Evaluate The Expression 24 Divided By 2 Squared Minus 10 Divided By 2

Evaluating mathematical expressions accurately is a fundamental skill in mathematics. This article delves into the step-by-step evaluation of the expression $\frac{24}{2^2} - \frac{10}{2}$, ensuring clarity and a comprehensive understanding of each operation involved. By breaking down the problem into smaller, manageable parts, we can confidently arrive at the correct answer. This approach not only helps in solving similar problems but also reinforces the order of operations, a crucial concept in mathematics. Understanding how to simplify expressions involving fractions and exponents is vital for more advanced mathematical studies. Therefore, a thorough analysis of this expression serves as a valuable exercise in enhancing mathematical proficiency. Let's embark on a detailed exploration of this expression, simplifying it systematically and revealing the final result.

Understanding the Order of Operations

Before we begin, it's crucial to understand the order of operations, often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This order dictates the sequence in which we perform operations to ensure we arrive at the correct result. Ignoring this order can lead to errors in our calculations. In the expression $\frac{24}{2^2} - \frac{10}{2}$, we first need to address the exponent, then the divisions, and finally the subtraction. Mastering the order of operations is not just about following rules; it's about understanding the logic behind mathematical expressions. This understanding allows us to tackle complex problems with confidence and accuracy. By consistently applying PEMDAS, we ensure that our mathematical reasoning remains sound and our solutions are reliable. This principle is fundamental across various branches of mathematics, from basic arithmetic to advanced calculus. Therefore, a firm grasp of PEMDAS is essential for anyone pursuing mathematical studies.

Step 1: Simplify the Exponent

The first step in evaluating the expression $\frac{24}{2^2} - \frac{10}{2}$ is to simplify the exponent. The term $2^2$ means 2 raised to the power of 2, which is equal to 2 multiplied by itself: $2^2 = 2 \times 2 = 4$. Replacing $2^2$ with 4 in the expression, we now have $\frac{24}{4} - \frac{10}{2}$. This simplification makes the expression easier to work with, as we have eliminated the exponent. Simplifying exponents is a crucial step in many mathematical problems, as it often reduces the complexity of the expression. Understanding exponents and their properties is fundamental in algebra and other advanced mathematical fields. By addressing the exponent first, we adhere to the order of operations and set the stage for the subsequent division operations. This step highlights the importance of breaking down complex expressions into simpler components, making them more manageable and less prone to errors. Consistent practice with exponents helps build a strong foundation in mathematical manipulation.

Step 2: Perform the Divisions

After simplifying the exponent, the next step is to perform the divisions. We have two division operations in the expression: $\frac{24}{4}$ and $\frac{10}{2}$. Let's evaluate each division separately. First, $\frac{24}{4}$ is equal to 6, since 24 divided by 4 is 6. Next, $\frac{10}{2}$ is equal to 5, as 10 divided by 2 is 5. Now, we replace the division expressions with their respective values, giving us the simplified expression $6 - 5$. Performing divisions accurately is essential for solving mathematical problems involving fractions and ratios. This step demonstrates the importance of understanding basic arithmetic operations and their application in more complex expressions. By performing the divisions, we further simplify the original expression, bringing us closer to the final answer. This process highlights how breaking down a problem into smaller steps can make it easier to solve. Consistent practice with division helps reinforce these fundamental mathematical skills.

Step 3: Perform the Subtraction

With the divisions completed, the final step in evaluating the expression $\frac{24}{2^2} - \frac{10}{2}$ is to perform the subtraction. We have simplified the expression to $6 - 5$. Subtracting 5 from 6 gives us 1. Therefore, the value of the expression is 1. This step demonstrates the culmination of the previous operations, where each simplification led us closer to the final result. Subtraction is a fundamental arithmetic operation, and its accurate execution is crucial for mathematical problem-solving. By performing the subtraction, we complete the evaluation of the expression, arriving at a single numerical answer. This step underscores the importance of following the order of operations and executing each step with precision. Consistent practice with subtraction and other arithmetic operations helps build a strong foundation in mathematics.

Final Answer: 1

After meticulously following the order of operations and simplifying each part of the expression $\frac{24}{2^2} - \frac{10}{2}$, we arrive at the final answer: 1. This result is obtained by first simplifying the exponent, then performing the divisions, and finally completing the subtraction. This step-by-step approach ensures accuracy and demonstrates a clear understanding of mathematical principles. The final answer of 1 is a concise numerical representation of the entire expression's value. Achieving this result reinforces the importance of precision and attention to detail in mathematical calculations. Understanding how to evaluate expressions like this is a crucial skill in mathematics, applicable across various fields of study and real-world scenarios. Therefore, mastering these fundamental operations is essential for anyone pursuing mathematical proficiency.

Conclusion

In conclusion, evaluating the expression $\frac{24}{2^2} - \frac{10}{2}$ involves a systematic approach, emphasizing the importance of the order of operations. By first simplifying the exponent, then performing the divisions, and finally completing the subtraction, we accurately determine the value of the expression to be 1. This process not only provides the correct answer but also reinforces the fundamental principles of mathematics. Understanding and applying these principles is crucial for solving more complex mathematical problems. Each step in the evaluation, from addressing the exponent to performing the final subtraction, highlights the importance of precision and attention to detail. Mastering these basic operations forms a solid foundation for further mathematical studies. Therefore, consistent practice and a clear understanding of the order of operations are essential for achieving mathematical proficiency.