Evaluating Algebraic Expressions Find -3a ÷ 6 When A Equals -2
Evaluate the expression -3a ÷ 6 when a = -2. Write the answer in simplest form.
Introduction
In the realm of mathematics, evaluating algebraic expressions is a fundamental skill. This involves substituting given values for variables within an expression and simplifying the result to obtain a numerical answer. This article will delve into a specific example, guiding you through the process of evaluating the expression -3a ÷ 6 when a = -2. We will break down each step, ensuring a clear understanding of the underlying principles and techniques involved. This comprehensive guide aims to equip you with the knowledge and confidence to tackle similar problems with ease.
Understanding algebraic expressions is crucial for various mathematical concepts and real-world applications. From solving equations to modeling physical phenomena, the ability to evaluate expressions accurately is essential. This article serves as a stepping stone in mastering this fundamental skill, providing a solid foundation for further exploration in mathematics. By following the steps outlined in this guide, you will develop a strong understanding of variable substitution, order of operations, and simplification techniques, empowering you to confidently tackle more complex mathematical challenges. Let's embark on this journey of mathematical discovery together!
Step 1: Substitute the Value of the Variable
The first crucial step in evaluating an algebraic expression is to substitute the given value for the variable. In our case, we are given the expression -3a ÷ 6 and the value a = -2. This means we need to replace the variable 'a' in the expression with the number -2. This substitution transforms the algebraic expression into a numerical expression, which we can then simplify using arithmetic operations. Careful substitution is paramount to ensure accuracy in the subsequent steps. Any error in this initial substitution will propagate through the rest of the solution, leading to an incorrect answer. Therefore, double-checking the substitution is always a good practice.
Substituting a = -2 into the expression -3a ÷ 6, we get: -3(-2) ÷ 6. Notice how the variable 'a' has been replaced by the numerical value -2. The parentheses around -2 are important, especially when dealing with negative numbers. They indicate multiplication and help avoid confusion with subtraction. This step lays the groundwork for the rest of the solution, transforming the algebraic problem into a straightforward arithmetic calculation. The next step will involve performing the multiplication operation as per the order of operations.
Step 2: Perform Multiplication
Now that we have substituted the value of 'a', the next step is to perform the multiplication operation. In the expression -3(-2) ÷ 6, we have a multiplication operation: -3 multiplied by -2. Recall the rules of multiplication with negative numbers: a negative number multiplied by a negative number results in a positive number. This is a fundamental concept in arithmetic and is crucial for accurate calculations. Ignoring this rule will lead to an incorrect result. Therefore, it is essential to remember and apply this principle correctly.
Multiplying -3 by -2, we get: (-3) * (-2) = 6. The expression now becomes 6 ÷ 6. We have successfully simplified the multiplication part of the expression. This simplification brings us closer to the final answer. The next step involves performing the division operation, which is the remaining operation in the expression. Remember to always follow the order of operations (PEMDAS/BODMAS) to ensure accurate evaluation of expressions. In this case, multiplication precedes division because it appears earlier in the expression when read from left to right.
Step 3: Perform Division
With the multiplication completed, we now proceed to the division operation. Our expression is currently 6 ÷ 6. Division is the inverse operation of multiplication, and it is a fundamental arithmetic operation. Dividing a number by itself always results in 1, assuming the number is not zero. This is a basic mathematical principle that applies universally. Understanding this principle allows for quick and efficient simplification of expressions.
Performing the division, we get: 6 ÷ 6 = 1. Therefore, the final result of the expression is 1. This concludes the evaluation of the algebraic expression -3a ÷ 6 when a = -2. We have systematically worked through each step, from substitution to simplification, following the correct order of operations. This step-by-step approach ensures accuracy and clarity in the solution. The result, 1, is the simplest form of the expression after substituting the given value for the variable.
Step 4: Write the Answer in Simplest Form
The final step in evaluating an algebraic expression is to write the answer in its simplest form. In our case, the result of the calculation is 1. The number 1 is already in its simplest form as it is a whole number and cannot be further reduced or simplified. In some cases, the result might be a fraction or a decimal, which might require further simplification. For example, a fraction might need to be reduced to its lowest terms, or a decimal might need to be rounded to a certain number of decimal places. However, in this instance, the answer 1 is already in the simplest form, so no further simplification is necessary.
Therefore, the simplest form of the expression -3a ÷ 6 when a = -2 is 1. This completes the entire process of evaluating the algebraic expression. We have successfully substituted the value of the variable, performed the necessary arithmetic operations, and simplified the result to its simplest form. This step emphasizes the importance of presenting the answer in a clear and concise manner, ensuring that it is easily understood and interpreted. The ability to simplify expressions is a crucial skill in mathematics, allowing for efficient communication and problem-solving.
Conclusion
In this comprehensive guide, we have meticulously walked through the process of evaluating the algebraic expression -3a ÷ 6 when a = -2. We began by emphasizing the fundamental nature of evaluating algebraic expressions in mathematics and its relevance to various applications. Each step was carefully explained, starting with the crucial substitution of the variable 'a' with its given value, followed by the sequential execution of multiplication and division operations. The importance of adhering to the order of operations (PEMDAS/BODMAS) was highlighted to ensure accuracy throughout the evaluation process.
We then demonstrated the simplification of the expression step-by-step, ultimately arriving at the simplest form of the answer, which is 1. The significance of presenting the answer in its simplest form was underscored, emphasizing clarity and conciseness in mathematical communication. This step-by-step approach not only provides a solution to the specific problem but also equips readers with a robust framework for tackling similar algebraic evaluations. By understanding the underlying principles and techniques demonstrated in this guide, individuals can confidently approach a wide range of mathematical challenges involving algebraic expressions.
This exercise serves as a valuable illustration of how algebraic expressions can be evaluated systematically and accurately. The skills acquired through this guide will undoubtedly prove beneficial in further mathematical studies and real-world applications, fostering a deeper understanding and appreciation for the power of algebra.