Evaluate The Expression: ${ \frac{3 3}{5-2}-\frac{(4-2) 2}{2} }$

by ADMIN 66 views

Introduction

In mathematics, evaluating expressions is a fundamental concept that involves simplifying mathematical expressions by performing operations such as addition, subtraction, multiplication, and division. In this article, we will evaluate the given expression: 335−2−(4−2)22\frac{3^3}{5-2}-\frac{(4-2)^2}{2}. We will break down the expression into smaller parts, simplify each part, and then combine them to get the final result.

Evaluating the First Term

The first term in the expression is 335−2\frac{3^3}{5-2}. To evaluate this term, we need to follow the order of operations (PEMDAS):

  1. Evaluate the exponent: 33=273^3 = 27
  2. Evaluate the denominator: 5−2=35-2 = 3
  3. Divide the numerator by the denominator: 273=9\frac{27}{3} = 9

So, the first term simplifies to 99.

Evaluating the Second Term

The second term in the expression is (4−2)22\frac{(4-2)^2}{2}. To evaluate this term, we need to follow the order of operations (PEMDAS):

  1. Evaluate the expression inside the parentheses: 4−2=24-2 = 2
  2. Square the result: 22=42^2 = 4
  3. Divide the result by 22: 42=2\frac{4}{2} = 2

So, the second term simplifies to 22.

Combining the Terms

Now that we have simplified both terms, we can combine them to get the final result:

335−2−(4−2)22=9−2=7\frac{3^3}{5-2}-\frac{(4-2)^2}{2} = 9 - 2 = 7

Therefore, the final result of the expression is 77.

Conclusion

In this article, we evaluated the given expression: 335−2−(4−2)22\frac{3^3}{5-2}-\frac{(4-2)^2}{2}. We broke down the expression into smaller parts, simplified each part, and then combined them to get the final result. The final result of the expression is 77. This article demonstrates the importance of following the order of operations and simplifying mathematical expressions to get the correct result.

Tips and Tricks

  • When evaluating expressions, always follow the order of operations (PEMDAS).
  • Simplify each term in the expression before combining them.
  • Use parentheses to group expressions and avoid confusion.
  • Check your work by plugging in numbers or using a calculator to verify the result.

Frequently Asked Questions

  • Q: What is the order of operations (PEMDAS)? A: The order of operations is a set of rules that tells us which operations to perform first when evaluating an expression. The acronym PEMDAS stands for:
    • Parentheses: Evaluate expressions inside parentheses first.
    • Exponents: Evaluate any exponential expressions next.
    • Multiplication and Division: Evaluate any multiplication and division operations from left to right.
    • Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
  • Q: How do I simplify mathematical expressions? A: To simplify a mathematical expression, follow these steps:
    1. Evaluate any exponential expressions.
    2. Evaluate any expressions inside parentheses.
    3. Simplify any fractions or decimals.
    4. Combine like terms.
    5. Check your work by plugging in numbers or using a calculator to verify the result.

Further Reading

  • For more information on evaluating expressions, see the article "Evaluating Expressions: A Step-by-Step Guide".
  • For more information on simplifying mathematical expressions, see the article "Simplifying Mathematical Expressions: A Guide".
  • For more information on the order of operations, see the article "The Order of Operations: A Guide to PEMDAS".

Introduction

In our previous article, we evaluated the expression: 335−2−(4−2)22\frac{3^3}{5-2}-\frac{(4-2)^2}{2}. We broke down the expression into smaller parts, simplified each part, and then combined them to get the final result. In this article, we will answer some frequently asked questions about evaluating expressions.

Q&A

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

A: The order of operations is a set of rules that tells us which operations to perform first when evaluating an expression. The acronym PEMDAS stands for:

  • Parentheses: Evaluate expressions inside parentheses first.
  • Exponents: Evaluate any exponential expressions next.
  • Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  • Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify mathematical expressions?

A: To simplify a mathematical expression, follow these steps:

  1. Evaluate any exponential expressions.
  2. Evaluate any expressions inside parentheses.
  3. Simplify any fractions or decimals.
  4. Combine like terms.
  5. Check your work by plugging in numbers or using a calculator to verify the result.

Q: What is the difference between an expression and an equation?

A: An expression is a mathematical statement that contains variables and constants, but does not contain an equal sign (=). An equation is a mathematical statement that contains an equal sign (=) and is used to solve for a variable.

Q: How do I evaluate expressions with fractions?

A: To evaluate expressions with fractions, follow these steps:

  1. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD).
  2. Evaluate any exponential expressions.
  3. Evaluate any expressions inside parentheses.
  4. Combine like terms.
  5. Check your work by plugging in numbers or using a calculator to verify the result.

Q: What is the difference between a variable and a constant?

A: A variable is a letter or symbol that represents a value that can change. A constant is a value that does not change.

Q: How do I evaluate expressions with exponents?

A: To evaluate expressions with exponents, follow these steps:

  1. Evaluate any exponential expressions.
  2. Simplify any fractions or decimals.
  3. Combine like terms.
  4. Check your work by plugging in numbers or using a calculator to verify the result.

Q: What is the difference between a positive exponent and a negative exponent?

A: A positive exponent is a number that is raised to a power, such as 232^3. A negative exponent is a number that is raised to a power, but the exponent is negative, such as 2−32^{-3}.

Q: How do I evaluate expressions with negative exponents?

A: To evaluate expressions with negative exponents, follow these steps:

  1. Rewrite the negative exponent as a positive exponent by flipping the fraction.
  2. Evaluate any exponential expressions.
  3. Simplify any fractions or decimals.
  4. Combine like terms.
  5. Check your work by plugging in numbers or using a calculator to verify the result.

Conclusion

In this article, we answered some frequently asked questions about evaluating expressions. We covered topics such as the order of operations, simplifying mathematical expressions, and evaluating expressions with fractions, exponents, and negative exponents. We hope that this article has been helpful in answering your questions and providing you with a better understanding of evaluating expressions.

Tips and Tricks

  • When evaluating expressions, always follow the order of operations (PEMDAS).
  • Simplify each term in the expression before combining them.
  • Use parentheses to group expressions and avoid confusion.
  • Check your work by plugging in numbers or using a calculator to verify the result.

Further Reading

  • For more information on evaluating expressions, see the article "Evaluating Expressions: A Step-by-Step Guide".
  • For more information on simplifying mathematical expressions, see the article "Simplifying Mathematical Expressions: A Guide".
  • For more information on the order of operations, see the article "The Order of Operations: A Guide to PEMDAS".