What Is The Value Of 3 [ − ( − 3 + 17 ) ] − ( − 4 ) × 2 3[-(-3+17)]-(-4) \times 2 3 [ − ( − 3 + 17 )] − ( − 4 ) × 2 ?

Introduction

In mathematics, expressions involving multiple operations and parentheses can be challenging to evaluate. The order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction), is a set of rules that helps us evaluate such expressions. In this article, we will explore the value of the expression $3[-(-3+17)]-(-4) \times 2$ using the order of operations.

Understanding the Order of Operations

The order of operations is a set of rules that dictates the order in which we perform operations in an expression. The rules are as follows:

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.

Evaluating the Expression

Let's break down the expression $3[-(-3+17)]-(-4) \times 2$ step by step using the order of operations.

Step 1: Evaluate the expression inside the parentheses

The expression inside the parentheses is $-3+17$. To evaluate this expression, we need to follow the order of operations.

• Parentheses: Evaluate the expression inside the parentheses first. In this case, there are no parentheses inside the parentheses, so we can move on to the next step.
• Exponents: There are no exponential expressions in this case, so we can move on to the next step.
• Multiplication and Division: There are no multiplication and division operations in this case, so we can move on to the next step.
• Addition and Subtraction: Finally, we can evaluate the addition and subtraction operations. In this case, we have $-3+17$. To evaluate this expression, we need to add 3 and 17. The result is 14.

So, the expression inside the parentheses evaluates to 14.

Step 2: Evaluate the expression $3[-(-3+17)]$

Now that we have evaluated the expression inside the parentheses, we can rewrite the original expression as $3[-14]$. To evaluate this expression, we need to follow the order of operations.

• Parentheses: Evaluate the expression inside the parentheses first. In this case, we have $-14$.
• Exponents: There are no exponential expressions in this case, so we can move on to the next step.
• Multiplication and Division: There are no multiplication and division operations in this case, so we can move on to the next step.
• Addition and Subtraction: Finally, we can evaluate the addition and subtraction operations. In this case, we have $3 \times -14$. To evaluate this expression, we need to multiply 3 and -14. The result is -42.

So, the expression $3[-(-3+17)]$ evaluates to -42.

Step 3: Evaluate the expression $-(-4) \times 2$

Now that we have evaluated the expression $3[-(-3+17)]$, we can rewrite the original expression as $-42-(-4) \times 2$. To evaluate this expression, we need to follow the order of operations.

• Parentheses: Evaluate the expression inside the parentheses first. In this case, we have $-4 \times 2$. To evaluate this expression, we need to multiply -4 and 2. The result is -8.
• Exponents: There are no exponential expressions in this case, so we can move on to the next step.
• Multiplication and Division: There are no multiplication and division operations in this case, so we can move on to the next step.
• Addition and Subtraction: Finally, we can evaluate the addition and subtraction operations. In this case, we have $-42-(-8)$. To evaluate this expression, we need to subtract -8 from -42. The result is -50.

So, the expression $-(-4) \times 2$ evaluates to -50.

Step 4: Evaluate the final expression

Now that we have evaluated the expression $-(-4) \times 2$, we can rewrite the original expression as $-42-(-50)$. To evaluate this expression, we need to follow the order of operations.

• Parentheses: Evaluate the expression inside the parentheses first. In this case, we have $-50$.
• Exponents: There are no exponential expressions in this case, so we can move on to the next step.
• Multiplication and Division: There are no multiplication and division operations in this case, so we can move on to the next step.
• Addition and Subtraction: Finally, we can evaluate the addition and subtraction operations. In this case, we have $-42+50$. To evaluate this expression, we need to add 42 and 50. The result is 8.

So, the final expression evaluates to 8.

Conclusion

In this article, we evaluated the expression $3[-(-3+17)]-(-4) \times 2$ using the order of operations. We broke down the expression into smaller parts and evaluated each part step by step. By following the order of operations, we were able to evaluate the expression and find its value.

Final Answer

Introduction

In our previous article, we evaluated the expression $3[-(-3+17)]-(-4) \times 2$ using the order of operations. In this article, we will answer some common questions related to evaluating expressions with multiple operations.

Q: What is the order of operations?

A: The order of operations is a set of rules that dictates the order in which we perform operations in an expression. The rules are as follows:

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: How do I evaluate an expression with multiple operations?

A: To evaluate an expression with multiple 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 if I have multiple sets of parentheses?

A: If you have multiple sets of parentheses, evaluate the innermost set of parentheses first, and then work your way outwards.

Q: What if I have a negative number inside parentheses?

A: If you have a negative number inside parentheses, evaluate the expression inside the parentheses first, and then multiply or divide the result by the negative number.

Q: What if I have a fraction inside parentheses?

A: If you have a fraction inside parentheses, evaluate the expression inside the parentheses first, and then multiply or divide the result by the fraction.

Q: Can I use the order of operations to simplify complex expressions?

A: Yes, you can use the order of operations to simplify complex expressions. By following the order of operations, you can break down complex expressions into smaller parts and evaluate each part step by step.

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

A: Some common mistakes to avoid when evaluating expressions with multiple operations include:

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

Conclusion

In this article, we answered some common questions related to evaluating expressions with multiple operations. By following the order of operations and breaking down complex expressions into smaller parts, you can evaluate expressions with multiple operations with confidence.

Final Tips

• Always follow the order of operations when evaluating expressions with multiple operations.
• Evaluate expressions inside parentheses first.
• Evaluate exponential expressions next.
• Evaluate multiplication and division operations from left to right.
• Finally, evaluate addition and subtraction operations from left to right.

By following these tips and practicing regularly, you can become proficient in evaluating expressions with multiple operations.