Evaluate The Expression: \[$(27 \div 3)(3+12)\$\]

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Introduction

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In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Evaluating an expression involves simplifying it to a single value. In this article, we will evaluate the expression $(27 \div 3)(3+12)$ using the order of operations (PEMDAS).

Understanding the Order of Operations

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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 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

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Let's apply the order of operations to evaluate the expression $(27 \div 3)(3+12)$.

Step 1: Evaluate the Expression Inside the Parentheses

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The expression inside the parentheses is $3+12$. We need to evaluate this expression first.

$3+12 = 15$

So, the expression becomes $(27 \div 3)(15)$.

Step 2: Evaluate the Division Operation

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Next, we need to evaluate the division operation $27 \div 3$.

$27 \div 3 = 9$

So, the expression becomes $(9)(15)$.

Step 3: Evaluate the Multiplication Operation

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Finally, we need to evaluate the multiplication operation $9 \times 15$.

$9 \times 15 = 135$

Therefore, the final value of the expression $(27 \div 3)(3+12)$ is $135$.

Conclusion

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In this article, we evaluated the expression $(27 \div 3)(3+12)$ using the order of operations (PEMDAS). We first evaluated the expression inside the parentheses, then the division operation, and finally the multiplication operation. The final value of the expression is $135$.

Frequently Asked Questions

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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 using the order of operations?

A: To evaluate an expression using the order of operations, follow these steps:

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

Q: What is the final value of the expression $(27 \div 3)(3+12)$?

A: The final value of the expression $(27 \div 3)(3+12)$ is $135$.

Additional Resources

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For more information on the order of operations and how to evaluate expressions, check out the following resources:

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

By following the order of operations and using the steps outlined in this article, you can evaluate expressions like $(27 \div 3)(3+12)$ and become more confident in your math skills.

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Introduction

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Evaluating expressions is a fundamental concept in mathematics, and it's essential to understand the order of operations to simplify complex expressions. In this article, we'll answer some frequently asked questions about evaluating expressions, including the order of operations, how to evaluate expressions with multiple operations, and more.

Q&A

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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:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next (e.g., 2^3).
3. Multiplication and Division: Evaluate 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 an expression using the order of operations?

A: To evaluate an expression using the order of operations, follow these steps:

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

Q: What is the difference between multiplication and division?

A: Multiplication and division are both operations that involve numbers, but they have different effects on the result. Multiplication involves adding a number a certain number of times, while division involves finding the result of a number divided by another number.

Q: How do I evaluate an expression with multiple operations?

A: To evaluate an expression with multiple operations, follow the order of operations:

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

Q: What is the final value of the expression $(27 \div 3)(3+12)$?

A: The final value of the expression $(27 \div 3)(3+12)$ is $135$.

Q: How do I simplify complex expressions?

A: To simplify complex expressions, follow these steps:

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

Q: What are some common mistakes to avoid when evaluating expressions?

A: Some common mistakes to avoid when evaluating expressions include:

• Not following the order of operations
• Not evaluating expressions inside parentheses first
• Not evaluating exponential expressions next
• Not evaluating multiplication and division operations from left to right
• Not evaluating addition and subtraction operations from left to right

Conclusion

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Evaluating expressions is a fundamental concept in mathematics, and it's essential to understand the order of operations to simplify complex expressions. By following the order of operations and using the steps outlined in this article, you can evaluate expressions like $(27 \div 3)(3+12)$ and become more confident in your math skills.

Additional Resources

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For more information on evaluating expressions and the order of operations, check out the following resources:

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

By practicing and reviewing the concepts outlined in this article, you can become more proficient in evaluating expressions and solving math problems.