Step-by-Step Guide Dividing 990 By 13

Hey guys! Ever get that feeling when you're staring at a math problem and it seems like it's in a different language? Well, today we're going to tackle one of those head-scratchers together: dividing 990 by 13. Don't worry, we'll break it down step-by-step so it's super easy to follow. Math can actually be fun when you understand the process, so let's dive in!

Understanding Division: The Basics

Before we jump into the problem, let's quickly review the basics of division. At its core, division is just splitting a number into equal groups. Think of it like sharing a bag of candy among friends. The number you're splitting (in our case, 990) is called the dividend. The number you're dividing by (13) is the divisor. And the result you get is the quotient. Sometimes, you might have some left over, and that's called the remainder. So, in our division problem, we're trying to figure out how many groups of 13 we can make from 990, and if there will be any candy left over.

Long division might seem intimidating at first, but it's just a systematic way of breaking down a larger division problem into smaller, manageable steps. We're going to use this method to conquer 990 divided by 13. The key is to take it slow, one step at a time. We'll focus on each digit of the dividend, working our way from left to right. By understanding each step, you'll not only be able to solve this problem but also gain confidence in tackling other division problems in the future. Remember, practice makes perfect, so don't be afraid to work through a few examples to solidify your understanding. With a little patience and attention to detail, you'll be dividing like a pro in no time!

Step 1: Setting Up the Problem

Okay, first things first, let's set up our problem for long division. We write the dividend (990) inside the division symbol, which looks like a little house, and the divisor (13) outside on the left. This visual setup helps us keep everything organized as we work through the steps. It's like setting the stage for a play – everything needs to be in its place before the action begins. This organized approach is crucial for avoiding mistakes and making the process smoother.

Now that we have our problem set up, we're ready to start the actual division process. We're going to look at the first digit (or digits) of the dividend and see how many times the divisor can fit into it. This is where our multiplication skills come in handy. We'll be thinking, "How many times does 13 go into this part of 990?" It might seem a little daunting at first, but trust me, we'll break it down into small, manageable steps. Remember, the goal here is to be organized and methodical. By setting up the problem correctly and understanding what we're trying to do, we're already halfway to the solution. So, let's take a deep breath and get ready to dive into the next step!

Step 2: Dividing the First Digits

Now, let's look at the first digit of our dividend, which is 9. Can 13 go into 9? Nope, it's too small. So, we need to consider the first two digits together, which gives us 99. This is where things get a little more interesting. We need to figure out how many times 13 can fit into 99. Think of it like this: how many groups of 13 can we make from 99? To figure this out, we can use a little trial and error, or even some mental math if you're feeling confident. Try multiplying 13 by different numbers until you get as close to 99 as possible without going over.

For example, we could try 13 multiplied by 5, which equals 65. That's less than 99, so we can try a bigger number. Let's try 13 multiplied by 7, which equals 91. That's pretty close! If we try 13 multiplied by 8, we get 104, which is too big. So, 7 is the magic number here. This means 13 goes into 99 seven times. We write the 7 above the 9 in the tens place of the dividend, as this is the digit we used in the 99. This step is all about finding the right fit, like a puzzle piece sliding into place. It might take a little practice to get the hang of it, but with each problem you solve, you'll become more comfortable with estimating and finding the closest multiple.

Step 3: Multiplying and Subtracting

Alright, we've figured out that 13 goes into 99 seven times. Now, we need to multiply 7 (our quotient for this step) by 13 (our divisor). We already did this calculation in the previous step – 7 multiplied by 13 equals 91. We write 91 directly below the 99 in our long division setup. This step is like checking our work: we're confirming how much of the dividend we've accounted for so far. It's a crucial step in the process because it sets us up for the next subtraction.

Next, we subtract 91 from 99. This is a simple subtraction problem: 99 minus 91 equals 8. We write the 8 below the 91. This subtraction tells us how much is left over after taking out seven groups of 13 from 99. It's the remainder from this particular step, and it's important because it carries over to the next part of our division. Think of it as the “leftover candy” from our earlier analogy. This remainder is what we'll use in the next step to continue the division process. So far, we've successfully divided the first part of the dividend and found the initial remainder. We're making great progress!

Step 4: Bring Down the Next Digit

Okay, we've subtracted and have a remainder of 8. Now it's time to bring down the next digit from our dividend, which is 0. We write this 0 next to the 8, creating the new number 80. Bringing down the next digit is like adding more items to our pile that we need to divide. In this case, we're adding the ones place to our existing remainder, giving us a new number to work with. This step is essential because it allows us to continue the division process with the remaining portion of the dividend.

Now we have 80, and we need to figure out how many times 13 goes into 80. This is similar to what we did in Step 2, but with a different number. We're essentially starting the division process again, but this time with 80 instead of 99. We'll use the same strategy of estimating and multiplying to find the closest multiple of 13 that fits into 80. Remember, the key is to take it one step at a time and focus on the task at hand. We're almost there, guys! We've successfully brought down the next digit and are ready to continue the division. Let's keep going!

Step 5: Divide Again

Now we focus on our new number, 80. We need to figure out how many times 13 goes into 80. Just like before, we can use trial and error or mental math. Let's try multiplying 13 by different numbers. 13 multiplied by 5 is 65. That seems promising! Let's try 13 multiplied by 6, which is 78. That's even closer! If we try 13 multiplied by 7, we get 91, which is too big. So, 6 is the number we're looking for. This means 13 goes into 80 six times. We write the 6 above the 0 in the ones place of the dividend. This step is all about repeating the division process with our new number. We're essentially doing the same thing we did in Step 2, but with a different value. It's a testament to the cyclical nature of long division: divide, multiply, subtract, bring down, and repeat. By understanding this pattern, you can confidently tackle any long division problem.

Step 6: Multiply and Subtract (Again)

Great! We know 13 goes into 80 six times. So, we multiply 6 (our new quotient) by 13 (our divisor). We already calculated this in the previous step: 6 multiplied by 13 equals 78. We write 78 below the 80. Just like in Step 3, this multiplication step is a check: we're confirming how much of 80 we've accounted for. It's an essential part of the process, ensuring we stay on track and don't make any errors.

Next, we subtract 78 from 80. This is another simple subtraction problem: 80 minus 78 equals 2. We write the 2 below the 78. This 2 is our remainder for this part of the division. It represents the amount left over after taking out six groups of 13 from 80. Since there are no more digits to bring down from the dividend, this remainder is also the final remainder for the entire problem. We're almost at the finish line! We've successfully completed the multiplication and subtraction steps for the final part of our division.

Step 7: The Final Answer

We've reached the end of our long division journey! We have a quotient of 76 and a remainder of 2. This means that 990 divided by 13 equals 76 with 2 left over. We can write this as 76 R 2, where R stands for remainder. So, there you have it, guys! We've successfully divided 990 by 13, step by step. It might have seemed a little complicated at first, but by breaking it down into smaller, manageable steps, we were able to conquer it together.

To double-check our answer, we can multiply the quotient (76) by the divisor (13) and then add the remainder (2). If we do this, we get (76 * 13) + 2 = 988 + 2 = 990, which is our original dividend. This confirms that our answer is correct. Remember, long division is a process that takes practice and patience. The more you do it, the more comfortable you'll become. So, don't be discouraged if you don't get it right away. Keep practicing, and you'll be a division master in no time! And that's how you divide 990 by 13, step by step. You got this!