Subtract: $8 \frac{1}{2} - 2 \frac{2}{3}$A. $6 \frac{1}{6}$ B. $6 \frac{1}{3}$ C. $5 \frac{5}{6}$ D. $5 \frac{1}{6}$

Introduction

When it comes to subtracting mixed numbers, it's essential to understand the concept of finding a common denominator and then performing the subtraction. In this article, we will delve into the process of subtracting mixed numbers, focusing on the given problem: $8 \frac{1}{2} - 2 \frac{2}{3}$. We will break down the steps involved in subtracting mixed numbers and provide a clear explanation of the solution.

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's written in the form of $a \frac{b}{c}$, where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator. For example, $3 \frac{2}{5}$ is a mixed number, where $3$ is the whole number, $2$ is the numerator, and $5$ is the denominator.

Finding a Common Denominator

To subtract mixed numbers, we need to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators of the two mixed numbers. In this case, the denominators are $2$ and $3$. The LCM of $2$ and $3$ is $6$. Therefore, we need to convert both mixed numbers to have a denominator of $6$.

Converting Mixed Numbers to Have a Common Denominator

To convert $8 \frac{1}{2}$ to have a denominator of $6$, we need to multiply the numerator and denominator by $3$, since $2 \times 3 = 6$. This gives us $8 \frac{3}{6}$. Similarly, to convert $2 \frac{2}{3}$ to have a denominator of $6$, we need to multiply the numerator and denominator by $2$, since $3 \times 2 = 6$. This gives us $2 \frac{4}{6}$.

Subtracting the Mixed Numbers

Now that we have both mixed numbers with a common denominator of $6$, we can subtract them. We subtract the numerators while keeping the denominator the same. Therefore, $8 \frac{3}{6} - 2 \frac{4}{6} = 6 \frac{3-4}{6} = 6 \frac{-1}{6}$.

Simplifying the Result

Since we have a negative fraction, we can simplify it by writing it as a positive fraction with a negative sign. Therefore, $6 \frac{-1}{6} = 6 - \frac{1}{6}$. We can further simplify this by converting the whole number to a fraction with a denominator of $6$. This gives us $\frac{36}{6} - \frac{1}{6} = \frac{35}{6}$.

Converting the Result to a Mixed Number

To convert the improper fraction $\frac{35}{6}$ to a mixed number, we need to divide the numerator by the denominator. This gives us $5$ with a remainder of $5$. Therefore, the mixed number is $5 \frac{5}{6}$.

Conclusion

In conclusion, the correct answer to the problem $8 \frac{1}{2} - 2 \frac{2}{3}$ is $5 \frac{5}{6}$. We found the common denominator, converted the mixed numbers to have a common denominator, subtracted the mixed numbers, simplified the result, and finally converted the result to a mixed number.

Final Answer

The final answer is: C. $5 \frac{5}{6}$

Introduction

In our previous article, we explored the process of subtracting mixed numbers, focusing on the problem $8 \frac{1}{2} - 2 \frac{2}{3}$. We broke down the steps involved in subtracting mixed numbers and provided a clear explanation of the solution. In this article, we will address some common questions and concerns related to subtracting mixed numbers.

Q&A

Q: What is the first step in subtracting mixed numbers?

A: The first step in subtracting mixed numbers is to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators of the two mixed numbers.

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. For example, if the denominators are $2$ and $3$, the multiples of $2$ are $2, 4, 6, 8, 10, ...$ and the multiples of $3$ are $3, 6, 9, 12, 15, ...$. The smallest multiple that is common to both is $6$, so the common denominator is $6$.

Q: What if the denominators are not multiples of each other?

A: If the denominators are not multiples of each other, you need to find the least common multiple (LCM) of the two denominators. The LCM is the smallest number that is a multiple of both denominators. For example, if the denominators are $4$ and $6$, the multiples of $4$ are $4, 8, 12, 16, 20, ...$ and the multiples of $6$ are $6, 12, 18, 24, 30, ...$. The smallest number that is a multiple of both is $12$, so the LCM is $12$.

Q: How do I convert mixed numbers to have a common denominator?

A: To convert a mixed number to have a common denominator, you need to multiply the numerator and denominator by the same number. For example, if the mixed number is $3 \frac{2}{4}$ and the common denominator is $12$, you need to multiply the numerator and denominator by $3$, since $4 \times 3 = 12$. This gives you $3 \frac{6}{12}$.

Q: What if I have a negative fraction?

A: If you have a negative fraction, you can simplify it by writing it as a positive fraction with a negative sign. For example, if you have $- \frac{1}{2}$, you can write it as $\frac{-1}{2}$.

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

A: To convert an improper fraction to a mixed number, you need to divide the numerator by the denominator. This gives you a whole number and a remainder. For example, if you have $\frac{17}{4}$, you can divide the numerator by the denominator to get $4$ with a remainder of $1$. Therefore, the mixed number is $4 \frac{1}{4}$.

Conclusion

In conclusion, subtracting mixed numbers requires finding a common denominator, converting the mixed numbers to have a common denominator, subtracting the mixed numbers, simplifying the result, and finally converting the result to a mixed number. We hope this Q&A article has addressed some common questions and concerns related to subtracting mixed numbers.

Final Answer

The final answer is: C. $5 \frac{5}{6}$