Număr Natural Cu Cifra Unităților 3: Cum Îl Aflăm?
Hey guys! Today we're diving into a cool math problem that involves figuring out a mystery number. This number has a '3' in the units place, and when we remove that '3', the number shrinks by 4566. Sounds like a puzzle, right? Let's break it down and solve it together! Understanding how to approach such problems not only helps with math class but also sharpens our logical thinking skills. So, buckle up, and let's get started!
Descoperind Numărul Inițial
So, the million-dollar question is: how do we find this initial number? Let's start by representing the unknown. We can express the initial number as 10x + 3, where x represents the digits to the left of the units digit (which is 3). Think of it like this: if our number was 43, x would be 4. Makes sense, right? When we remove the 3, we're left with just x. And here’s the key: the problem tells us that removing the 3 reduces the number by 4566. We can translate this into a simple, yet powerful, equation: (10x + 3) - x = 4566. This equation is the backbone of our solution, guys. It mathematically represents the relationship described in the problem. It states that the original number (10x + 3) minus the new number (x) equals the difference (4566). By solving for x, we essentially unravel the mystery of the missing digits. So, let’s roll up our sleeves and solve this equation together!
Construirea Ecuației
Let's take a closer look at how we built that equation, because it's super important! Our original number is 10x + 3. The 10x part represents all the digits except the units digit (which is 3). We multiply x by 10 because each digit to the left of the units place has a value ten times greater than the digit to its right. Think about place values: tens, hundreds, thousands, and so on. The + 3 simply adds the units digit to the mix. When we remove the 3, we're left with just x. The problem states that this removal causes a decrease of 4566. This “decrease” is the difference between the original number and the new number. That's why we subtract x from 10x + 3. The phrase “reduces by 4566” directly translates to “equals 4566” in our equation. So, we put it all together: (10x + 3) - x = 4566. This equation perfectly captures the essence of the problem, transforming the word puzzle into a solvable mathematical statement. Understanding this translation process is key to tackling similar problems in the future. It’s not just about memorizing formulas, it's about understanding the underlying logic and being able to express real-world scenarios mathematically.
Rezolvarea Ecuației Pas cu Pas
Alright, let's get our hands dirty and solve this equation step-by-step! (10x + 3) - x = 4566 is our starting point. First, we need to simplify the left side of the equation. We have 10x and we're subtracting x, which leaves us with 9x. So, the equation becomes 9x + 3 = 4566. Simple enough, right? Now, we want to isolate the term with x (that's the 9x). To do that, we need to get rid of the + 3. The golden rule of equation solving is: what you do to one side, you must do to the other. So, we subtract 3 from both sides: 9x + 3 - 3 = 4566 - 3. This simplifies to 9x = 4563. We're getting closer! We now have 9x equal to a number. To find x, we need to divide both sides by 9: 9x / 9 = 4563 / 9. This gives us x = 507. Woohoo! We've solved for x. But wait, we're not quite done yet. Remember, we need to find the original number, not just x.
Determinarea Numărului Inițial
Okay, we've found that x = 507. But what does that actually mean in the context of our problem? Remember, we said our original number could be represented as 10x + 3. We figured this out by understanding that x represents the digits to the left of the units digit, which is 3. Now we know that those digits are actually the number 507. So, to find the original number, we simply substitute x with 507 in our expression: 10 * 507 + 3. Let's do the math: 10 * 507 = 5070, and then 5070 + 3 = 5073. Boom! We've got it! The original number is 5073. This makes perfect sense, guys. If we remove the 3 from 5073, we get 507. And 5073 - 507 does indeed equal 4566. So, our answer fits the conditions of the problem. This final step of substituting our value of x back into the original expression is crucial. It transforms our algebraic solution back into the real-world answer we're looking for. And remember, always check your answer to make sure it makes sense within the context of the problem. It’s like putting the final piece in a puzzle – satisfying and assuring!
Verificarea Soluției
Checking our solution is a super important step, guys, because it’s like giving yourself a gold star for accuracy! We found that the original number is 5073. The problem stated that if we remove the 3, the number decreases by 4566. So, let's see if that holds true. If we remove the 3 from 5073, we get 507. Now we need to check if the difference between 5073 and 507 is indeed 4566. Let's do the subtraction: 5073 - 507 = 4566. Bingo! It checks out! Our solution satisfies the condition given in the problem. This verification step not only confirms our answer but also reinforces our understanding of the problem and the steps we took to solve it. It’s a confidence booster and a great way to avoid careless mistakes. Never skip the verification step, guys! It's your chance to double-check your work and ensure you're on the right track. Think of it as the final polish that makes your solution shine.
Concluzie
So, we've successfully navigated this math puzzle! The original number, the one with 3 in the units place that shrinks by 4566 when we remove the 3, is drumroll please… 5073! We cracked this problem by translating the words into a mathematical equation, solving for the unknown (x), and then using that value to find our original number. We even double-checked our answer to make sure it made sense. You see, guys, math problems like this aren't just about numbers and calculations. They're about logical thinking, problem-solving, and the ability to break down complex situations into manageable steps. And the best part is, these skills are super useful in all areas of life, not just in math class! So, keep practicing, keep questioning, and keep those brains working. You've got this!