Simplify The Expression:${ 20 - \frac{1}{3}(x + 2) }$

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for students and professionals alike. In this article, we will focus on simplifying the expression 20−13(x+2)20 - \frac{1}{3}(x + 2). We will break down the steps involved in simplifying this expression and provide a clear understanding of the concepts used.

Understanding the Expression

The given expression is 20−13(x+2)20 - \frac{1}{3}(x + 2). This expression consists of two terms: a constant term 2020 and a term involving a variable xx. The variable xx is multiplied by a fraction 13\frac{1}{3}, and then added to 22. Our goal is to simplify this expression by combining like terms and eliminating any unnecessary operations.

Step 1: Distribute the Fraction

To simplify the expression, we need to distribute the fraction 13\frac{1}{3} to the terms inside the parentheses. This means multiplying the fraction by each term inside the parentheses.

\frac{1}{3}(x + 2) = \frac{1}{3}x + \frac{1}{3}(2)

Step 2: Simplify the Fraction

Now that we have distributed the fraction, we can simplify the expression further by combining like terms. The term 13(2)\frac{1}{3}(2) can be simplified by multiplying the fraction by the constant term 22.

\frac{1}{3}(2) = \frac{2}{3}

Step 3: Rewrite the Expression

Now that we have simplified the fraction, we can rewrite the original expression using the simplified terms.

20 - \frac{1}{3}(x + 2) = 20 - \frac{1}{3}x - \frac{2}{3}

Step 4: Combine Like Terms

The final step in simplifying the expression is to combine like terms. In this case, we can combine the constant terms 2020 and −23-\frac{2}{3}.

20 - \frac{2}{3} = \frac{60}{3} - \frac{2}{3} = \frac{58}{3}

Step 5: Final Expression

The final simplified expression is:

20 - \frac{1}{3}(x + 2) = \frac{58}{3} - \frac{1}{3}x

Conclusion

Simplifying algebraic expressions is an essential skill for students and professionals alike. By following the steps outlined in this article, we can simplify the expression 20−13(x+2)20 - \frac{1}{3}(x + 2) and arrive at the final simplified expression. Remember to always distribute fractions, simplify fractions, rewrite the expression, combine like terms, and finally arrive at the final simplified expression.

Tips and Tricks

  • Always distribute fractions to the terms inside the parentheses.
  • Simplify fractions by multiplying the fraction by the constant term.
  • Combine like terms to simplify the expression further.
  • Use the order of operations (PEMDAS) to ensure that the expression is simplified correctly.

Common Mistakes

  • Failing to distribute fractions to the terms inside the parentheses.
  • Not simplifying fractions by multiplying the fraction by the constant term.
  • Not combining like terms to simplify the expression further.
  • Using the wrong order of operations (PEMDAS).

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications. For example, in physics, algebraic expressions are used to describe the motion of objects. In engineering, algebraic expressions are used to design and optimize systems. In economics, algebraic expressions are used to model and analyze economic systems.

Final Thoughts

Simplifying algebraic expressions is a crucial skill for students and professionals alike. By following the steps outlined in this article, we can simplify complex expressions and arrive at the final simplified expression. Remember to always distribute fractions, simplify fractions, rewrite the expression, combine like terms, and finally arrive at the final simplified expression. With practice and patience, you will become proficient in simplifying algebraic expressions and applying them to real-world problems.

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Introduction

In our previous article, we explored the steps involved in simplifying the expression 20−13(x+2)20 - \frac{1}{3}(x + 2). We broke down the process into manageable steps and provided a clear understanding of the concepts used. In this article, we will address some of the most frequently asked questions related to simplifying algebraic expressions.

Q&A

Q: What is the first step in simplifying an algebraic expression?

A: The first step in simplifying an algebraic expression is to distribute any fractions to the terms inside the parentheses.

Q: How do I simplify a fraction in an algebraic expression?

A: To simplify a fraction in an algebraic expression, multiply the fraction by the constant term inside the parentheses.

Q: What is the difference between combining like terms and simplifying fractions?

A: Combining like terms involves adding or subtracting terms with the same variable and coefficient, while simplifying fractions involves reducing a fraction to its simplest form.

Q: How do I know when to combine like terms?

A: You should combine like terms when you have two or more terms with the same variable and coefficient.

Q: What is the order of operations (PEMDAS) and how does it apply to simplifying algebraic expressions?

A: The order of operations (PEMDAS) is a set of rules that dictates the order in which operations should be performed when simplifying algebraic expressions. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: Can I simplify an algebraic expression by rearranging the terms?

A: Yes, you can simplify an algebraic expression by rearranging the terms. However, be careful not to change the value of the expression.

Q: How do I know if an algebraic expression is simplified?

A: An algebraic expression is simplified when there are no like terms that can be combined and no fractions that can be simplified.

Q: Can I use a calculator to simplify an algebraic expression?

A: Yes, you can use a calculator to simplify an algebraic expression. However, be aware that calculators may not always provide the simplest form of the expression.

Tips and Tricks

  • Always distribute fractions to the terms inside the parentheses.
  • Simplify fractions by multiplying the fraction by the constant term.
  • Combine like terms to simplify the expression further.
  • Use the order of operations (PEMDAS) to ensure that the expression is simplified correctly.
  • Be careful not to change the value of the expression when rearranging the terms.

Common Mistakes

  • Failing to distribute fractions to the terms inside the parentheses.
  • Not simplifying fractions by multiplying the fraction by the constant term.
  • Not combining like terms to simplify the expression further.
  • Using the wrong order of operations (PEMDAS).
  • Changing the value of the expression when rearranging the terms.

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications. For example, in physics, algebraic expressions are used to describe the motion of objects. In engineering, algebraic expressions are used to design and optimize systems. In economics, algebraic expressions are used to model and analyze economic systems.

Final Thoughts

Simplifying algebraic expressions is a crucial skill for students and professionals alike. By following the steps outlined in this article and addressing the frequently asked questions, you will become proficient in simplifying algebraic expressions and applying them to real-world problems. Remember to always distribute fractions, simplify fractions, rewrite the expression, combine like terms, and finally arrive at the final simplified expression. With practice and patience, you will become a master of simplifying algebraic expressions.