Calculate The Following Expression:${ 5 \frac{3}{5} - 2 \frac{1}{5} }$

Introduction

In mathematics, mixed numbers are a combination of a whole number and a fraction. They are often used to represent quantities that are not whole, but can be expressed as a sum of a whole number and a fraction. In this article, we will explore how to simplify mixed numbers, with a focus on calculating the expression $5 \frac{3}{5} - 2 \frac{1}{5}$.

Understanding Mixed Numbers

A mixed number is a combination of a whole number and a fraction. It is written in the form $a \frac{b}{c}$, 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 that represents the quantity $3 + \frac{2}{5}$.

Simplifying Mixed Numbers

To simplify a mixed number, we need to convert it to an improper fraction. 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. We then write the result as a fraction with the denominator.

For example, to simplify $3 \frac{2}{5}$, we multiply the whole number $3$ by the denominator $5$ to get $15$. We then add the numerator $2$ to get $17$. We write the result as a fraction with the denominator: $\frac{17}{5}$.

Calculating the Expression

Now that we have a basic understanding of mixed numbers and how to simplify them, we can calculate the expression $5 \frac{3}{5} - 2 \frac{1}{5}$.

To calculate this expression, we need to simplify each mixed number separately. We can do this by converting each mixed number to an improper fraction.

For the first mixed number, $5 \frac{3}{5}$, we multiply the whole number $5$ by the denominator $5$ to get $25$. We then add the numerator $3$ to get $28$. We write the result as a fraction with the denominator: $\frac{28}{5}$.

For the second mixed number, $2 \frac{1}{5}$, we multiply the whole number $2$ by the denominator $5$ to get $10$. We then add the numerator $1$ to get $11$. We write the result as a fraction with the denominator: $\frac{11}{5}$.

Now that we have simplified each mixed number, we can calculate the expression by subtracting the second mixed number from the first mixed number.

$\frac{28}{5} - \frac{11}{5} = \frac{17}{5}$

Conclusion

In this article, we explored how to simplify mixed numbers and calculate the expression $5 \frac{3}{5} - 2 \frac{1}{5}$. We learned how to convert mixed numbers to improper fractions and how to subtract fractions with the same denominator. By following these steps, we were able to simplify the expression and arrive at the final answer.

Common Mistakes to Avoid

When working with mixed numbers, it's easy to make mistakes. Here are a few common mistakes to avoid:

• Not converting mixed numbers to improper fractions: Failing to convert mixed numbers to improper fractions can lead to incorrect calculations.
• Not using the same denominator: When subtracting fractions, it's essential to use the same denominator. Failing to do so can lead to incorrect results.
• Not simplifying fractions: Failing to simplify fractions can lead to incorrect results.

Real-World Applications

Mixed numbers have many real-world applications. Here are a few examples:

• Cooking: When cooking, you may need to measure ingredients in mixed numbers. For example, you may need to measure 3 cups and 2 tablespoons of flour.
• Building: When building, you may need to measure materials in mixed numbers. For example, you may need to measure 5 feet and 3 inches of lumber.
• Science: In science, mixed numbers are often used to represent quantities that are not whole. For example, you may need to measure the volume of a liquid in mixed numbers.

Conclusion

Introduction

In our previous article, we explored how to simplify mixed numbers and calculate the expression $5 \frac{3}{5} - 2 \frac{1}{5}$. In this article, we will answer some of the most frequently asked questions about mixed numbers.

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. It is written in the form $a \frac{b}{c}$, where $a$ is the whole number, $b$ is the numerator, and $c$ is 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 by the denominator and add the numerator. You then write the result as a fraction with the denominator.

For example, to convert $3 \frac{2}{5}$ to an improper fraction, you multiply the whole number $3$ by the denominator $5$ to get $15$. You then add the numerator $2$ to get $17$. You write the result as a fraction with the denominator: $\frac{17}{5}$.

Q: How do I subtract mixed numbers?

A: To subtract mixed numbers, you need to convert each mixed number to an improper fraction. You then subtract the fractions.

For example, to subtract $5 \frac{3}{5}$ and $2 \frac{1}{5}$, you convert each mixed number to an improper fraction:

$\frac{28}{5} - \frac{11}{5} = \frac{17}{5}$

Q: Can I add mixed numbers?

A: Yes, you can add mixed numbers. To add mixed numbers, you need to convert each mixed number to an improper fraction. You then add the fractions.

For example, to add $3 \frac{2}{5}$ and $2 \frac{4}{5}$, you convert each mixed number to an improper fraction:

$\frac{17}{5} + \frac{14}{5} = \frac{31}{5}$

Q: Can I multiply mixed numbers?

A: Yes, you can multiply mixed numbers. To multiply mixed numbers, you need to convert each mixed number to an improper fraction. You then multiply the fractions.

For example, to multiply $3 \frac{2}{5}$ and $2 \frac{4}{5}$, you convert each mixed number to an improper fraction:

$\frac{17}{5} \times \frac{14}{5} = \frac{238}{25}$

Q: Can I divide mixed numbers?

A: Yes, you can divide mixed numbers. To divide mixed numbers, you need to convert each mixed number to an improper fraction. You then divide the fractions.

For example, to divide $3 \frac{2}{5}$ by $2 \frac{4}{5}$, you convert each mixed number to an improper fraction:

$\frac{17}{5} \div \frac{14}{5} = \frac{17}{14}$

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

A: Here are some common mistakes to avoid when working with mixed numbers:

• Not converting mixed numbers to improper fractions: Failing to convert mixed numbers to improper fractions can lead to incorrect calculations.
• Not using the same denominator: When subtracting fractions, it's essential to use the same denominator. Failing to do so can lead to incorrect results.
• Not simplifying fractions: Failing to simplify fractions can lead to incorrect results.

Conclusion

In conclusion, mixed numbers are an essential part of mathematics. They are used to represent quantities that are not whole and are often used in real-world applications. By understanding how to simplify mixed numbers and calculate expressions, we can solve a wide range of problems. We hope this Q&A article has been helpful in answering some of the most frequently asked questions about mixed numbers.