mixed number, we can find the sum of two mixed numbers with a denominator of 24. In this article, we have seen how to find the sum of $3 \frac{5}{6}$ and $5 \frac{3}{8}$, and we have expressed the result in the form of a mixed number with a denominator of 24.

Final Answer

The final answer is: $\boxed{9 \frac{5}{24}}$

Introduction

In our previous article, we explored how to find the sum of two mixed numbers, specifically $3 \frac{5}{6}$ and $5 \frac{3}{8}$, and expressed the result in the form of a mixed number with a denominator of 24. In this article, we will answer some of the most frequently asked questions related to finding the sum of mixed numbers.

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 multiply the whole number by the denominator and add the numerator. The result is then written as the numerator over the denominator.

Q: What is the least common multiple (LCM) and why is it important?

A: The LCM is the smallest number that both denominators can divide into evenly. It is important because it allows us to add fractions with different denominators.

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

A: To find the LCM of two numbers, you list the multiples of each number and find the first number that appears in both lists.

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

A: No, you cannot add fractions with different denominators without finding the LCM. If you try to add fractions with different denominators, you will get an incorrect result.

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

A: To convert an improper fraction to a mixed number, you divide the numerator by the denominator and write the remainder as the numerator of the fraction.

Q: What is the final answer to the problem $3 \frac{5}{6} + 5 \frac{3}{8}$?

A: The final answer to the problem $3 \frac{5}{6} + 5 \frac{3}{8}$ is $9 \frac{5}{24}$.

Q: Can I use a calculator to find the sum of mixed numbers?

A: Yes, you can use a calculator to find the sum of mixed numbers. However, it is always a good idea to understand the underlying math and be able to do the problem by hand.

Q: How do I apply this knowledge to real-world problems?

A: You can apply this knowledge to real-world problems by using mixed numbers to represent quantities that have both a whole number and a fractional part. For example, you might use mixed numbers to represent the number of items in a box or the amount of money in a bank account.

Conclusion

Finding the sum of mixed numbers can be a challenging task, but with the right techniques and approach, it can be a straightforward process. By understanding the difference between mixed numbers and improper fractions, converting mixed numbers to improper fractions, finding the LCM, adding fractions, and converting the result to a mixed number, you can find the sum of two mixed numbers with a denominator of 24. We hope this Q&A article has been helpful in answering some of the most frequently asked questions related to finding the sum of mixed numbers.

Final Answer

The final answer is: $\boxed{9 \frac{5}{24}}$