Select The Best Answer For The Question.4. Simplify $(3 \times 22) \div 6+\left[28-(4)^2\right]=$ ?A. 32 B. 55 C. 46 D. 23

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Introduction

Mathematical expressions can be complex and challenging to simplify. However, with a clear understanding of the order of operations and basic arithmetic rules, we can break down even the most daunting expressions into manageable parts. In this article, we will explore a step-by-step approach to simplifying mathematical expressions, using the given expression as a case study.

The Given Expression

The given expression is:

(3×22)÷6+[28−(4)2]=(3 \times 22) \div 6+\left[28-(4)^2\right]=

Our goal is to simplify this expression and arrive at a final answer.

Step 1: Evaluate the Exponents

The first step in simplifying the expression is to evaluate the exponents. In this case, we have (4)2(4)^2, which can be evaluated as follows:

(4)2=4×4=16(4)^2 = 4 \times 4 = 16

Step 2: Simplify the Expression Inside the Square Brackets

Now that we have evaluated the exponent, we can simplify the expression inside the square brackets:

28−(4)2=28−16=1228 - (4)^2 = 28 - 16 = 12

Step 3: Multiply 3 and 22

Next, we need to multiply 3 and 22:

3×22=663 \times 22 = 66

Step 4: Divide 66 by 6

Now, we can divide 66 by 6:

66÷6=1166 \div 6 = 11

Step 5: Add 11 and 12

Finally, we can add 11 and 12:

11+12=2311 + 12 = 23

Conclusion

By following the order of operations and simplifying the expression step-by-step, we have arrived at a final answer of 23.

Answer

The correct answer is:

  • D. 23

Why This Answer?

This answer is correct because we have followed the order of operations and simplified the expression step-by-step. We have evaluated the exponents, simplified the expression inside the square brackets, multiplied 3 and 22, divided 66 by 6, and finally added 11 and 12.

Common Mistakes

When simplifying mathematical expressions, it's easy to make mistakes. Here are some common mistakes to avoid:

  • Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when simplifying expressions.
  • Not evaluating exponents: Make sure to evaluate exponents before simplifying the expression.
  • Not simplifying expressions inside parentheses: Make sure to simplify expressions inside parentheses before simplifying the expression.

Final Thoughts

Simplifying mathematical expressions can be challenging, but with a clear understanding of the order of operations and basic arithmetic rules, we can break down even the most daunting expressions into manageable parts. By following the steps outlined in this article, we can arrive at a final answer with confidence.

Frequently Asked Questions

Q: What is the order of operations?

A: The order of operations is PEMDAS, which 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 simplified correctly and consistently.

Q: What is the difference between multiplication and division?

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

Q: Why is it important to simplify expressions inside parentheses?

A: Simplifying expressions inside parentheses ensures that the expression is simplified correctly and consistently.

Q: What is the difference between addition and subtraction?

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

Conclusion

In conclusion, simplifying mathematical expressions requires a clear understanding of the order of operations and basic arithmetic rules. By following the steps outlined in this article, we can arrive at a final answer with confidence. Remember to evaluate exponents, simplify expressions inside parentheses, and follow the order of operations to ensure that mathematical expressions are simplified correctly and consistently.

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Introduction

Simplifying mathematical expressions can be a challenging task, but with a clear understanding of the order of operations and basic arithmetic rules, we can break down even the most daunting expressions into manageable parts. In this article, we will answer some frequently asked questions about simplifying mathematical expressions.

Q&A

Q: What is the order of operations?

A: The order of operations is PEMDAS, which 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 simplified correctly and consistently. It helps to avoid errors and ensures that the expression is evaluated in the correct order.

Q: What is the difference between multiplication and division?

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

Q: Why is it important to simplify expressions inside parentheses?

A: Simplifying expressions inside parentheses ensures that the expression is simplified correctly and consistently. It helps to avoid errors and ensures that the expression is evaluated in the correct order.

Q: What is the difference between addition and subtraction?

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

Q: How do I simplify expressions with multiple operations?

A: To simplify expressions with multiple operations, follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses, then evaluate any exponents, followed by multiplication and division (from left to right), and finally addition and subtraction (from left to right).

Q: What is the rule for evaluating expressions with multiple operations?

A: The rule for evaluating expressions with multiple operations is to follow the order of operations (PEMDAS). This means that you should evaluate any expressions inside parentheses first, followed by any exponents, then multiplication and division (from left to right), and finally addition and subtraction (from left to right).

Q: How do I simplify expressions with fractions?

A: To simplify expressions with fractions, follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses, then evaluate any exponents, followed by multiplication and division (from left to right), and finally addition and subtraction (from left to right). When simplifying fractions, you can multiply the numerator and denominator by the same number to eliminate any common factors.

Q: What is the rule for simplifying fractions?

A: The rule for simplifying fractions is to multiply the numerator and denominator by the same number to eliminate any common factors. This will result in a simplified fraction.

Q: How do I simplify expressions with decimals?

A: To simplify expressions with decimals, follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses, then evaluate any exponents, followed by multiplication and division (from left to right), and finally addition and subtraction (from left to right). When simplifying decimals, you can round the decimal to the nearest hundredth or thousandth to simplify the expression.

Q: What is the rule for simplifying decimals?

A: The rule for simplifying decimals is to round the decimal to the nearest hundredth or thousandth to simplify the expression.

Conclusion

In conclusion, simplifying mathematical expressions requires a clear understanding of the order of operations and basic arithmetic rules. By following the steps outlined in this article, we can arrive at a final answer with confidence. Remember to evaluate exponents, simplify expressions inside parentheses, and follow the order of operations to ensure that mathematical expressions are simplified correctly and consistently.

Additional Resources

For more information on simplifying mathematical expressions, check out the following resources:

  • Mathway: A online math problem solver that can help you simplify mathematical expressions.
  • Khan Academy: A free online learning platform that offers video lessons and practice exercises on simplifying mathematical expressions.
  • Math Open Reference: A free online math reference book that offers detailed explanations and examples on simplifying mathematical expressions.

Final Thoughts

Simplifying mathematical expressions can be a challenging task, but with a clear understanding of the order of operations and basic arithmetic rules, we can break down even the most daunting expressions into manageable parts. By following the steps outlined in this article, we can arrive at a final answer with confidence. Remember to evaluate exponents, simplify expressions inside parentheses, and follow the order of operations to ensure that mathematical expressions are simplified correctly and consistently.