Evaluate The Expression: ${ [6 + 9 \times (4 - 2)] \div 4 + 2 }$

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Introduction

In mathematics, evaluating expressions is a crucial skill that involves simplifying complex mathematical statements to obtain a final value. This skill is essential in various mathematical operations, including algebra, arithmetic, and calculus. In this article, we will evaluate the expression ${ [6 + 9 \times (4 - 2)] \div 4 + 2 }$ step by step, using the order of operations (PEMDAS) to simplify the expression.

Understanding the Order of Operations (PEMDAS)

Before we begin evaluating the expression, it's essential to understand the order of operations, which is a set of rules that dictate the order in which mathematical operations should be performed. PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. This order of operations helps to avoid confusion and ensures that mathematical expressions are evaluated consistently.

Parentheses

Parentheses are used to group numbers and operations together. When parentheses are present, the operations inside the parentheses should be evaluated first.

Exponents

Exponents are used to represent repeated multiplication. For example, 232^3 represents 22 multiplied by itself 33 times.

Multiplication and Division

Multiplication and division operations should be performed from left to right. This means that if there are multiple multiplication and division operations in an expression, they should be evaluated from left to right.

Addition and Subtraction

Addition and subtraction operations should be performed from left to right. This means that if there are multiple addition and subtraction operations in an expression, they should be evaluated from left to right.

Evaluating the Expression

Now that we have a good understanding of the order of operations, let's evaluate the expression ${ [6 + 9 \times (4 - 2)] \div 4 + 2 }$ step by step.

Step 1: Evaluate the Expression Inside the Parentheses

The expression inside the parentheses is (4−2)(4 - 2). Using the order of operations, we evaluate this expression first.

(4−2)=2(4 - 2) = 2

Step 2: Multiply 9 by the Result

Next, we multiply 99 by the result of the expression inside the parentheses.

9×2=189 \times 2 = 18

Step 3: Add 6 to the Result

Now, we add 66 to the result of the multiplication.

6+18=246 + 18 = 24

Step 4: Divide the Result by 4

Next, we divide the result by 44.

24Ă·4=624 \div 4 = 6

Step 5: Add 2 to the Result

Finally, we add 22 to the result of the division.

6+2=86 + 2 = 8

Conclusion

In this article, we evaluated the expression ${ [6 + 9 \times (4 - 2)] \div 4 + 2 }$ step by step, using the order of operations (PEMDAS) to simplify the expression. We started by evaluating the expression inside the parentheses, then multiplied 99 by the result, added 66 to the result, divided the result by 44, and finally added 22 to the result. The final value of the expression is 88.

Frequently Asked Questions

  • What is the order of operations (PEMDAS)? The order of operations (PEMDAS) is a set of rules that dictate the order in which mathematical operations should be performed. The order is as follows: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
  • How do I evaluate an expression using the order of operations? To evaluate an expression using the order of operations, follow these steps: Evaluate the expression inside the parentheses, then evaluate any exponents, followed by multiplication and division operations, and finally addition and subtraction operations.
  • What is the final value of the expression ${ [6 + 9 \times (4 - 2)] \div 4 + 2 }$? The final value of the expression ${ [6 + 9 \times (4 - 2)] \div 4 + 2 }$ is 88.

Further Reading

  • Order of Operations (PEMDAS)
  • Evaluating Expressions
  • Algebra
  • Arithmetic
  • Calculus

References

  • "Order of Operations" by Math Open Reference
  • "Evaluating Expressions" by Khan Academy
  • "Algebra" by Wikipedia
  • "Arithmetic" by Wikipedia
  • "Calculus" by Wikipedia

Introduction

In our previous article, we evaluated the expression ${ [6 + 9 \times (4 - 2)] \div 4 + 2 }$ step by step, using the order of operations (PEMDAS) to simplify the expression. In this article, we will answer some frequently asked questions about evaluating expressions with PEMDAS.

Q&A

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that dictate the order in which mathematical operations should be performed. The order is as follows: 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 these steps:

  1. Evaluate the expression inside the parentheses.
  2. Evaluate any exponents.
  3. Perform multiplication and division operations from left to right.
  4. Perform addition and subtraction operations from left to right.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both arithmetic operations that involve numbers. However, multiplication involves repeated addition, while division involves sharing or grouping.

Q: How do I handle multiple operations with the same precedence?

A: When there are multiple operations with the same precedence, such as multiple multiplication and division operations, perform them from left to right.

Q: Can I use PEMDAS to evaluate expressions with fractions?

A: Yes, you can use PEMDAS to evaluate expressions with fractions. However, be sure to follow the rules for working with fractions, such as simplifying fractions and performing operations with fractions.

Q: How do I evaluate expressions with negative numbers?

A: To evaluate expressions with negative numbers, follow the same steps as you would for positive numbers. However, be sure to handle the negative sign correctly, such as by multiplying or dividing by a negative number.

Q: Can I use PEMDAS to evaluate expressions with variables?

A: Yes, you can use PEMDAS to evaluate expressions with variables. However, be sure to follow the rules for working with variables, such as substituting values for variables and performing operations with variables.

Q: How do I evaluate expressions with multiple levels of parentheses?

A: To evaluate expressions with multiple levels of parentheses, follow the same steps as you would for a single level of parentheses. However, be sure to evaluate the innermost parentheses first and work your way outwards.

Q: Can I use PEMDAS to evaluate expressions with exponents?

A: Yes, you can use PEMDAS to evaluate expressions with exponents. However, be sure to follow the rules for working with exponents, such as simplifying exponents and performing operations with exponents.

Conclusion

In this article, we answered some frequently asked questions about evaluating expressions with PEMDAS. We covered topics such as the order of operations, handling multiple operations with the same precedence, and evaluating expressions with fractions, negative numbers, variables, and exponents. By following the rules of PEMDAS, you can evaluate complex expressions with confidence.

Frequently Asked Questions

  • What is the order of operations (PEMDAS)?
  • How do I evaluate an expression using the order of operations?
  • What is the difference between multiplication and division?
  • How do I handle multiple operations with the same precedence?
  • Can I use PEMDAS to evaluate expressions with fractions?
  • How do I evaluate expressions with negative numbers?
  • Can I use PEMDAS to evaluate expressions with variables?
  • How do I evaluate expressions with multiple levels of parentheses?
  • Can I use PEMDAS to evaluate expressions with exponents?

Further Reading

  • Order of Operations (PEMDAS)
  • Evaluating Expressions
  • Algebra
  • Arithmetic
  • Calculus

References

  • "Order of Operations" by Math Open Reference
  • "Evaluating Expressions" by Khan Academy
  • "Algebra" by Wikipedia
  • "Arithmetic" by Wikipedia
  • "Calculus" by Wikipedia