Complete The Expression: Yuna Ran Three Times As Many Kilometers.Evaluate When $k=12.2$.1. First, Write The Expression As $3k$.2. Second, Substitute $12.2$ In For The Variable, $k$.3. Third, Multiply $3$

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Understanding Algebraic Expressions

Algebraic expressions are a fundamental concept in mathematics, and they play a crucial role in solving various mathematical problems. An algebraic expression is a combination of variables, constants, and mathematical operations that can be evaluated to obtain a numerical value. In this article, we will focus on evaluating a specific algebraic expression, which involves substituting a given value into the expression and simplifying it to obtain the final result.

The Expression: Yuna Ran Three Times as Many Kilometers

The given expression is: Yuna ran three times as many kilometers. To write this expression as an algebraic expression, we can represent the number of kilometers Yuna ran as a variable, k. Therefore, the expression can be written as 3k, where k represents the number of kilometers Yuna ran.

Step 1: Write the Expression as 3k

The first step is to write the expression as 3k. This means that we are representing the number of kilometers Yuna ran as three times the value of k.

3k

Step 2: Substitute k = 12.2 into the Expression

The second step is to substitute the given value of k into the expression. In this case, we are given that k = 12.2. Therefore, we need to substitute 12.2 in place of k in the expression 3k.

3(12.2)

Step 3: Multiply 3 by 12.2

The final step is to multiply 3 by 12.2 to obtain the final result.

3(12.2) = 36.6

Therefore, the final result is 36.6.

Conclusion

In this article, we have evaluated an algebraic expression by substituting a given value into the expression and simplifying it to obtain the final result. We have followed a step-by-step approach to ensure that we obtain the correct result. By understanding and applying algebraic expressions, we can solve a wide range of mathematical problems and make informed decisions in various fields.

Real-World Applications of Algebraic Expressions

Algebraic expressions have numerous real-world applications in various fields, including:

  • Science: Algebraic expressions are used to model and analyze scientific data, such as the motion of objects, the growth of populations, and the behavior of physical systems.
  • Engineering: Algebraic expressions are used to design and optimize systems, such as electronic circuits, mechanical systems, and computer algorithms.
  • Economics: Algebraic expressions are used to model and analyze economic data, such as the behavior of markets, the growth of economies, and the impact of policy changes.
  • Computer Science: Algebraic expressions are used to develop algorithms and data structures, such as sorting and searching algorithms, and graph algorithms.

Common Algebraic Expressions

Here are some common algebraic expressions that you may encounter:

  • Linear Expressions: A linear expression is an expression of the form ax + b, where a and b are constants, and x is a variable.
  • Quadratic Expressions: A quadratic expression is an expression of the form ax^2 + bx + c, where a, b, and c are constants, and x is a variable.
  • Polynomial Expressions: A polynomial expression is an expression of the form a_n x^n + a_(n-1) x^(n-1) + ... + a_1 x + a_0, where a_n, a_(n-1), ..., a_1, and a_0 are constants, and x is a variable.

Tips for Evaluating Algebraic Expressions

Here are some tips for evaluating algebraic expressions:

  • Read the expression carefully: Before evaluating an algebraic expression, read it carefully to ensure that you understand what it represents.
  • Identify the variables and constants: Identify the variables and constants in the expression, and make sure you understand their values.
  • Follow the order of operations: Follow the order of operations (PEMDAS) to ensure that you evaluate the expression correctly.
  • Check your work: Check your work to ensure that you have obtained the correct result.

Frequently Asked Questions

In this article, we will address some of the most frequently asked questions about evaluating algebraic expressions.

Q: What is an algebraic expression?

A: An algebraic expression is a combination of variables, constants, and mathematical operations that can be evaluated to obtain a numerical value.

Q: How do I write an algebraic expression?

A: To write an algebraic expression, you need to represent the variables and constants in the expression using mathematical notation. For example, if you want to represent the number of kilometers Yuna ran as three times the value of k, you can write the expression as 3k.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when evaluating an algebraic expression. The order of operations is:

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

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need to follow the order of operations and substitute any given values into the expression. For example, if you want to evaluate the expression 3(12.2), you would first substitute 12.2 in place of the variable, and then multiply 3 by 12.2.

Q: What are some common algebraic expressions?

A: Some common algebraic expressions include:

  • Linear Expressions: A linear expression is an expression of the form ax + b, where a and b are constants, and x is a variable.
  • Quadratic Expressions: A quadratic expression is an expression of the form ax^2 + bx + c, where a, b, and c are constants, and x is a variable.
  • Polynomial Expressions: A polynomial expression is an expression of the form a_n x^n + a_(n-1) x^(n-1) + ... + a_1 x + a_0, where a_n, a_(n-1), ..., a_1, and a_0 are constants, and x is a variable.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms and eliminate any unnecessary operations. For example, if you have the expression 2x + 3x, you can combine the like terms to get 5x.

Q: What are some real-world applications of algebraic expressions?

A: Algebraic expressions have numerous real-world applications in various fields, including:

  • Science: Algebraic expressions are used to model and analyze scientific data, such as the motion of objects, the growth of populations, and the behavior of physical systems.
  • Engineering: Algebraic expressions are used to design and optimize systems, such as electronic circuits, mechanical systems, and computer algorithms.
  • Economics: Algebraic expressions are used to model and analyze economic data, such as the behavior of markets, the growth of economies, and the impact of policy changes.
  • Computer Science: Algebraic expressions are used to develop algorithms and data structures, such as sorting and searching algorithms, and graph algorithms.

Q: How do I check my work when evaluating an algebraic expression?

A: To check your work when evaluating an algebraic expression, you need to:

  • Read the expression carefully: Before evaluating an algebraic expression, read it carefully to ensure that you understand what it represents.
  • Identify the variables and constants: Identify the variables and constants in the expression, and make sure you understand their values.
  • Follow the order of operations: Follow the order of operations (PEMDAS) to ensure that you evaluate the expression correctly.
  • Check your work: Check your work to ensure that you have obtained the correct result.

By following these tips and understanding the concepts of algebraic expressions, you can evaluate expressions with confidence and accuracy.