Solve For \[$ X \$\]:$\[ X = 41 \frac{3}{4} + 3 \frac{5}{6} + 7 \frac{9}{10} \\]

Introduction to the Problem

In this problem, we are given an equation that involves adding three mixed numbers. The goal is to simplify the expression and find the value of $x$. To solve this problem, we need to understand how to add mixed numbers and fractions.

Understanding Mixed Numbers and Fractions

A mixed number is a combination of a whole number and a fraction. For example, $41 \frac{3}{4}$ is a mixed number that represents $41$ whole units plus $\frac{3}{4}$ of a unit. A fraction is a way of representing a part of a whole. For example, $\frac{3}{4}$ represents three-fourths of a unit.

Adding Mixed Numbers and Fractions

To add mixed numbers and fractions, we need to follow a specific procedure. First, we need to convert the mixed numbers to improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, $41 \frac{3}{4}$ can be converted to an improper fraction as follows:

$$41 \frac{3}{4} = \frac{(41 \times 4) + 3}{4} = \frac{164 + 3}{4} = \frac{167}{4}$$

Similarly, we can convert the other two mixed numbers to improper fractions:

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

$$7 \frac{9}{10} = \frac{(7 \times 10) + 9}{10} = \frac{70 + 9}{10} = \frac{79}{10}$$

Adding the Improper Fractions

Now that we have converted the mixed numbers to improper fractions, we can add them together. To add fractions, we need to have the same denominator. In this case, the denominators are 4, 6, and 10. We can find the least common multiple (LCM) of these denominators, which is 60.

$$\frac{167}{4} = \frac{167 \times 15}{4 \times 15} = \frac{2505}{60}$$

$$\frac{23}{6} = \frac{23 \times 10}{6 \times 10} = \frac{230}{60}$$

$$\frac{79}{10} = \frac{79 \times 6}{10 \times 6} = \frac{474}{60}$$

Adding the Fractions

Now that we have the same denominator, we can add the fractions together:

$$\frac{2505}{60} + \frac{230}{60} + \frac{474}{60} = \frac{2505 + 230 + 474}{60} = \frac{3209}{60}$$

Simplifying the Result

The result is an improper fraction. We can simplify it by dividing the numerator by the denominator:

$$\frac{3209}{60} = 53 \frac{29}{60}$$

Conclusion

In this problem, we were given an equation that involved adding three mixed numbers. We converted the mixed numbers to improper fractions, added them together, and simplified the result. The final answer is $53 \frac{29}{60}$.

Final Answer

The final answer is: $\boxed{53 \frac{29}{60}}$

Introduction

In the previous article, we solved the equation $x = 41 \frac{3}{4} + 3 \frac{5}{6} + 7 \frac{9}{10}$ and found the value of $x$ to be $53 \frac{29}{60}$. In this article, we will answer some frequently asked questions related to the problem.

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, multiply the whole number by the denominator and add the numerator. Then, write the result as a fraction with the denominator.

Q: What is the least common multiple (LCM) of 4, 6, and 10?

A: The LCM of 4, 6, and 10 is 60.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, find the least common multiple (LCM) of the denominators and convert each fraction to have the LCM as the denominator. Then, add the fractions.

Q: What is the final answer to the equation $x = 41 \frac{3}{4} + 3 \frac{5}{6} + 7 \frac{9}{10}$?

A: The final answer is $53 \frac{29}{60}$.

Q: Can I simplify the result of the equation $x = 41 \frac{3}{4} + 3 \frac{5}{6} + 7 \frac{9}{10}$ further?

A: Yes, the result can be simplified further by dividing the numerator by the denominator.

Q: What is the purpose of converting mixed numbers to improper fractions?

A: Converting mixed numbers to improper fractions makes it easier to add and subtract fractions with different denominators.

Q: Can I use a calculator to solve the equation $x = 41 \frac{3}{4} + 3 \frac{5}{6} + 7 \frac{9}{10}$?

A: Yes, you can use a calculator to solve the equation, but it's also important to understand the steps involved in solving the equation.

Conclusion

In this article, we answered some frequently asked questions related to the problem $x = 41 \frac{3}{4} + 3 \frac{5}{6} + 7 \frac{9}{10}$. We hope that this article has been helpful in clarifying any doubts you may have had about the problem.

Final Answer

The final answer is: $\boxed{53 \frac{29}{60}}$