Solving The Percentage Problem: 8 % 5

Hey there, math enthusiasts! Today, we're diving into a fun little problem that involves a unique percentage operation. We're given a special rule and asked to apply it. Let's break it down step-by-step and uncover the solution. The core concept here is understanding how this new percentage operator works and then applying it to the specific values. It's all about following the rules! It is a mathematical problem that can be solved with arithmetic, which involves understanding the given formula and substituting the values correctly. Keep your thinking caps on, because we're about to explore the world of mathematical operations and arrive at the correct answer. The task is pretty straightforward: we're given a peculiar definition of a percentage operation and we need to evaluate a specific expression using that definition. So, what exactly is our mission today? Well, we have this interesting operation denoted by the percentage symbol, but it doesn’t work the way we're used to. Typically, when we see a percentage, we think of fractions or proportions, but not today! Instead, this percentage symbol represents a custom-defined operation. We have to follow the instructions and that is the only way to crack this puzzle.

Understanding the Special Percentage Rule

Our problem introduces a special rule for calculating the percentage. Unlike the standard percentage, which usually involves finding a proportion of a number, this operation uses a formula. The formula is: $x % y = (x + y) * (x - y)$ This means that when we see $x % y$, we don't calculate a fraction or a proportion. Instead, we use this formula to find the result. The formula uses basic arithmetic operations: addition and subtraction, multiplication involving the two numbers $x$ and $y$. The core concept here is to understand that the percentage symbol is being used in a non-standard way. Forget what you know about regular percentages for a moment. This is a unique operation, a custom-built function if you will. The formula tells us precisely how to combine the numbers. The formula is our guide. It dictates every step of the calculation. The expression $x % y$ means you take the sum of $x$ and $y$, then you multiply that sum by the difference between $x$ and $y$. This is the secret to solving the problem: understanding and applying this formula. The rest is just plugging in the numbers and doing the math. This problem is designed to test your ability to read and interpret mathematical notation. It's a reminder that math isn't just about formulas; it's also about understanding the rules and applying them correctly. So, if you're ready, let's move on and solve the actual problem. We will put this knowledge to the test.

Applying the Rule to 8 % 5

Now comes the fun part: applying our special percentage rule to the expression $8 % 5$. We've got our formula, and we've got our numbers. All we need to do is substitute the values into the formula and do the math. Remember, our formula is: $x % y = (x + y) * (x - y)$. In our case, $x$ is 8 and $y$ is 5. So, let's plug in those values: $8 % 5 = (8 + 5) * (8 - 5)$. Now, simplify the equation step by step, which we can solve using the order of operations: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). First, we calculate what’s inside the parentheses: $8 + 5 = 13$ and $8 - 5 = 3$. Now our expression looks like this: $8 % 5 = 13 * 3$. Finally, we multiply 13 by 3, which gives us 39. Therefore, $8 % 5 = 39$. And there you have it! We've successfully used our special percentage rule to solve the problem. The solution is 39. This might not seem like a typical percentage answer, but remember, this isn’t a typical percentage. We’re using a custom operation that follows a specific formula. It's a great example of how mathematical notation can be used to define new and unique operations. Now, let’s recap the whole process: understand the rule, substitute the values, perform the arithmetic. When faced with similar problems, remember this approach, and you'll be well-equipped to tackle them! The beauty of this problem lies in its simplicity. With a clear understanding of the formula and careful attention to the calculations, we arrived at the correct answer. The key takeaway is to always pay attention to the defined rules and follow them accurately. Don't let the unusual symbol throw you off. Instead, focus on the instructions and use them to guide you to the solution. This is not about the standard percentage; it's about following a new set of rules.

Key Takeaways

• Custom Operations: Always understand how the operation is defined before starting the calculation. Don’t assume anything. Read the instructions carefully. This is important in all math problems. The rules are the foundation.
• Formula Application: Substitute values correctly into the formula. This is a must if you want to get the right answer.
• Order of Operations: Don't forget the order of operations (PEMDAS/BODMAS). This is important to ensure accuracy. If you follow the wrong order of operations, you may come up with the wrong answers.
• Practice: Practice similar problems to strengthen your understanding. Mathematics is best learned through practice. The more you practice, the easier it will be to understand new concepts.

Conclusion

So, there you have it! We started with a new type of percentage operation, learned its unique formula, and applied it to a specific problem. By following the given rules and performing some basic arithmetic, we found the solution. This type of problem is designed to test your ability to understand and apply mathematical definitions. Always read the instructions carefully, and break down the problem into smaller steps. With practice, you’ll become more comfortable with these types of problems. Remember, math is about understanding and applying the rules. It's about thinking logically and breaking down complex problems into smaller, manageable steps. Keep practicing, keep learning, and enjoy the world of mathematics!

To delve deeper into mathematical concepts, check out this great resource: Khan Academy.