Evaluate The Expression:${ 12 - 8 \div 2 + 1 }$

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Introduction

In mathematics, 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 order of operations is often remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. In this article, we will evaluate the expression 12 - 8 ÷ 2 + 1 using the order of operations.

Understanding 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 order of operations is as follows:

  1. Parentheses: Evaluate any 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

Now that we have a good understanding of the order of operations, let's evaluate the expression 12 - 8 ÷ 2 + 1.

Step 1: Evaluate the Division Operation

The first step in evaluating the expression is to evaluate the division operation. The expression contains the division operation 8 ÷ 2. To evaluate this operation, we need to divide 8 by 2.

8 ÷ 2 = 4

So, the expression now becomes 12 - 4 + 1.

Step 2: Evaluate the Subtraction Operation

The next step in evaluating the expression is to evaluate the subtraction operation. The expression contains the subtraction operation 12 - 4. To evaluate this operation, we need to subtract 4 from 12.

12 - 4 = 8

So, the expression now becomes 8 + 1.

Step 3: Evaluate the Addition Operation

The final step in evaluating the expression is to evaluate the addition operation. The expression contains the addition operation 8 + 1. To evaluate this operation, we need to add 8 and 1.

8 + 1 = 9

Therefore, the final value of the expression 12 - 8 ÷ 2 + 1 is 9.

Conclusion

In this article, we evaluated the expression 12 - 8 ÷ 2 + 1 using the order of operations. We followed the order of operations, which is Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction, to evaluate the expression. The final value of the expression is 9.

Frequently Asked Questions

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.

Q: What is the acronym PEMDAS?

A: PEMDAS is an 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 the order of operations, which is Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Example Problems

Problem 1: Evaluate the expression 24 ÷ 3 + 2

To evaluate this expression, we need to follow the order of operations. First, we need to evaluate the division operation 24 ÷ 3.

24 ÷ 3 = 8

So, the expression now becomes 8 + 2.

Next, we need to evaluate the addition operation 8 + 2.

8 + 2 = 10

Therefore, the final value of the expression 24 ÷ 3 + 2 is 10.

Problem 2: Evaluate the expression 12 - 4 + 3

To evaluate this expression, we need to follow the order of operations. First, we need to evaluate the subtraction operation 12 - 4.

12 - 4 = 8

So, the expression now becomes 8 + 3.

Next, we need to evaluate the addition operation 8 + 3.

8 + 3 = 11

Therefore, the final value of the expression 12 - 4 + 3 is 11.

Summary

In this article, we evaluated the expression 12 - 8 ÷ 2 + 1 using the order of operations. We followed the order of operations, which is Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction, to evaluate the expression. The final value of the expression is 9. We also provided example problems to help illustrate the order of operations.

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Introduction

In our previous article, we evaluated the expression 12 - 8 ÷ 2 + 1 using the order of operations. In this article, we will answer some frequently asked questions about the order of operations.

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.

Q: What is the acronym PEMDAS?

A: PEMDAS is an 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 the order of operations, which is Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both arithmetic operations that involve numbers. However, multiplication involves multiplying two or more numbers together, while division involves dividing one number by another.

Q: What is the difference between addition and subtraction?

A: Addition and subtraction are both arithmetic operations that involve numbers. However, addition involves adding two or more numbers together, while subtraction involves subtracting one number from another.

Q: Can I use the order of operations to evaluate expressions with fractions?

A: Yes, you can use the order of operations to evaluate expressions with fractions. However, you need to follow the order of operations carefully to ensure that you are evaluating the expression correctly.

Q: Can I use the order of operations to evaluate expressions with decimals?

A: Yes, you can use the order of operations to evaluate expressions with decimals. However, you need to follow the order of operations carefully to ensure that you are evaluating the expression correctly.

Q: What is the order of operations for expressions with multiple operations?

A: The order of operations for expressions with multiple operations is as follows:

  1. Parentheses: Evaluate any 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: Can I use the order of operations to evaluate expressions with negative numbers?

A: Yes, you can use the order of operations to evaluate expressions with negative numbers. However, you need to follow the order of operations carefully to ensure that you are evaluating the expression correctly.

Q: Can I use the order of operations to evaluate expressions with variables?

A: Yes, you can use the order of operations to evaluate expressions with variables. However, you need to follow the order of operations carefully to ensure that you are evaluating the expression correctly.

Example Problems

Problem 1: Evaluate the expression 24 ÷ 3 + 2

To evaluate this expression, we need to follow the order of operations. First, we need to evaluate the division operation 24 ÷ 3.

24 ÷ 3 = 8

So, the expression now becomes 8 + 2.

Next, we need to evaluate the addition operation 8 + 2.

8 + 2 = 10

Therefore, the final value of the expression 24 ÷ 3 + 2 is 10.

Problem 2: Evaluate the expression 12 - 4 + 3

To evaluate this expression, we need to follow the order of operations. First, we need to evaluate the subtraction operation 12 - 4.

12 - 4 = 8

So, the expression now becomes 8 + 3.

Next, we need to evaluate the addition operation 8 + 3.

8 + 3 = 11

Therefore, the final value of the expression 12 - 4 + 3 is 11.

Conclusion

In this article, we answered some frequently asked questions about the order of operations. We also provided example problems to help illustrate the order of operations. Remember to follow the order of operations carefully to ensure that you are evaluating expressions correctly.

Additional Resources

Summary

In this article, we answered some frequently asked questions about the order of operations. We also provided example problems to help illustrate the order of operations. Remember to follow the order of operations carefully to ensure that you are evaluating expressions correctly.