Simplify The Following Expression:$51 + 27 - 6 \div (4 - 7$\]A. 76 B. 80 C. 24 D. -24

Introduction

Mathematical expressions can be complex and challenging to simplify, especially when they involve multiple operations and parentheses. In this article, we will focus on simplifying a specific expression: $51 + 27 - 6 \div (4 - 7)$. We will break down the expression step by step, using the order of operations (PEMDAS) to ensure that we arrive at the correct solution.

Understanding the Order of Operations

Before we dive into simplifying the expression, it's essential to understand the order of operations, also known as PEMDAS. PEMDAS stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next (e.g., 2^3).
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Simplifying the Expression

Now that we understand the order of operations, let's simplify the expression step by step:

Step 1: Evaluate the Expression Inside the Parentheses

The expression inside the parentheses is $4 - 7$. To evaluate this expression, we simply subtract 7 from 4:

$4 - 7 = -3$

So, the expression now becomes:

$51 + 27 - 6 \div (-3)$

Step 2: Evaluate the Division Operation

Next, we need to evaluate the division operation: $6 \div (-3)$. To do this, we simply divide 6 by -3:

$6 \div (-3) = -2$

So, the expression now becomes:

$51 + 27 - (-2)$

Step 3: Evaluate the Addition and Subtraction Operations

Finally, we need to evaluate the addition and subtraction operations. To do this, we simply add 51 and 27, and then subtract -2:

$51 + 27 = 78$

$78 - (-2) = 78 + 2 = 80$

Therefore, the simplified expression is:

80

Conclusion

Simplifying mathematical expressions can be challenging, but by following the order of operations (PEMDAS), we can ensure that we arrive at the correct solution. In this article, we simplified the expression $51 + 27 - 6 \div (4 - 7)$ step by step, using the order of operations to evaluate the expression inside the parentheses, the division operation, and finally the addition and subtraction operations. The simplified expression is 80.

Common Mistakes to Avoid

When simplifying mathematical expressions, it's essential to avoid common mistakes, such as:

• Not following the order of operations: Failing to evaluate expressions inside parentheses, exponents, multiplication and division, and addition and subtraction in the correct order can lead to incorrect solutions.
• Not evaluating expressions inside parentheses correctly: Failing to evaluate expressions inside parentheses correctly can lead to incorrect solutions.
• Not evaluating division operations correctly: Failing to evaluate division operations correctly can lead to incorrect solutions.

Practice Problems

To practice simplifying mathematical expressions, try the following problems:

• Simplify the expression: $2 + 5 - 3 \div (1 - 2)$
• Simplify the expression: $10 - 2 + 3 \div (4 - 1)$
• Simplify the expression: $15 + 2 - 3 \div (2 - 1)$

Additional Resources

For additional resources on simplifying mathematical expressions, try the following:

• Khan Academy: Simplifying Expressions
• Mathway: Simplifying Expressions
• Wolfram Alpha: Simplifying Expressions

Introduction

In our previous article, we simplified the expression $51 + 27 - 6 \div (4 - 7)$ step by step, using the order of operations (PEMDAS). In this article, we will answer some frequently asked questions (FAQs) about simplifying mathematical expressions.

Q&A

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when simplifying mathematical expressions. The acronym PEMDAS stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next (e.g., 2^3).
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: Why is it important to follow the order of operations?

A: Following the order of operations is essential to ensure that we arrive at the correct solution when simplifying mathematical expressions. If we don't follow the order of operations, we may get incorrect answers.

Q: What happens if I have multiple parentheses in an expression?

A: If you have multiple parentheses in an expression, you need to evaluate the expressions inside the innermost parentheses first, and then work your way outwards.

Q: How do I handle negative numbers in an expression?

A: When simplifying an expression with negative numbers, you need to follow the order of operations as usual. For example, if you have the expression $-3 + 2 \div (4 - 1)$, you would first evaluate the expression inside the parentheses, which is $4 - 1 = 3$. Then, you would divide 2 by 3, which is $2 \div 3 = \frac{2}{3}$. Finally, you would add -3 and $\frac{2}{3}$, which is $-3 + \frac{2}{3} = -\frac{7}{3}$.

Q: Can I simplify an expression with multiple operations in a single step?

A: Yes, you can simplify an expression with multiple operations in a single step. For example, if you have the expression $2 + 3 \times 4 - 5$, you can simplify it in a single step by following the order of operations: $2 + 3 \times 4 - 5 = 2 + 12 - 5 = 9$.

Q: What if I have a fraction in an expression?

A: If you have a fraction in an expression, you need to follow the order of operations as usual. For example, if you have the expression $2 + \frac{1}{3} \div (4 - 1)$, you would first evaluate the expression inside the parentheses, which is $4 - 1 = 3$. Then, you would divide $\frac{1}{3}$ by 3, which is $\frac{1}{3} \div 3 = \frac{1}{9}$. Finally, you would add 2 and $\frac{1}{9}$, which is $2 + \frac{1}{9} = \frac{19}{9}$.

Practice Problems

To practice simplifying mathematical expressions, try the following problems:

• Simplify the expression: $2 + 5 - 3 \div (1 - 2)$
• Simplify the expression: $10 - 2 + 3 \div (4 - 1)$
• Simplify the expression: $15 + 2 - 3 \div (2 - 1)$

Additional Resources

For additional resources on simplifying mathematical expressions, try the following:

• Khan Academy: Simplifying Expressions
• Mathway: Simplifying Expressions
• Wolfram Alpha: Simplifying Expressions

By following the order of operations and practicing with sample problems, you can become more confident in your ability to simplify mathematical expressions.