Evaluate The Following Expression: 3 + ( 18 × 3 ) − 16 + ( 4 × 8 ) + 5 = 3 + (18 \times 3) - 16 + (4 \times 8) + 5 = 3 + ( 18 × 3 ) − 16 + ( 4 × 8 ) + 5 =

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Introduction

In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Evaluating an expression involves performing the operations in the correct order to obtain the final result. In this article, we will evaluate the given expression: $3 + (18 \times 3) - 16 + (4 \times 8) + 5 =$. We will follow the order of operations (PEMDAS) to simplify the expression and find the final answer.

Understanding the Order of Operations

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. PEMDAS is a popular acronym that 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.

Evaluating the Expression

Now that we understand the order of operations, let's evaluate the given expression:

$3 + (18 \times 3) - 16 + (4 \times 8) + 5 =$

Step 1: Evaluate Expressions Inside Parentheses

We will start by evaluating the expressions inside the parentheses:

$(18 \times 3) = 54$

$(4 \times 8) = 32$

So, the expression becomes:

$3 + 54 - 16 + 32 + 5 =$

Step 2: Evaluate Exponential Expressions (None in this case)

There are no exponential expressions in this expression, so we can move on to the next step.

Step 3: Evaluate Multiplication and Division Operations

There are no multiplication and division operations in this expression, so we can move on to the next step.

Step 4: Evaluate Addition and Subtraction Operations

Now, we will evaluate the addition and subtraction operations from left to right:

$3 + 54 = 57$

$57 - 16 = 41$

$41 + 32 = 73$

$73 + 5 = 78$

Therefore, the final answer is:

$3 + (18 \times 3) - 16 + (4 \times 8) + 5 = 78$

Conclusion

In this article, we evaluated the given expression: $3 + (18 \times 3) - 16 + (4 \times 8) + 5 =$. We followed the order of operations (PEMDAS) to simplify the expression and find the final answer. The final answer is 78.

Frequently Asked Questions

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. PEMDAS is a popular acronym that stands for: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I evaluate an expression?

A: To evaluate an expression, follow the order of operations (PEMDAS). First, evaluate expressions inside parentheses. Then, evaluate any exponential expressions. Next, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the final answer to the expression $3 + (18 \times 3) - 16 + (4 \times 8) + 5 =$?

A: The final answer to the expression $3 + (18 \times 3) - 16 + (4 \times 8) + 5 =$ is 78.

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Introduction

In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Evaluating an expression involves performing the operations in the correct order to obtain the final result. In this article, we will provide a comprehensive guide to evaluating expressions, including a step-by-step approach and a list of frequently asked questions.

Understanding the Order of Operations

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. PEMDAS is a popular acronym that 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.

Evaluating Expressions: A Step-by-Step Approach

To evaluate an expression, follow these steps:

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

Frequently Asked Questions

Here are some frequently asked questions about evaluating 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. PEMDAS is a popular acronym that stands for: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I evaluate an expression?

A: To evaluate an expression, follow the order of operations (PEMDAS). First, evaluate expressions inside parentheses. Then, evaluate any exponential expressions. Next, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between PEMDAS and BODMAS?

A: PEMDAS and BODMAS are two popular acronyms that stand for the order of operations. PEMDAS is commonly used in the United States, while BODMAS is commonly used in the United Kingdom and other countries. Both acronyms represent the same order of operations: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

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

A: When evaluating an expression with negative numbers, follow the same order of operations as before. However, when subtracting a negative number, it is equivalent to adding a positive number. For example, 5 - (-3) is equivalent to 5 + 3.

Q: Can I use a calculator to evaluate an expression?

A: Yes, you can use a calculator to evaluate an expression. However, it is still important to understand the order of operations and how to evaluate expressions manually.

Q: What is the final answer to the expression $3 + (18 \times 3) - 16 + (4 \times 8) + 5 =$?

A: The final answer to the expression $3 + (18 \times 3) - 16 + (4 \times 8) + 5 =$ is 78.

Conclusion

Evaluating expressions is an essential skill in mathematics. By following the order of operations (PEMDAS) and understanding how to evaluate expressions, you can simplify complex expressions and find the final answer. Remember to always evaluate expressions inside parentheses first, followed by exponential expressions, multiplication and division operations, and finally addition and subtraction operations.

Additional Resources

If you need additional help with evaluating expressions, here are some additional resources:

• Mathway: A online math problem solver that can help you evaluate expressions.
• Khan Academy: A free online learning platform that offers video lessons and practice exercises on evaluating expressions.
• Math Open Reference: A free online math reference book that offers detailed explanations and examples on evaluating expressions.

Final Answer

The final answer to the expression $3 + (18 \times 3) - 16 + (4 \times 8) + 5 =$ is 78.