Find The Value Of Each Expression: 108 ÷ ( 27 + 9 ) × 8 108 \div (27+9) \times 8 108 ÷ ( 27 + 9 ) × 8 A. 104 B. 3 C. 76 D. 24 Please Select The Best Answer From The Choices Provided: A B C D

Introduction

Mathematical expressions are a fundamental part of mathematics, and solving them requires a clear understanding of the order of operations and the rules of arithmetic. In this article, we will focus on finding the value of a specific mathematical expression: $108 \div (27+9) \times 8$. We will break down the solution step by step, using the correct order of operations and arithmetic rules.

Understanding the Order of Operations

The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
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.

Solving the Expression

Now that we have a clear understanding of the order of operations, let's apply it to the given expression: $108 \div (27+9) \times 8$.

Step 1: Evaluate the Expression Inside the Parentheses

The first step is to evaluate the expression inside the parentheses: $27+9$. Using the rules of arithmetic, we can add 27 and 9 to get:

$27+9 = 36$

So, the expression becomes: $108 \div 36 \times 8$.

Step 2: Divide 108 by 36

Next, we need to divide 108 by 36. Using the rules of arithmetic, we can divide 108 by 36 to get:

$108 \div 36 = 3$

So, the expression becomes: $3 \times 8$.

Step 3: Multiply 3 by 8

Finally, we need to multiply 3 by 8. Using the rules of arithmetic, we can multiply 3 by 8 to get:

$3 \times 8 = 24$

Therefore, the value of the expression $108 \div (27+9) \times 8$ is 24.

Conclusion

In this article, we have solved a mathematical expression using the correct order of operations and arithmetic rules. We have broken down the solution step by step, using the PEMDAS acronym to remember the order of operations. By following these steps, we have found the value of the expression $108 \div (27+9) \times 8$ to be 24.

Answer

The correct answer is:

• D. 24

Discussion

This problem requires a clear understanding of the order of operations and the rules of arithmetic. It is essential to follow the correct order of operations to avoid errors and ensure accurate results. In this case, the expression inside the parentheses was evaluated first, followed by the division and multiplication operations. By following these steps, we have found the value of the expression to be 24.

Related Topics

• Order of operations
• Arithmetic rules
• Mathematical expressions
• PEMDAS

Further Reading

For more information on mathematical expressions and the order of operations, please refer to the following resources:

• Khan Academy: Order of Operations
• Mathway: Order of Operations
• Wolfram MathWorld: Order of Operations
  Frequently Asked Questions: Mathematical Expressions =====================================================

Introduction

In our previous article, we solved a mathematical expression using the correct order of operations and arithmetic rules. In this article, we will address some frequently asked questions related to mathematical expressions and the order of operations.

Q&A

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
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 essential to follow the order of operations?

A: Following the order of operations is crucial to avoid errors and ensure accurate results. If the order of operations is not followed, the result of the expression may be incorrect.

Q: What happens if there are multiple operations with the same precedence?

A: If there are multiple operations with the same precedence, the operations should be evaluated from left to right. For example, if we have the expression $3+4 \times 5$, we would evaluate the multiplication operation first, since it is on the left.

Q: Can I use a calculator to solve mathematical expressions?

A: Yes, you can use a calculator to solve mathematical expressions. However, it is essential to understand the order of operations and the rules of arithmetic to ensure accurate results.

Q: How do I evaluate expressions with exponents?

A: To evaluate expressions with exponents, you should follow the order of operations. Exponents should be evaluated after parentheses and before multiplication and division.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both arithmetic operations that involve numbers. However, multiplication involves combining numbers to get a product, while division involves dividing a number by another number to get a quotient.

Q: Can I use a calculator to evaluate expressions with exponents?

A: Yes, you can use a calculator to evaluate expressions with exponents. However, it is essential to understand the order of operations and the rules of arithmetic to ensure accurate results.

Conclusion

In this article, we have addressed some frequently asked questions related to mathematical expressions and the order of operations. We have provided clear explanations and examples to help you understand the concepts. By following the order of operations and the rules of arithmetic, you can ensure accurate results and avoid errors.

Related Topics

• Order of operations
• Arithmetic rules
• Mathematical expressions
• PEMDAS

Further Reading

For more information on mathematical expressions and the order of operations, please refer to the following resources:

• Khan Academy: Order of Operations
• Mathway: Order of Operations
• Wolfram MathWorld: Order of Operations

Practice Problems

Try solving the following practice problems to test your understanding of mathematical expressions and the order of operations:

1. Evaluate the expression $12 \div (4+2) \times 3$.
2. Evaluate the expression $8 \times (2+5) - 3$.
3. Evaluate the expression $9 \div (3+1) + 2$.

Answer Key

1. $12 \div (4+2) \times 3 = 12 \div 6 \times 3 = 2 \times 3 = 6$
2. $8 \times (2+5) - 3 = 8 \times 7 - 3 = 56 - 3 = 53$
3. $9 \div (3+1) + 2 = 9 \div 4 + 2 = 2.25 + 2 = 4.25$