Solving Percentage Problems What Number Is 15% Of 6
Hey guys! Let's dive into this math problem together. We need to figure out what number has 15% equal to 6. It might sound tricky, but we'll break it down step by step so it’s super clear. We'll explore the basics of percentages, how to convert them into decimals, and how to set up and solve the equation. By the end, you'll not only know the answer but also understand the process, so you can tackle similar problems with confidence. So, grab your thinking caps, and let’s get started!
Understanding Percentages
Before we jump into solving the problem, let's make sure we all understand what percentages actually mean. The word "percent" comes from the Latin "per centum," which means "out of one hundred." So, when we say 15%, we literally mean 15 out of 100. Think of it as a fraction with a denominator of 100. This understanding is crucial because it allows us to convert percentages into decimals or fractions, which are easier to work with in calculations. Percentages are used everywhere in daily life, from calculating discounts at the store to understanding interest rates on loans. So, grasping this concept is super useful, not just for math class but for real-world situations too. Imagine you're at a store and see a sign that says "20% off!" Knowing what a percentage means helps you quickly figure out how much you're saving. Or, if you're figuring out a tip at a restaurant, understanding percentages makes it easy to calculate the right amount. In our case, understanding that 15% means "15 out of 100" is the first step in solving our problem of finding the number where 15% equals 6. It's like having the first piece of the puzzle – now we just need to fit the rest together!
Converting Percentages to Decimals
The next key skill we need is how to convert a percentage into a decimal. This is super straightforward! Since a percentage is just a fraction with 100 as the denominator, all we need to do is divide the percentage by 100. So, to convert 15% to a decimal, we divide 15 by 100. Mathematically, this looks like 15 / 100, which equals 0.15. That's it! We've turned 15% into its decimal equivalent, 0.15. This conversion is important because it allows us to perform calculations more easily. When we're solving for an unknown number, like in our problem, using the decimal form of the percentage makes the equation much simpler to work with. Think of it like changing from one language to another – some languages are better suited for certain tasks. In this case, decimals are the language of math calculations! So, remember, to convert a percentage to a decimal, just divide by 100. This little trick will come in handy in so many situations, from solving math problems to figuring out discounts while shopping. Now that we've got this conversion down, we're one step closer to cracking our original question.
Setting Up the Equation
Okay, we've got the percentage basics covered, and we know how to turn percentages into decimals. Now comes the fun part: setting up the equation! This is where we translate the words of the problem into a mathematical statement. Our problem asks: "15% of what number is 6?" Let's break this down. We know 15% is the same as 0.15 (from our conversion earlier). The phrase "of what number" tells us we're looking for an unknown value, so let's call that "x." And the word "is" in math often means equals, so we'll use the equals sign (=). Putting it all together, we get the equation: 0.15 * x = 6. See how we turned the words into a simple, clear mathematical equation? This is a super important skill for solving all sorts of problems, not just in math but in science, engineering, and even everyday life. Think of setting up an equation like creating a roadmap. It shows you exactly what steps you need to take to get to the solution. In our case, the roadmap tells us that 0.15 times our mystery number (x) gives us 6. Now that we have this roadmap, we're ready to solve for x and find our answer!
Solving for the Unknown
Alright, we've set up the equation: 0.15 * x = 6. Now it’s time to solve for x, which means we need to get x all by itself on one side of the equation. To do this, we'll use a little bit of algebraic magic. Remember, whatever we do to one side of the equation, we have to do to the other side to keep things balanced. In this case, since x is being multiplied by 0.15, we'll do the opposite operation: we'll divide both sides of the equation by 0.15. So, we have (0.15 * x) / 0.15 = 6 / 0.15. On the left side, the 0.15s cancel each other out, leaving us with just x. On the right side, we have 6 divided by 0.15. If you do that calculation (either by hand or with a calculator), you'll find that 6 / 0.15 = 40. So, our equation simplifies to x = 40. Hooray! We've solved for x! This means that the number we were looking for, the one where 15% of it is 6, is 40. Isn't it cool how we used a little bit of algebra to unlock the answer? Solving for an unknown is like being a detective – you have clues (the equation), and you use them to find the hidden value. Now that we've found our x, we're ready to check our answer and make sure it makes sense.
Verifying the Solution
So, we've found that x = 40, which means we think 15% of 40 is 6. But before we celebrate, it's always a good idea to check our work and make sure our answer makes sense. This is a crucial step in problem-solving because it helps us catch any mistakes and build confidence in our solution. To verify our solution, we'll calculate 15% of 40 and see if it equals 6. We already know that 15% is the same as 0.15, so we'll multiply 0.15 by 40. If you do that calculation, you'll find that 0.15 * 40 = 6. Bingo! Our answer checks out. This confirms that 40 is indeed the number we were looking for. Verifying the solution is like putting the last piece in a jigsaw puzzle – it completes the picture and gives you a sense of accomplishment. Plus, it ensures that you're not just guessing but actually understanding the problem and its solution. So, always take that extra step to verify your answers, and you'll become a math-solving superstar!
Final Answer
After all our hard work, we've arrived at the final answer! We set up the equation, solved for x, and verified our solution. We know that 15% of 40 is equal to 6. Looking back at the options given (A) 30, B) 40, C) 50, D) 60), we can see that the correct answer is B) 40. Yay! We did it! It's awesome to see how all the pieces fit together, from understanding percentages to setting up equations and solving for the unknown. This whole process isn't just about getting the right answer; it's about building problem-solving skills that you can use in all sorts of situations. Think of math problems like little challenges that exercise your brain. Each time you solve one, you get a little bit stronger and more confident. So, the next time you see a percentage problem, don't sweat it! Remember the steps we took, and you'll be able to tackle it like a pro. And who knows, maybe you'll even start to enjoy the thrill of the math puzzle!
Conclusion
So, guys, we've successfully solved the mystery of finding the number where 15% equals 6. We walked through understanding percentages, converting them to decimals, setting up the equation, solving for the unknown, and verifying our solution. Remember, the answer is 40! But more importantly, we've learned a valuable process for tackling percentage problems and building our math skills. Whether it's calculating discounts, understanding statistics, or just flexing our brainpower, these skills will come in handy. Keep practicing, keep exploring, and remember that every math problem is just a puzzle waiting to be solved. You've got this!
