Solve The Following Expressions And Select The Correct Answers From The Options Provided.1. Evaluate: $\[ 24 \frac{2(-3)-(5)-48+(-3))}{5-6)} \\]A. 22 B. 19 C. 92. Evaluate: $\[ \sqrt{45} - 2^3 + \sqrt{216} + 3 \\]A. 1 B. [Provide

Introduction

Mathematical expressions are a crucial part of mathematics, and solving them requires a deep understanding of mathematical concepts and operations. In this article, we will solve two mathematical expressions and select the correct answers from the options provided.

Expression 1: Evaluating a Complex Expression

The first expression is:

{ 24 \frac{2(-3)-(5)-48+(-3))}{5-6)} \}

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Evaluate the expressions inside the parentheses:
   • $2(-3) = -6$
   • $-6 - 5 = -11$
   • $-11 - 48 = -59$
   • $-59 + (-3) = -62$
2. Simplify the expression:
   • $24 \frac{-62}{5-6}$
3. Evaluate the expression inside the parentheses:
   • $5 - 6 = -1$
4. Simplify the expression:
   • $24 \frac{-62}{-1}$
5. Evaluate the expression:
   • $24 \times 62 = 1488$
   • $-1 \times -62 = 62$
   • $1488 + 62 = 1550$

However, the expression is not in the correct format. Let's re-evaluate the expression:

{ 24 \frac{2(-3)-(5)-48+(-3))}{5-6)} \}

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Evaluate the expressions inside the parentheses:
   • $2(-3) = -6$
   • $-6 - 5 = -11$
   • $-11 - 48 = -59$
   • $-59 + (-3) = -62$
2. Simplify the expression:
   • $24 \frac{-62}{5-6}$
3. Evaluate the expression inside the parentheses:
   • $5 - 6 = -1$
4. Simplify the expression:
   • $24 \frac{-62}{-1}$
5. Evaluate the expression:
   • $24 \times -62 = -1488$
   • $-1 \times -62 = 62$
   • $-1488 + 62 = -1426$

The correct answer is:

A. 22 is incorrect B. 19 is incorrect C. 92 is incorrect D. -1426 is correct

Expression 2: Evaluating a Radical Expression

The second expression is:

{ \sqrt{45} - 2^3 + \sqrt{216} + 3 \}

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Evaluate the expressions inside the parentheses:
   • $\sqrt{45} = 6.708$
   • $2^3 = 8$
   • $\sqrt{216} = 14.697$
2. Simplify the expression:
   • $6.708 - 8 + 14.697 + 3$
3. Evaluate the expression:
   • $6.708 - 8 = -1.292$
   • $-1.292 + 14.697 = 13.405$
   • $13.405 + 3 = 16.405$

The correct answer is:

A. 1 is incorrect B. [Provide the correct answer] is incorrect C. 16.405 is correct

Conclusion

Solving mathematical expressions requires a deep understanding of mathematical concepts and operations. In this article, we solved two mathematical expressions and selected the correct answers from the options provided. We hope that this article has provided valuable insights and knowledge on solving mathematical expressions.

References

• Order of Operations (PEMDAS)
• Radical Expressions

Discussion

Introduction

Mathematical expressions are a crucial part of mathematics, and solving them requires a deep understanding of mathematical concepts and operations. In this article, we will answer some frequently asked questions about mathematical expressions.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which 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: How do I evaluate expressions with radicals?

A: To evaluate expressions with radicals, we need to follow the order of operations. First, we need to evaluate any expressions inside the parentheses. Then, we need to simplify the radical expression by finding the square root of the number inside the radical sign.

For example, to evaluate the expression $\sqrt{45}$, we need to find the square root of 45. The square root of 45 is 6.708.

Q: What is the difference between a variable and a constant?

A: A variable is a letter or symbol that represents a value that can change. A constant is a value that does not change.

For example, in the expression 2x + 3, x is a variable because its value can change. The number 3 is a constant because its value does not change.

Q: How do I simplify complex expressions?

A: To simplify complex expressions, we need to follow the order of operations. First, we need to evaluate any expressions inside the parentheses. Then, we need to simplify the expression by combining like terms.

For example, to simplify the expression 2x + 3x + 4, we need to combine the like terms 2x and 3x. The result is 5x + 4.

Q: What is the difference between an equation and an expression?

A: An equation is a statement that says two expressions are equal. An expression is a group of numbers, variables, and operators that can be evaluated to produce a value.

For example, the equation 2x + 3 = 5 is an equation because it says that the expression 2x + 3 is equal to the value 5. The expression 2x + 3 is an expression because it is a group of numbers, variables, and operators that can be evaluated to produce a value.

Q: How do I evaluate expressions with fractions?

A: To evaluate expressions with fractions, we need to follow the order of operations. First, we need to evaluate any expressions inside the parentheses. Then, we need to simplify the fraction by finding the least common denominator (LCD).

For example, to evaluate the expression $\frac{1}{2} + \frac{1}{3}$, we need to find the LCD of 2 and 3, which is 6. Then, we need to rewrite the fractions with the LCD:

$\frac{1}{2} = \frac{3}{6}$ $\frac{1}{3} = \frac{2}{6}$

Now, we can add the fractions:

$\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$

Conclusion

Mathematical expressions are a crucial part of mathematics, and solving them requires a deep understanding of mathematical concepts and operations. In this article, we answered some frequently asked questions about mathematical expressions. We hope that this article has provided valuable insights and knowledge on solving mathematical expressions.

References

• Order of Operations (PEMDAS)
• Radical Expressions
• Equations and Expressions

Discussion

What are some common mistakes that people make when solving mathematical expressions? How can we improve our understanding of mathematical concepts and operations? Share your thoughts and insights in the comments below!