Como Resolver A Divisão De 43215 Por 3 Obtendo O Resultado Exato

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Hey guys! Today, we're diving deep into a math problem that might seem tricky at first glance: dividing 43215 by 3. Don't worry, we'll break it down step by step, making sure everyone understands the process. Whether you're a student brushing up on your division skills or just a curious mind, this guide is for you. So, let’s jump right in and conquer this division challenge together!

Understanding Division

Before we tackle the main problem, let's quickly recap what division actually means. Division is one of the four basic arithmetic operations (the others being addition, subtraction, and multiplication) and it's essentially the process of splitting a whole into equal parts. Think of it like sharing a pizza among friends. If you have a pizza with 8 slices and 4 friends, you're dividing the pizza (the whole) into 4 equal parts (slices for each friend). So, each friend gets 2 slices.

In mathematical terms, division involves three main components:

  • Dividend: This is the number being divided (in our case, 43215).
  • Divisor: This is the number by which we are dividing (in our case, 3).
  • Quotient: This is the result of the division (the number we're trying to find).

Sometimes, division doesn't result in a whole number. You might end up with a remainder, which is the amount left over after dividing as much as possible into whole parts. For example, if you had 9 slices of pizza and 4 friends, each friend would still get 2 slices, but there would be 1 slice left over (the remainder).

Understanding these basic concepts is super important before we move on to the long division method, which we'll use to solve 43215 ÷ 3. Grasping the fundamentals of division will make the entire process smoother and less intimidating. So, keep these definitions in mind as we move forward, and you'll see how they fit into the bigger picture of solving our problem. We're building a solid foundation here, guys, so that even the trickiest divisions won’t seem so tough anymore!

The Long Division Method: A Step-by-Step Approach

Now, let's get into the nitty-gritty of how to actually perform long division. This method is your best friend when dealing with larger numbers, and it’s a systematic way to break down the problem into manageable steps. We're going to walk through it slowly, using our problem 43215 ÷ 3 as our example. Trust me, once you get the hang of this, you'll be able to divide almost anything!

  1. Set up the problem: First, write down the dividend (43215) inside the division symbol (a sideways L with a line over it) and the divisor (3) outside, to the left of the symbol. This sets up your workspace and makes it clear what you’re dividing by what.
  2. Divide the first digit: Look at the first digit of the dividend (4). Ask yourself, “How many times does 3 go into 4?” It goes in once. Write the “1” above the 4 in the quotient area (the space above the division symbol). This is our first digit of the answer.
  3. Multiply and subtract: Multiply the quotient digit (1) by the divisor (3). 1 × 3 = 3. Write this “3” below the first digit of the dividend (4). Now, subtract 3 from 4, which gives you 1. This is the remainder from our first step.
  4. Bring down the next digit: Bring down the next digit from the dividend (3) next to the remainder (1), forming the number 13. This is like adding the next piece of the puzzle to our division problem.
  5. Repeat the process: Now, repeat steps 2-4 with the new number (13). How many times does 3 go into 13? It goes in 4 times. Write “4” next to the “1” in the quotient area. Multiply 4 × 3 = 12. Write 12 below 13 and subtract, leaving a remainder of 1. Bring down the next digit (2) from the dividend, forming the number 12.
  6. Continue until finished: Keep repeating the process. How many times does 3 go into 12? It goes in 4 times. Write “4” in the quotient. Multiply 4 × 3 = 12. Subtract 12 from 12, leaving 0. Bring down the next digit (1). How many times does 3 go into 1? It doesn’t, so write “0” in the quotient. Bring down the last digit (5), forming 15. How many times does 3 go into 15? It goes in 5 times. Write “5” in the quotient. Multiply 5 × 3 = 15. Subtract 15 from 15, leaving 0.
  7. The result: The quotient (the number at the top) is your answer. In this case, it’s 14405. And since our final remainder is 0, the division is exact!

See? Long division isn’t so scary when you break it down. It's like following a recipe – each step leads you closer to the final delicious result. We've just shown how systematically going through each digit makes even a large division problem manageable. So, let's take a breather and celebrate this small victory before we dive deeper into verifying our solution and understanding the nuances of remainders. You're doing great, guys! Keep up the awesome work!

Verifying the Solution: Ensuring Accuracy

Okay, we've gone through the long division process and arrived at a quotient. But how do we know for sure that our answer is correct? It's always a good idea to double-check your work, especially in math. Verifying the solution is like adding a safety net – it catches any potential errors and gives you confidence in your result. So, let’s put on our detective hats and make sure we've cracked this case!

The easiest way to verify a division problem is to use the inverse operation: multiplication. Remember, division is essentially the opposite of multiplication. If we divided 43215 by 3 and got 14405, then multiplying 14405 by 3 should give us back 43215. Simple, right?

Let's do the math:

14405 (quotient) × 3 (divisor) =

  • 3 × 5 = 15 (write down 5, carry over 1)
  • 3 × 0 = 0 + 1 (carried over) = 1
  • 3 × 4 = 12 (write down 2, carry over 1)
  • 3 × 4 = 12 + 1 (carried over) = 13 (write down 3, carry over 1)
  • 3 × 1 = 3 + 1 (carried over) = 4

So, 14405 × 3 = 43215

Guess what? It matches our original dividend! This means our division is correct. We've successfully verified our solution using multiplication. High five!

But what if we had a remainder? How would we verify the answer then? Good question! If there's a remainder, you multiply the quotient by the divisor and add the remainder. The result should equal the dividend. For example, if we had divided 43217 by 3 and got a quotient of 14405 with a remainder of 2, we would calculate (14405 × 3) + 2. This would also equal 43217, confirming our division was accurate.

Verifying your answer is such a crucial step, guys. It’s like proofreading a paper before you submit it – you want to catch any mistakes before they count against you. So, always take the extra minute to check your work. Your future self will thank you for it!

Real-World Applications of Division

Now that we've mastered the art of dividing 43215 by 3, you might be wondering,