Evaluate: \left(\frac{-43}{50}\right) - \frac{3}{4} + \left(\frac{-3}{5}\right ]Provide An Answer As A Reduced Fraction Or Mixed Number.

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Introduction

When evaluating expressions involving fractions, it's essential to follow the order of operations (PEMDAS/BODMAS) and perform the necessary calculations to simplify the expression. In this case, we're given the expression $\left(\frac{-43}{50}\right) - \frac{3}{4} + \left(\frac{-3}{5}\right)$, and we need to evaluate it and provide the answer as a reduced fraction or mixed number.

Step 1: Find a Common Denominator

To add or subtract fractions, we need to have a common denominator. The least common multiple (LCM) of 50, 4, and 5 is 100. We can rewrite each fraction with a denominator of 100.

Converting Fractions to Have a Common Denominator

$\frac{-43}{50} = \frac{-43 \times 2}{50 \times 2} = \frac{-86}{100}$

$\frac{3}{4} = \frac{3 \times 25}{4 \times 25} = \frac{75}{100}$

$\frac{-3}{5} = \frac{-3 \times 20}{5 \times 20} = \frac{-60}{100}$

Step 2: Subtract and Add the Fractions

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

Subtracting and Adding Fractions

$\frac{-86}{100} - \frac{75}{100} + \frac{-60}{100} = \frac{-86 - 75 - 60}{100} = \frac{-221}{100}$

Step 3: Simplify the Fraction (if necessary)

In this case, the fraction $\frac{-221}{100}$ cannot be simplified further, so it is already in its simplest form.

Step 4: Convert the Fraction to a Mixed Number (if necessary)

Since the fraction $\frac{-221}{100}$ is negative, we can convert it to a mixed number.

Converting a Fraction to a Mixed Number

$\frac{-221}{100} = -2\frac{21}{100}$

Conclusion

In conclusion, the value of the expression $\left(\frac{-43}{50}\right) - \frac{3}{4} + \left(\frac{-3}{5}\right)$ is $-2\frac{21}{100}$.

Final Answer

The final answer is: $\boxed{-2\frac{21}{100}}$

Discussion

When evaluating expressions involving fractions, it's essential to follow the order of operations (PEMDAS/BODMAS) and perform the necessary calculations to simplify the expression. In this case, we used the least common multiple (LCM) to find a common denominator and then subtracted and added the fractions. We also converted the fraction to a mixed number to provide the answer in a more readable format.

Tips and Tricks

• When evaluating expressions involving fractions, always follow the order of operations (PEMDAS/BODMAS).
• Use the least common multiple (LCM) to find a common denominator.
• Subtract and add fractions with a common denominator.
• Convert fractions to mixed numbers to provide the answer in a more readable format.

Related Topics

• Evaluating expressions involving fractions
• Finding the least common multiple (LCM)
• Subtracting and adding fractions
• Converting fractions to mixed numbers
  

Introduction

Evaluating expressions involving fractions can be a challenging task, but with the right approach and techniques, it can be made easier. In this article, we will provide a Q&A section to help you understand the concepts and techniques involved in evaluating expressions involving fractions.

Q1: What is the order of operations (PEMDAS/BODMAS) and how does it apply to evaluating expressions involving fractions?

A1:

The order of operations (PEMDAS/BODMAS) is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. PEMDAS/BODMAS stands for:

• Parentheses/Brackets
• Exponents/Orders
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

When evaluating expressions involving fractions, it's essential to follow the order of operations to ensure that the correct calculations are performed.

Q2: How do I find a common denominator when evaluating expressions involving fractions?

A2:

To find a common denominator, you need to find the least common multiple (LCM) of the denominators of the fractions. The LCM is the smallest number that is a multiple of all the denominators. You can find the LCM by listing the multiples of each denominator and finding the smallest number that appears in all the lists.

For example, if you have two fractions with denominators 4 and 6, the LCM is 12. You can then rewrite each fraction with a denominator of 12.

Q3: How do I subtract and add fractions with a common denominator?

A3:

When subtracting and adding fractions with a common denominator, you simply subtract or add the numerators (the numbers on top) and keep the denominator the same.

For example, if you have two fractions with a common denominator of 12:

$\frac{3}{12} - \frac{2}{12} = \frac{3 - 2}{12} = \frac{1}{12}$

Q4: How do I convert a fraction to a mixed number?

A4:

To convert a fraction to a mixed number, you need to divide the numerator by the denominator and write the result as a mixed number.

For example, if you have a fraction $\frac{17}{4}$, you can convert it to a mixed number by dividing 17 by 4:

$17 \div 4 = 4\frac{1}{4}$

Q5: What are some common mistakes to avoid when evaluating expressions involving fractions?

A5:

Some common mistakes to avoid when evaluating expressions involving fractions include:

• Not following the order of operations (PEMDAS/BODMAS)
• Not finding a common denominator
• Not subtracting and adding fractions with a common denominator correctly
• Not converting fractions to mixed numbers correctly

Q6: How can I practice evaluating expressions involving fractions?

A6:

You can practice evaluating expressions involving fractions by working through examples and exercises in a textbook or online resource. You can also try creating your own examples and challenging yourself to solve them.

Q7: What are some real-world applications of evaluating expressions involving fractions?

A7:

Evaluating expressions involving fractions has many real-world applications, including:

• Cooking and recipe scaling
• Finance and budgeting
• Science and engineering
• Architecture and design

Conclusion

Evaluating expressions involving fractions can be a challenging task, but with the right approach and techniques, it can be made easier. By following the order of operations (PEMDAS/BODMAS), finding a common denominator, subtracting and adding fractions with a common denominator, and converting fractions to mixed numbers, you can evaluate expressions involving fractions with confidence.

Final Tips and Tricks

• Practice, practice, practice! The more you practice evaluating expressions involving fractions, the more comfortable you will become with the concepts and techniques.
• Use online resources and tools to help you visualize and understand the concepts.
• Challenge yourself to create your own examples and exercises to practice evaluating expressions involving fractions.
• Review and practice regularly to reinforce your understanding and build your confidence.