Evaluating Algebraic Expressions A Step-by-Step Guide With Examples

Let's delve into the world of algebraic expressions and explore how to evaluate them in practical scenarios. This article will focus on a problem involving Felix dividing his shirts into equal groups. We'll dissect the problem, identify the correct expression, and determine the solution. Furthermore, we will emphasize the significance of understanding variables and their role in mathematical expressions. This problem not only reinforces the concept of evaluating expressions but also illustrates how mathematical concepts can be applied to everyday situations. Understanding these concepts is crucial for building a solid foundation in mathematics and for tackling more complex problems in the future.

Understanding the Problem

The core of the problem lies in understanding the scenario: Felix has a certain number of shirts, represented by the variable s, and he divides them into three equal groups. The key here is the word "divided," which immediately suggests the mathematical operation of division. When we encounter such problems, it's crucial to identify the knowns and unknowns. In this case, we know that the number of groups is three, and the total number of shirts is represented by the variable s. The unknown is the number of shirts in each group. To find this, we need to translate the word problem into a mathematical expression. This involves representing the division operation using mathematical symbols. The ability to translate word problems into mathematical expressions is a fundamental skill in algebra and is essential for solving a wide range of problems. This skill helps in bridging the gap between real-world scenarios and mathematical representations, making problem-solving more intuitive and effective. Therefore, practicing such translations is vital for enhancing mathematical proficiency.

Identifying the Correct Expression

Now, let's analyze the given options for the expression. We need an expression that represents dividing the total number of shirts (s) into three equal groups.

• The first option, $\frac{s}{18}$, suggests dividing the number of shirts by 18. This doesn't align with the problem, which states division into three groups.
• The second option, $\frac{18}{3}$, represents dividing 18 by 3. While this is a valid division operation, it doesn't incorporate the variable s, which represents the total number of shirts Felix has. Therefore, this option is also incorrect.
• The third option, $\frac{s}{3}$, perfectly captures the scenario. It represents dividing the total number of shirts (s) by 3, which corresponds to dividing the shirts into three equal groups. This expression accurately translates the problem's conditions into a mathematical form. The variable s plays a crucial role in this expression, allowing us to calculate the number of shirts in each group for any given value of s. This demonstrates the power of algebraic expressions in representing and solving real-world problems. By correctly identifying the expression, we set the stage for evaluating it and finding the solution.

Therefore, the correct expression is $\frac{s}{3}$.

Evaluating the Expression

The problem provides us with the value of s: s = 18. This means Felix has 18 shirts. Now we can evaluate the expression $\frac{s}{3}$ by substituting s with 18.

$\frac{s}{3} = \frac{18}{3}$

Performing the division, we get:

$\frac{18}{3} = 6$

This tells us that when Felix divides his 18 shirts into three equal groups, there are 6 shirts in each group. The process of evaluation involves replacing variables with their given values and then performing the necessary mathematical operations to arrive at a numerical result. This is a fundamental step in algebra and is used extensively in solving equations and inequalities. Understanding the order of operations (PEMDAS/BODMAS) is crucial during evaluation to ensure accurate results. In this case, the division operation was straightforward, but in more complex expressions, following the correct order is paramount. The result of the evaluation, 6, provides a concrete answer to the problem, illustrating the practical application of algebraic expressions.

Checking the Options

Now, let's revisit the options provided in the problem and check which ones apply:

• The expression is $\frac{s}{18}$. - Incorrect. We've already established that the correct expression is $\frac{s}{3}$. This option represents dividing the number of shirts by 18, which is not what the problem describes.
• The expression is $\frac{18}{3}$. - Correct. This expression represents the specific calculation we performed when s = 18. It shows the division of 18 shirts into three groups. While $\frac{s}{3}$ is the general expression, $\frac{18}{3}$ is the numerical expression for this specific case.
• The expression is $\frac{s}{3}$. - Correct. This is the general expression that accurately represents the problem: dividing the total number of shirts (s) into three equal groups. This expression can be used to find the number of shirts in each group for any value of s.

Conclusion

In summary, the correct expression for dividing Felix's shirts into three equal groups is $\frac{s}{3}$. When s = 18, the value of the expression is 6. The options that apply are: "The expression is $\frac{18}{3}$" and "The expression is $\frac{s}{3}$." This exercise highlights the importance of translating word problems into mathematical expressions, evaluating expressions with given values, and understanding the meaning of variables in algebraic contexts. By mastering these skills, students can confidently approach a wide range of mathematical problems and appreciate the practical applications of algebra in everyday life. The ability to correctly identify and evaluate expressions is a cornerstone of algebraic proficiency and paves the way for more advanced mathematical concepts.

Rewrite the question to be easier to understand: If Felix divides his shirts into three equal groups and he has 18 shirts (s=18), which expression represents this situation, and what is the result?

Evaluating Algebraic Expressions A Step-by-Step Guide with Examples