Which Shows Steps For Correctly Evaluating 9 ÷ 3 + ( 13 − 7 ) × 2 9 \div 3+(13-7) \times 2 9 ÷ 3 + ( 13 − 7 ) × 2 ?A.${ \begin{array}{c} 9 \div 3+(13-7) \times 2 \ 9 \div 3+6 \times 2 \ 3+6 \times 2 \ 3+12 \ 15 \end{array} } B . B. B . [ \begin{array}{c} 9 \div 3+(13-7)

Introduction

Evaluating mathematical expressions is a crucial skill that students and professionals alike need to master. It involves following a set of rules and guidelines to simplify complex expressions and arrive at a final answer. In this article, we will explore the steps involved in correctly evaluating mathematical expressions, using the expression $9 \div 3+(13-7) \times 2$ as an example.

Understanding the Order of Operations

Before we dive into the steps involved in evaluating the expression, it's essential to understand 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 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 first step in evaluating the expression $9 \div 3+(13-7) \times 2$ is to evaluate the expression inside the parentheses. In this case, we need to evaluate the expression $13-7$. To do this, we simply subtract 7 from 13, which gives us $6$.

Step 2: Rewrite the Expression with the Result

Now that we have evaluated the expression inside the parentheses, we can rewrite the original expression with the result. The expression now becomes $9 \div 3+6 \times 2$.

Step 3: Evaluate Division and Multiplication Operations

The next step is to evaluate the division and multiplication operations in the expression. In this case, we need to evaluate the division operation $9 \div 3$ and the multiplication operation $6 \times 2$. To do this, we simply divide 9 by 3, which gives us $3$, and multiply 6 by 2, which gives us $12$.

Step 4: Rewrite the Expression with the Results

Now that we have evaluated the division and multiplication operations, we can rewrite the expression with the results. The expression now becomes $3+12$.

Step 5: Evaluate Addition Operation

The final step is to evaluate the addition operation in the expression. In this case, we simply add 3 and 12, which gives us $15$.

Conclusion

In conclusion, evaluating mathematical expressions involves following a set of rules and guidelines to simplify complex expressions and arrive at a final answer. By understanding the order of operations and following the steps outlined in this article, you can correctly evaluate expressions like $9 \div 3+(13-7) \times 2$.

Example Solutions

There are two example solutions provided below:

Solution A

{ \begin{array}{c} 9 \div 3+(13-7) \times 2 \\ 9 \div 3+6 \times 2 \\ 3+6 \times 2 \\ 3+12 \\ 15 \end{array} \}

Solution B

{ \begin{array}{c} 9 \div 3+(13-7) \\ 3+6 \times 2 \\ 3+12 \\ 15 \end{array} \}

Discussion

Solution A is the correct solution, as it follows the order of operations and evaluates the expression step by step. Solution B is incorrect, as it does not follow the order of operations and evaluates the expression incorrectly.

Final Answer

The final answer is $\boxed{15}$.

Introduction

Evaluating mathematical expressions is a crucial skill that students and professionals alike need to master. It involves following a set of rules and guidelines to simplify complex expressions and arrive at a final answer. In this article, we will explore the steps involved in correctly evaluating mathematical expressions, using the expression $9 \div 3+(13-7) \times 2$ as an example.

Understanding the Order of Operations

Before we dive into the steps involved in evaluating the expression, it's essential to understand 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 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 first step in evaluating the expression $9 \div 3+(13-7) \times 2$ is to evaluate the expression inside the parentheses. In this case, we need to evaluate the expression $13-7$. To do this, we simply subtract 7 from 13, which gives us $6$.

Step 2: Rewrite the Expression with the Result

Now that we have evaluated the expression inside the parentheses, we can rewrite the original expression with the result. The expression now becomes $9 \div 3+6 \times 2$.

Step 3: Evaluate Division and Multiplication Operations

The next step is to evaluate the division and multiplication operations in the expression. In this case, we need to evaluate the division operation $9 \div 3$ and the multiplication operation $6 \times 2$. To do this, we simply divide 9 by 3, which gives us $3$, and multiply 6 by 2, which gives us $12$.

Step 4: Rewrite the Expression with the Results

Now that we have evaluated the division and multiplication operations, we can rewrite the expression with the results. The expression now becomes $3+12$.

Step 5: Evaluate Addition Operation

The final step is to evaluate the addition operation in the expression. In this case, we simply add 3 and 12, which gives us $15$.

Conclusion

In conclusion, evaluating mathematical expressions involves following a set of rules and guidelines to simplify complex expressions and arrive at a final answer. By understanding the order of operations and following the steps outlined in this article, you can correctly evaluate expressions like $9 \div 3+(13-7) \times 2$.

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 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 expressions inside parentheses?

A: To evaluate expressions inside parentheses, you simply need to perform the operation inside the parentheses. For example, if the expression is $13-7$, you would subtract 7 from 13, which gives you $6$.

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 multiplying two or more numbers together, while division involves dividing one number by another.

Q: How do I evaluate addition and subtraction operations?

A: To evaluate addition and subtraction operations, you simply need to add or subtract the numbers in the expression. For example, if the expression is $3+12$, you would add 3 and 12, which gives you $15$.

Q: What is the final answer to the expression $9 \div 3+(13-7) \times 2$?

A: The final answer to the expression $9 \div 3+(13-7) \times 2$ is $15$.

Q: Can you provide an example of a mathematical expression that requires the order of operations?

A: Yes, here is an example of a mathematical expression that requires the order of operations:

$3 \times 2 + 12 \div 4 - 5$

To evaluate this expression, you would follow the order of operations:

1. Evaluate the multiplication operation: $3 \times 2 = 6$
2. Evaluate the division operation: $12 \div 4 = 3$
3. Evaluate the addition operation: $6 + 3 = 9$
4. Evaluate the subtraction operation: $9 - 5 = 4$

The final answer is $4$.

Final Answer

The final answer is $\boxed{15}$.