Evaluate The Following Expression: 8 + 10 ÷ 2 − 4 ⋅ 2 8 + 10 \div 2 - 4 \cdot 2 8 + 10 ÷ 2 − 4 ⋅ 2

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Introduction

In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Evaluating an expression involves performing the operations in the correct order to obtain the final result. In this article, we will evaluate the expression 8+10÷2−4⋅28 + 10 \div 2 - 4 \cdot 2 using the order of operations (PEMDAS).

Understanding the Order of Operations

The order of operations is a set of rules that tells us which operations to perform first when there are 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

Now that we understand the order of operations, let's evaluate the expression 8+10÷2−4⋅28 + 10 \div 2 - 4 \cdot 2.

Step 1: Evaluate the Division Operation

The first operation to perform is the division operation: 10÷210 \div 2. According to the order of operations, we need to perform this operation before any multiplication or addition operations.

10÷2=510 \div 2 = 5

So, the expression becomes: 8+5−4⋅28 + 5 - 4 \cdot 2

Step 2: Evaluate the Multiplication Operation

The next operation to perform is the multiplication operation: 4⋅24 \cdot 2. Again, according to the order of operations, we need to perform this operation before any addition or subtraction operations.

4⋅2=84 \cdot 2 = 8

So, the expression becomes: 8+5−88 + 5 - 8

Step 3: Evaluate the Addition and Subtraction Operations

Now that we have performed all the multiplication and division operations, we can perform the addition and subtraction operations from left to right.

8+5=138 + 5 = 13

13−8=513 - 8 = 5

Therefore, the final result of the expression 8+10÷2−4⋅28 + 10 \div 2 - 4 \cdot 2 is 55.

Conclusion

Evaluating an expression involves performing the operations in the correct order to obtain the final result. In this article, we evaluated the expression 8+10÷2−4⋅28 + 10 \div 2 - 4 \cdot 2 using the order of operations (PEMDAS). We followed the steps of evaluating the division operation, then the multiplication operation, and finally the addition and subtraction operations. The final result of the expression is 55.

Frequently Asked Questions

  • What is the order of operations? The order of operations is a set of rules that tells us which operations to perform first when there are multiple operations in an expression. PEMDAS is a popular acronym that stands for: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
  • Why is it important to follow the order of operations? Following the order of operations ensures that mathematical expressions are evaluated consistently and accurately. It helps to avoid confusion and errors when working with complex expressions.
  • Can I use a calculator to evaluate an expression? Yes, you can use a calculator to evaluate an expression. However, it's always a good idea to understand the order of operations and how to evaluate expressions manually to build your mathematical skills.

Additional Resources

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

References

  • "Order of Operations" by Khan Academy
  • "Order of Operations" by Mathway
  • "Order of Operations" by Wolfram Alpha

Introduction

Evaluating mathematical expressions can be a challenging task, especially when there are multiple operations involved. In this article, we will answer some frequently asked questions about evaluating mathematical expressions, including the order of operations, how to handle parentheses, and more.

Q&A

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 there are multiple operations in an expression. PEMDAS is a popular acronym that stands for: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: Why is it important to follow the order of operations?

A: Following the order of operations ensures that mathematical expressions are evaluated consistently and accurately. It helps to avoid confusion and errors when working with complex expressions.

Q: How do I handle parentheses in an expression?

A: When there are parentheses in an expression, you need to evaluate the expression inside the parentheses first. This is because parentheses have a higher priority than other operations.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both operations that involve numbers, but they have different priorities. Multiplication and division are evaluated from left to right, meaning that you need to perform the operation that is to the left of the other operation first.

Q: How do I handle exponents in an expression?

A: Exponents are evaluated before any multiplication or division operations. This means that you need to evaluate any exponential expressions (such as 2^3) before performing any other operations.

Q: Can I use a calculator to evaluate an expression?

A: Yes, you can use a calculator to evaluate an expression. However, it's always a good idea to understand the order of operations and how to evaluate expressions manually to build your mathematical skills.

Q: What is the correct order of operations for the expression 3 + 4 × 2 - 1?

A: To evaluate this expression, you need to follow the order of operations:

  1. Multiply 4 and 2: 4 × 2 = 8
  2. Add 3 and 8: 3 + 8 = 11
  3. Subtract 1 from 11: 11 - 1 = 10

Therefore, the final result of the expression is 10.

Q: What is the correct order of operations for the expression 12 ÷ 3 + 2 × 4 - 1?

A: To evaluate this expression, you need to follow the order of operations:

  1. Divide 12 by 3: 12 ÷ 3 = 4
  2. Multiply 2 and 4: 2 × 4 = 8
  3. Add 4 and 8: 4 + 8 = 12
  4. Subtract 1 from 12: 12 - 1 = 11

Therefore, the final result of the expression is 11.

Conclusion

Evaluating mathematical expressions can be a challenging task, but by following the order of operations and understanding how to handle parentheses, exponents, and other operations, you can ensure that you get the correct result. Remember to always follow the order of operations and to use a calculator only when necessary to build your mathematical skills.

Frequently Asked Questions

  • What is the order of operations?
  • Why is it important to follow the order of operations?
  • How do I handle parentheses in an expression?
  • What is the difference between multiplication and division?
  • How do I handle exponents in an expression?
  • Can I use a calculator to evaluate an expression?
  • What is the correct order of operations for the expression 3 + 4 × 2 - 1?
  • What is the correct order of operations for the expression 12 ÷ 3 + 2 × 4 - 1?

Additional Resources

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

References

  • "Order of Operations" by Khan Academy
  • "Order of Operations" by Mathway
  • "Order of Operations" by Wolfram Alpha