Evaluate The Expression: $\[ -4(-5) + 2[3 \times (-6)] + 9 \\]

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Introduction

In mathematics, evaluating expressions is a crucial skill that helps us solve problems and understand complex mathematical concepts. An expression is a combination of numbers, variables, and mathematical operations that can be simplified to a single value. In this article, we will evaluate the expression: ${ -4(-5) + 2[3 \times (-6)] + 9 }$ and provide a step-by-step guide on how to simplify it.

Understanding the Expression

The given expression is: ${ -4(-5) + 2[3 \times (-6)] + 9 }$. To evaluate this expression, we need to follow the order of operations (PEMDAS):

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

Step 1: Evaluate Expressions Inside Parentheses

The expression inside the parentheses is: −5-5. This is a simple number, so we can evaluate it directly.

Step 2: Evaluate Exponential Expressions

There are no exponential expressions in the given expression.

Step 3: Evaluate Multiplication and Division Operations

The expression contains two multiplication operations: −4(−5)-4(-5) and 3×(−6)3 \times (-6). We will evaluate these operations next.

Step 3.1: Evaluate −4(−5)-4(-5)

To evaluate −4(−5)-4(-5), we need to multiply −4-4 and −5-5. When multiplying two negative numbers, the result is a positive number.

−4(−5)=20-4(-5) = 20

Step 3.2: Evaluate 3×(−6)3 \times (-6)

To evaluate 3×(−6)3 \times (-6), we need to multiply 33 and −6-6. When multiplying a positive number and a negative number, the result is a negative number.

3×(−6)=−183 \times (-6) = -18

Step 4: Evaluate Addition and Subtraction Operations

The expression contains two addition operations: 20+2(−18)20 + 2(-18) and 99. We will evaluate these operations next.

Step 4.1: Evaluate 20+2(−18)20 + 2(-18)

To evaluate 20+2(−18)20 + 2(-18), we need to multiply 22 and −18-18 first, then add 2020.

2(−18)=−362(-18) = -36

20+(−36)=−1620 + (-36) = -16

Step 4.2: Evaluate −16+9-16 + 9

To evaluate −16+9-16 + 9, we need to add −16-16 and 99.

−16+9=−7-16 + 9 = -7

Conclusion

In conclusion, the expression ${ -4(-5) + 2[3 \times (-6)] + 9 }$ simplifies to −7-7. By following the order of operations (PEMDAS) and evaluating expressions inside parentheses, exponential expressions, multiplication and division operations, and addition and subtraction operations, we can simplify complex mathematical expressions.

Frequently Asked Questions

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

A: The order of operations (PEMDAS) is a set of rules that helps us evaluate mathematical expressions. It stands for:

  1. Parentheses
  2. Exponents
  3. Multiplication and Division
  4. Addition and Subtraction

Q: How do I evaluate expressions inside parentheses?

A: To evaluate expressions inside parentheses, we need to follow the order of operations (PEMDAS) and evaluate the expression inside the parentheses first.

Q: How do I evaluate exponential expressions?

A: To evaluate exponential expressions, we need to follow the order of operations (PEMDAS) and evaluate the exponential expression next.

Q: How do I evaluate multiplication and division operations?

A: To evaluate multiplication and division operations, we need to follow the order of operations (PEMDAS) and evaluate the multiplication and division operations from left to right.

Q: How do I evaluate addition and subtraction operations?

A: To evaluate addition and subtraction operations, we need to follow the order of operations (PEMDAS) and evaluate the addition and subtraction operations from left to right.

Final Thoughts

Evaluating expressions is a crucial skill in mathematics that helps us solve problems and understand complex mathematical concepts. By following the order of operations (PEMDAS) and evaluating expressions inside parentheses, exponential expressions, multiplication and division operations, and addition and subtraction operations, we can simplify complex mathematical expressions.

