Calculate The Result Of:${ \left(-\frac{4}{5}\right) - \frac{7}{8} }$

Introduction

Fractions are an essential part of mathematics, and understanding how to work with them is crucial for solving various mathematical problems. In this article, we will focus on calculating the result of a complex fraction, specifically the expression $\left(-\frac{4}{5}\right) - \frac{7}{8}$. We will break down the problem into manageable steps and provide a clear explanation of each step.

Understanding Complex Fractions

A complex fraction is a fraction that contains one or more fractions in its numerator or denominator. In the given expression, we have two fractions: $\frac{4}{5}$ and $\frac{7}{8}$. To calculate the result, we need to find a common denominator for both fractions.

Finding a Common Denominator

To find a common denominator, we need to identify the least common multiple (LCM) of the denominators. In this case, the denominators are 5 and 8. The LCM of 5 and 8 is 40.

Step 1: Convert Both Fractions to Have a Common Denominator

To convert both fractions to have a common denominator, we need to multiply the numerator and denominator of each fraction by the necessary multiples.

$\left(-\frac{4}{5}\right) = \left(-\frac{4 \times 8}{5 \times 8}\right) = \left(-\frac{32}{40}\right)$

$\frac{7}{8} = \frac{7 \times 5}{8 \times 5} = \frac{35}{40}$

Step 2: Subtract the Two Fractions

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

$\left(-\frac{32}{40}\right) - \frac{35}{40} = \frac{-32 - 35}{40} = \frac{-67}{40}$

Conclusion

Calculating the result of a complex fraction requires finding a common denominator and then performing the necessary operations. In this case, we found the LCM of the denominators, converted both fractions to have a common denominator, and then subtracted them. The result is $\frac{-67}{40}$.

Real-World Applications

Understanding how to work with complex fractions is essential in various real-world applications, such as:

• Finance: When working with financial data, complex fractions can be used to calculate interest rates, investment returns, and other financial metrics.
• Science: In scientific calculations, complex fractions can be used to represent ratios of quantities, such as the ratio of the volume of a substance to its mass.
• Engineering: In engineering applications, complex fractions can be used to represent ratios of physical quantities, such as the ratio of the length of a beam to its cross-sectional area.

Tips and Tricks

When working with complex fractions, here are some tips and tricks to keep in mind:

• Find the LCM: To find a common denominator, identify the LCM of the denominators.
• Convert fractions: Convert both fractions to have a common denominator by multiplying the numerator and denominator by the necessary multiples.
• Perform operations: Once both fractions have a common denominator, perform the necessary operations, such as addition or subtraction.

Common Mistakes to Avoid

When working with complex fractions, here are some common mistakes to avoid:

• Not finding the LCM: Failing to find the LCM of the denominators can lead to incorrect results.
• Not converting fractions: Failing to convert both fractions to have a common denominator can lead to incorrect results.
• Not performing operations correctly: Failing to perform the necessary operations correctly can lead to incorrect results.

Conclusion

Q: What is a complex fraction?

A: A complex fraction is a fraction that contains one or more fractions in its numerator or denominator.

Q: Why is it important to find a common denominator when working with complex fractions?

A: Finding a common denominator is essential when working with complex fractions because it allows us to perform operations, such as addition and subtraction, on the fractions.

Q: How do I find the least common multiple (LCM) of two numbers?

A: To find the LCM of two numbers, list the multiples of each number and identify the smallest multiple that appears in both lists.

Q: Can I use a calculator to find the LCM of two numbers?

A: Yes, you can use a calculator to find the LCM of two numbers. Most calculators have a built-in function to find the LCM.

Q: What is the difference between a complex fraction and a mixed number?

A: A complex fraction is a fraction that contains one or more fractions in its numerator or denominator, while a mixed number is a combination of a whole number and a fraction.

Q: Can I add or subtract complex fractions with different denominators?

A: No, you cannot add or subtract complex fractions with different denominators. You must first find a common denominator before performing the operation.

Q: How do I convert a complex fraction to a decimal?

A: To convert a complex fraction to a decimal, divide the numerator by the denominator.

Q: Can I use a calculator to convert a complex fraction to a decimal?

A: Yes, you can use a calculator to convert a complex fraction to a decimal. Most calculators have a built-in function to convert fractions to decimals.

Q: What is the difference between a complex fraction and a rational expression?

A: A complex fraction is a fraction that contains one or more fractions in its numerator or denominator, while a rational expression is a fraction that contains variables in the numerator or denominator.

Q: Can I simplify a complex fraction?

A: Yes, you can simplify a complex fraction by canceling out any common factors between the numerator and denominator.

Q: How do I simplify a complex fraction?

A: To simplify a complex fraction, factor the numerator and denominator, and then cancel out any common factors.

Q: Can I use a calculator to simplify a complex fraction?

A: Yes, you can use a calculator to simplify a complex fraction. Most calculators have a built-in function to simplify fractions.

Conclusion

Calculating complex fractions can be challenging, but with practice and patience, you can master the skills. Remember to find a common denominator, convert fractions, and perform operations correctly to avoid common mistakes. If you have any further questions or need additional help, don't hesitate to ask.

Additional Resources

• Online calculators: Use online calculators to find the LCM, convert fractions to decimals, and simplify complex fractions.
• Math textbooks: Consult math textbooks for additional practice and examples.
• Online tutorials: Watch online tutorials to learn more about complex fractions and how to work with them.

Common Mistakes to Avoid

• Not finding the LCM: Failing to find the LCM of the denominators can lead to incorrect results.
• Not converting fractions: Failing to convert both fractions to have a common denominator can lead to incorrect results.
• Not performing operations correctly: Failing to perform the necessary operations correctly can lead to incorrect results.

Conclusion

Calculating complex fractions requires attention to detail and practice. By following the steps outlined in this article and avoiding common mistakes, you can master the skills and apply complex fractions to real-world applications.