Solving Algebraic Expressions 11.123 ÷ X When X = 1.024

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In the realm of mathematics, algebraic expressions serve as the foundation for problem-solving and equation manipulation. These expressions, often involving variables and constants, require careful evaluation to arrive at accurate solutions. This article delves into the process of solving algebraic expressions, with a specific focus on the expression 11.123 ÷ x when the value of x is given as 1.024. We will navigate the steps involved, emphasizing precision and rounding techniques to achieve the nearest thousandth.

Understanding Algebraic Expressions

Algebraic expressions are mathematical phrases that combine variables, constants, and mathematical operations. Variables, represented by letters such as x, y, or z, symbolize unknown quantities. Constants, on the other hand, are fixed numerical values. Mathematical operations, including addition, subtraction, multiplication, and division, dictate the relationships between variables and constants within an expression.

To solve an algebraic expression, we substitute the given value for the variable and then perform the indicated operations. The order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), is crucial to ensure accurate calculations.

Evaluating 11.123 ÷ x when x = 1.024

Our primary objective is to solve the algebraic expression 11.123 ÷ x when x is equal to 1.024. This expression involves a simple division operation, where the constant 11.123 is divided by the variable x. To find the solution, we substitute 1.024 for x in the expression:

11.123 ÷ 1.024

Now, we perform the division operation. Using a calculator or long division, we find that:

11.123 ÷ 1.024 ≈ 10.86228515625

Rounding to the Nearest Thousandth

The problem statement requires us to round the result to the nearest thousandth. The thousandth place is the third digit after the decimal point. To round to the nearest thousandth, we examine the digit in the ten-thousandth place (the fourth digit after the decimal point). If this digit is 5 or greater, we round up the thousandth digit. If it is less than 5, we leave the thousandth digit as it is.

In our case, the digit in the ten-thousandth place is 2, which is less than 5. Therefore, we leave the thousandth digit (2) as it is. Rounding 10.86228515625 to the nearest thousandth gives us:

10.862

Therefore, the solution to the algebraic expression 11.123 ÷ x when x = 1.024, rounded to the nearest thousandth, is 10.862.

Key Concepts and Considerations

  • Order of Operations: Always adhere to the order of operations (PEMDAS) when evaluating algebraic expressions to ensure accurate results.
  • Substitution: Carefully substitute the given value for the variable in the expression.
  • Rounding: Understand the rules of rounding to the nearest decimal place as specified in the problem statement.
  • Calculator Use: Utilize a calculator for complex calculations to minimize errors and save time.
  • Precision: Be mindful of the level of precision required in the answer and round accordingly.

Additional Examples

To further solidify your understanding, let's explore a few more examples of solving algebraic expressions with varying values of x:

Example 1:

Solve the expression 5.25 ÷ x when x = 2.5 and round to the nearest hundredth.

  1. Substitute x = 2.5 into the expression: 5.25 ÷ 2.5
  2. Perform the division: 5.25 ÷ 2.5 = 2.1
  3. Round to the nearest hundredth: 2.10

Example 2:

Solve the expression 100 ÷ x when x = 7.8 and round to the nearest tenth.

  1. Substitute x = 7.8 into the expression: 100 ÷ 7.8
  2. Perform the division: 100 ÷ 7.8 ≈ 12.8205128205
  3. Round to the nearest tenth: 12.8

Example 3:

Solve the expression 1 ÷ x when x = 0.333 and round to the nearest thousandth.

  1. Substitute x = 0.333 into the expression: 1 ÷ 0.333
  2. Perform the division: 1 ÷ 0.333 ≈ 3.003003003
  3. Round to the nearest thousandth: 3.003

Conclusion

Solving algebraic expressions is a fundamental skill in mathematics. By understanding the principles of substitution, order of operations, and rounding, you can confidently tackle a wide range of algebraic problems. Remember to pay close attention to the problem statement, especially the required level of precision, and utilize calculators when necessary to ensure accurate results. With practice and a solid grasp of these concepts, you'll be well-equipped to excel in algebra and beyond.

In this article, we have thoroughly examined the process of solving the algebraic expression 11.123 ÷ x when x = 1.024, rounding the result to the nearest thousandth. We have also explored additional examples to demonstrate the application of these concepts in various scenarios. By mastering these techniques, you'll be well-prepared to handle algebraic expressions with confidence and accuracy.

Key Takeaways:

  • Algebraic expressions combine variables, constants, and mathematical operations.
  • The order of operations (PEMDAS) is crucial for accurate evaluation.
  • Substitution involves replacing variables with their given values.
  • Rounding ensures that the answer is presented to the required level of precision.
  • Practice is essential for mastering algebraic problem-solving.

By understanding and applying these key takeaways, you can confidently solve algebraic expressions and excel in your mathematical endeavors.

To reinforce your understanding of solving algebraic expressions, try solving the following problems:

  1. Solve 25.5 ÷ x when x = 4.2 and round to the nearest hundredth.
  2. Solve 150 ÷ x when x = 12.5 and round to the nearest tenth.
  3. Solve 2 ÷ x when x = 0.667 and round to the nearest thousandth.

Check your answers with a calculator and compare your results to the solutions provided below:

  1. 25.5 ÷ 4.2 ≈ 6.07
  2. 150 ÷ 12.5 = 12.0
  3. 2 ÷ 0.667 ≈ 2.999

By working through these practice problems, you'll further develop your skills in solving algebraic expressions and gain confidence in your mathematical abilities.

In conclusion, solving algebraic expressions is a fundamental skill that is essential for success in mathematics and related fields. By understanding the concepts and techniques discussed in this article, you'll be well-equipped to tackle a wide range of algebraic problems with accuracy and confidence.