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Introduction

Evaluating expressions is a crucial skill in mathematics that helps us solve problems and understand complex mathematical concepts. In our previous article, we evaluated the expression: ${ -4(-5) + 2[3 \times (-6)] + 9 }$ and provided a step-by-step guide on how to simplify it. In this article, we will answer some frequently asked questions about evaluating expressions.

Q&A

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

A: The order of operations (PEMDAS) is a set of rules that helps us evaluate mathematical expressions. It stands for:

  1. Parentheses
  2. Exponents
  3. Multiplication and Division
  4. Addition and Subtraction

Q: How do I evaluate expressions inside parentheses?

A: To evaluate expressions inside parentheses, you need to follow the order of operations (PEMDAS) and evaluate the expression inside the parentheses first.

Q: How do I evaluate exponential expressions?

A: To evaluate exponential expressions, you need to follow the order of operations (PEMDAS) and evaluate the exponential expression next.

Q: How do I evaluate multiplication and division operations?

A: To evaluate multiplication and division operations, you need to follow the order of operations (PEMDAS) and evaluate the multiplication and division operations from left to right.

Q: How do I evaluate addition and subtraction operations?

A: To evaluate addition and subtraction operations, you need to follow the order of operations (PEMDAS) and evaluate the 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 rules. Multiplication involves multiplying two or more numbers together, while division involves dividing one number by another.

Q: How do I evaluate expressions with multiple operations?

A: To evaluate expressions with multiple operations, you need to follow the order of operations (PEMDAS) and evaluate the operations from left to right.

Q: Can I use a calculator to evaluate expressions?

A: Yes, you can use a calculator to evaluate expressions, but it's always a good idea to understand the steps involved in evaluating the expression.

Q: How do I simplify complex expressions?

A: To simplify complex expressions, you need to follow the order of operations (PEMDAS) and evaluate the operations from left to right.

Q: What is the importance of evaluating expressions?

A: Evaluating expressions is an important skill in mathematics that helps us solve problems and understand complex mathematical concepts.

Tips and Tricks

Tip 1: Use the order of operations (PEMDAS) to evaluate expressions.

The order of operations (PEMDAS) is a set of rules that helps us evaluate mathematical expressions. It stands for:

  1. Parentheses
  2. Exponents
  3. Multiplication and Division
  4. Addition and Subtraction

Tip 2: Evaluate expressions inside parentheses first.

To evaluate expressions inside parentheses, you need to follow the order of operations (PEMDAS) and evaluate the expression inside the parentheses first.

Tip 3: Use a calculator to check your work.

If you're unsure about the answer to an expression, you can use a calculator to check your work.

Conclusion

Evaluating expressions is a crucial skill in mathematics that helps us solve problems and understand complex mathematical concepts. By following the order of operations (PEMDAS) and evaluating expressions inside parentheses, exponential expressions, multiplication and division operations, and addition and subtraction operations, we can simplify complex mathematical expressions. We hope this Q&A guide has been helpful in answering your questions about evaluating expressions.

Frequently Asked Questions (FAQs)

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

A: The order of operations (PEMDAS) is a set of rules that helps us evaluate mathematical expressions. It stands for:

  1. Parentheses
  2. Exponents
  3. Multiplication and Division
  4. Addition and Subtraction

Q: How do I evaluate expressions with multiple operations?

A: To evaluate expressions with multiple operations, you need to follow the order of operations (PEMDAS) and evaluate the operations from left to right.

Q: Can I use a calculator to evaluate expressions?

A: Yes, you can use a calculator to evaluate expressions, but it's always a good idea to understand the steps involved in evaluating the expression.

Q: How do I simplify complex expressions?

A: To simplify complex expressions, you need to follow the order of operations (PEMDAS) and evaluate the operations from left to right.

Final Thoughts

Evaluating expressions is an important skill in mathematics that helps us solve problems and understand complex mathematical concepts. By following the order of operations (PEMDAS) and evaluating expressions inside parentheses, exponential expressions, multiplication and division operations, and addition and subtraction operations, we can simplify complex mathematical expressions. We hope this Q&A guide has been helpful in answering your questions about evaluating expressions.