Work Out 9 3 8 − 2 1 2 9 \frac{3}{8} - 2 \frac{1}{2} 9 8 3 ​ − 2 2 1 ​ . Give Your Answer As A Mixed Number.

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Introduction

When working with mixed numbers, it's essential to understand the concept of subtracting fractions. A mixed number is a combination of a whole number and a fraction. In this case, we have two mixed numbers: $9 \frac{3}{8}$ and $2 \frac{1}{2}$. Our goal is to subtract the second mixed number from the first one and express the result as a mixed number.

Understanding Mixed Numbers

Before we dive into the subtraction process, let's review what mixed numbers are. A mixed number is a combination of a whole number and a fraction. It's written in the form $a \frac{b}{c}$, where $a$ is the whole number part, $b$ is the numerator of the fraction part, and $c$ is the denominator of the fraction part.

For example, $3 \frac{4}{5}$ is a mixed number where $3$ is the whole number part, $4$ is the numerator of the fraction part, and $5$ is the denominator of the fraction part.

Converting Mixed Numbers to Improper Fractions

To subtract mixed numbers, we need to convert them to 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 part by the denominator and add the numerator. The result is the new numerator, and the denominator remains the same.

For example, to convert $3 \frac{4}{5}$ to an improper fraction, we multiply $3$ by $5$ and add $4$. This gives us $15 + 4 = 19$. So, the improper fraction equivalent of $3 \frac{4}{5}$ is $\frac{19}{5}$.

Converting $9 \frac{3}{8}$ and $2 \frac{1}{2}$ to Improper Fractions

Now, let's convert the given mixed numbers to improper fractions.

Converting $9 \frac{3}{8}$ to an Improper Fraction

To convert $9 \frac{3}{8}$ to an improper fraction, we multiply $9$ by $8$ and add $3$. This gives us $72 + 3 = 75$. So, the improper fraction equivalent of $9 \frac{3}{8}$ is $\frac{75}{8}$.

Converting $2 \frac{1}{2}$ to an Improper Fraction

To convert $2 \frac{1}{2}$ to an improper fraction, we multiply $2$ by $2$ and add $1$. This gives us $4 + 1 = 5$. So, the improper fraction equivalent of $2 \frac{1}{2}$ is $\frac{5}{2}$.

Subtracting Improper Fractions

Now that we have the improper fractions, we can subtract them.

To subtract improper fractions, we need to have the same denominator. In this case, the denominators are $8$ and $2$. The least common multiple (LCM) of $8$ and $2$ is $8$. So, we can rewrite $\frac{5}{2}$ as $\frac{20}{8}$.

Now, we can subtract the fractions:

$$\frac{75}{8} - \frac{20}{8} = \frac{55}{8}$$

Converting the Result to a Mixed Number

The result is an improper fraction, but we need to express it as a mixed number. To do this, we divide the numerator by the denominator:

$$\frac{55}{8} = 6 \frac{7}{8}$$

So, the result of subtracting $2 \frac{1}{2}$ from $9 \frac{3}{8}$ is $6 \frac{7}{8}$.

Conclusion

In this article, we learned how to subtract mixed numbers by converting them to improper fractions first. We then subtracted the improper fractions and converted the result back to a mixed number. The result of subtracting $2 \frac{1}{2}$ from $9 \frac{3}{8}$ is $6 \frac{7}{8}$.

Introduction

Subtracting mixed numbers can be a challenging task, but with the right approach, it can be made easier. In this article, we'll answer some frequently asked questions about subtracting mixed numbers.

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

A: The first step in subtracting mixed numbers is to convert them to improper fractions. This involves multiplying the whole number part by the denominator and adding the numerator.

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 part by the denominator and add the numerator. For example, to convert $3 \frac{4}{5}$ to an improper fraction, you multiply $3$ by $5$ and add $4$. This gives you $15 + 4 = 19$. So, the improper fraction equivalent of $3 \frac{4}{5}$ is $\frac{19}{5}$.

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

A: The least common multiple (LCM) is the smallest number that both numbers can divide into evenly. In subtracting mixed numbers, the LCM is used to find a common denominator for the fractions. This is important because it allows us to subtract the fractions directly.

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

A: To find the LCM of two numbers, you can list the multiples of each number and find the smallest number that appears in both lists. Alternatively, you can use the prime factorization method to find the LCM.

Q: What is the difference between subtracting mixed numbers and subtracting fractions?

A: Subtracting mixed numbers involves converting the mixed numbers to improper fractions and then subtracting the fractions. Subtracting fractions, on the other hand, involves finding a common denominator and then subtracting the fractions.

Q: Can I subtract mixed numbers with different denominators?

A: Yes, you can subtract mixed numbers with different denominators. However, you need to find a common denominator first. This can be done by finding the least common multiple (LCM) of the two denominators.

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

A: To convert an improper fraction back to a mixed number, you divide the numerator by the denominator. The result is the whole number part, and the remainder is the new numerator.

Q: What is the result of subtracting $2 \frac{1}{2}$ from $9 \frac{3}{8}$?

A: The result of subtracting $2 \frac{1}{2}$ from $9 \frac{3}{8}$ is $6 \frac{7}{8}$.

Q: Can I use a calculator to subtract mixed numbers?

A: Yes, you can use a calculator to subtract mixed numbers. However, it's always a good idea to understand the concept behind the calculation.

Q: What are some common mistakes to avoid when subtracting mixed numbers?

A: Some common mistakes to avoid when subtracting mixed numbers include:

• Not converting the mixed numbers to improper fractions
• Not finding a common denominator
• Not subtracting the fractions correctly
• Not converting the result back to a mixed number

Conclusion

Subtracting mixed numbers can be a challenging task, but with the right approach, it can be made easier. By understanding the concept behind subtracting mixed numbers and following the steps outlined in this article, you can become more confident in your ability to subtract mixed numbers.