Simplify The Expression:$\[ 2 \frac{3}{7} - 1 \frac{5}{7} \\]

Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently. In this article, we will focus on simplifying the expression $2 \frac{3}{7} - 1 \frac{5}{7}$. We will break down the problem into manageable steps and provide a clear explanation of each step.

Understanding the Problem

The given expression is a subtraction problem involving mixed numbers. A mixed number is a combination of a whole number and a fraction. In this case, we have two mixed numbers: $2 \frac{3}{7}$ and $1 \frac{5}{7}$. Our goal is to simplify the expression by finding a common denominator and then subtracting the fractions.

Step 1: Convert Mixed Numbers to Improper Fractions

To simplify the expression, 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.

• $2 \frac{3}{7}$ can be converted to an improper fraction by multiplying the whole number by the denominator and then adding the numerator: $2 \times 7 + 3 = 17$. So, $2 \frac{3}{7} = \frac{17}{7}$.
• $1 \frac{5}{7}$ can be converted to an improper fraction by multiplying the whole number by the denominator and then adding the numerator: $1 \times 7 + 5 = 12$. So, $1 \frac{5}{7} = \frac{12}{7}$.

Step 2: Find a Common Denominator

Now that we have converted the mixed numbers to improper fractions, we need to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators of the two fractions.

In this case, the denominators are 7 and 7. Since they are the same, the common denominator is also 7.

Step 3: Subtract the Fractions

Now that we have a common denominator, we can subtract the fractions.

$\frac{17}{7} - \frac{12}{7} = \frac{17 - 12}{7} = \frac{5}{7}$

Conclusion

In this article, we simplified the expression $2 \frac{3}{7} - 1 \frac{5}{7}$ by converting the mixed numbers to improper fractions, finding a common denominator, and then subtracting the fractions. The final answer is $\frac{5}{7}$.

Tips and Tricks

• When simplifying expressions involving mixed numbers, it's essential to convert them to improper fractions first.
• Finding a common denominator is crucial when subtracting fractions.
• Make sure to subtract the numerators while keeping the common denominator the same.

Real-World Applications

Simplifying expressions involving mixed numbers has numerous real-world applications. For example:

• In cooking, you may need to simplify a recipe that involves mixed numbers of ingredients.
• In finance, you may need to simplify a budget that involves mixed numbers of expenses.
• In science, you may need to simplify a formula that involves mixed numbers of variables.

Common Mistakes to Avoid

When simplifying expressions involving mixed numbers, it's essential to avoid common mistakes such as:

• Not converting mixed numbers to improper fractions.
• Not finding a common denominator.
• Subtracting the denominators instead of the numerators.

Conclusion

Introduction

In our previous article, we simplified the expression $2 \frac{3}{7} - 1 \frac{5}{7}$ by converting the mixed numbers to improper fractions, finding a common denominator, and then subtracting the fractions. In this article, we will provide a Q&A guide to help you understand the concept better.

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. For example, $2 \frac{3}{7}$ is a mixed number where 2 is the whole number and $\frac{3}{7}$ is the fraction.

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 then add the numerator. For example, to convert $2 \frac{3}{7}$ to an improper fraction, you would multiply 2 by 7 and add 3, which gives you 17. So, $2 \frac{3}{7} = \frac{17}{7}$.

Q: What is a common denominator?

A: A common denominator is the least common multiple (LCM) of the denominators of two or more fractions. For example, if you have two fractions with denominators 4 and 6, the common denominator would be 12.

Q: How do I find a common denominator?

A: To find a common denominator, you need to list the multiples of each denominator and find the smallest multiple that is common to both. For example, to find the common denominator of 4 and 6, you would list the multiples of each and find that the smallest common multiple is 12.

Q: Can I subtract fractions with different denominators?

A: No, you cannot subtract fractions with different denominators. You need to find a common denominator first before you can subtract the fractions.

Q: What is the difference between a proper fraction and an improper fraction?

A: A proper fraction is a fraction where the numerator is less than the denominator. For example, $\frac{1}{2}$ is a proper fraction. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, $\frac{3}{2}$ is an improper fraction.

Q: Can I add and subtract mixed numbers?

A: Yes, you can add and subtract mixed numbers, but you need to convert them to improper fractions first.

Q: What are some real-world applications of simplifying expressions involving mixed numbers?

A: Simplifying expressions involving mixed numbers has numerous real-world applications, such as:

• In cooking, you may need to simplify a recipe that involves mixed numbers of ingredients.
• In finance, you may need to simplify a budget that involves mixed numbers of expenses.
• In science, you may need to simplify a formula that involves mixed numbers of variables.

Q: What are some common mistakes to avoid when simplifying expressions involving mixed numbers?

A: Some common mistakes to avoid when simplifying expressions involving mixed numbers include:

• Not converting mixed numbers to improper fractions.
• Not finding a common denominator.
• Subtracting the denominators instead of the numerators.

Conclusion

In conclusion, simplifying expressions involving mixed numbers requires a clear understanding of the concept and a step-by-step approach. By following the steps outlined in this article and avoiding common mistakes, you can simplify expressions like $2 \frac{3}{7} - 1 \frac{5}{7}$ and arrive at the correct answer. Remember to convert mixed numbers to improper fractions, find a common denominator, and then subtract the fractions. With practice and patience, you can become proficient in simplifying expressions involving mixed numbers.