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Dividing 36895 By 25 A Step-by-Step Guide

Jul 29, 2025 by Brainly ES FTUNILA 42 views

Dividing 36895 by 25 Step-by-Step Using the Long Division Method

Hey guys! Today, we're diving into a long division problem. We're going to break down how to divide 36895 by 25 using the step-by-step long division method, also known as the "cajón" technique in some places. Don't worry, it's not as scary as it sounds! We'll take it one step at a time, and you'll see how straightforward it can be. Let's get started!

Setting Up the Problem

Okay, first things first, let's set up our problem. In long division, we write the number we're dividing (36895) inside the "division bracket" (or the "cajón" as some call it) and the number we're dividing by (25) outside on the left. This setup helps us organize our work and keep track of the different steps. Think of it like setting the stage for a math play – everything needs to be in its place!

So, our setup looks like this:

      ________
25 | 36895

Now, we're ready to start the actual division process. The goal here is to figure out how many times 25 can fit into 36895, and we'll do it digit by digit. It's like figuring out how many boxes of 25 items we can fill from a pile of 36895 items.

Step 1: Dividing the First Digits

Let's focus on the first part of the number inside the bracket, which is 36. We want to figure out how many times 25 goes into 36. Think of it like this: if you have 36 cookies and want to put them into bags of 25, how many full bags can you make? The answer is 1, because 25 fits into 36 only once.

So, we write "1" above the 6 in 36895, because we're dividing into the first two digits. This "1" is the first digit of our quotient, which is the answer to the division problem. Underneath the 36, we write 25 (which is 1 times 25) and subtract it from 36. This subtraction helps us see how much is left over after taking out one group of 25. The result of 36 minus 25 is 11. This 11 is our remainder for this step.

Our problem now looks like this:

      1_____
25 | 36895
     -25
     ----
     11

Step 2: Bringing Down the Next Digit

Now, we bring down the next digit from the original number, which is 8, and write it next to the 11. This gives us 118. We're essentially saying, "Okay, we had 11 left over, and now we have another 8 to work with, so we have 118 in total." This step keeps the place value aligned and helps us continue the division process. Imagine we had 11 cookies left and someone gave us 8 more – now we have 118 to deal with!

Our problem now looks like this:

      1_____
25 | 36895
     -25
     ----
     118

Step 3: Dividing Again

Now we need to figure out how many times 25 goes into 118. This might require a little bit of estimation. We can think, "What number times 25 is close to 118 without going over?" If we try 4, we get 4 times 25 equals 100, which is less than 118. If we try 5, we get 5 times 25 equals 125, which is more than 118. So, 4 is the right number. We write "4" next to the "1" in our quotient above the 8 in the original number. Then, we write 100 (which is 4 times 25) underneath the 118 and subtract. This is where knowing your multiplication facts really comes in handy! The result of 118 minus 100 is 18.

Our problem now looks like this:

Step 4: Bring Down the Next Digit Again

Just like before, we bring down the next digit, which is 9, and write it next to the 18. This gives us 189. We're continuing the process, step by step, until we've used all the digits in the original number. It's like a conveyor belt of numbers, each one getting its turn in the division process!

Our problem now looks like this:

Step 5: Divide Again

Now we figure out how many times 25 goes into 189. Again, some estimation might be needed. We can think, "What number times 25 is close to 189 without going over?" If we try 7, we get 7 times 25 equals 175, which is less than 189. If we try 8, we get 8 times 25 equals 200, which is more than 189. So, 7 is the number we need. We write "7" next to the "14" in our quotient above the 9 in the original number. Then, we write 175 (which is 7 times 25) underneath the 189 and subtract. The result of 189 minus 175 is 14.

Our problem now looks like this:

Step 6: Bring Down the Final Digit

We bring down the last digit, which is 5, and write it next to the 14. This gives us 145. We're on the home stretch now!

Our problem now looks like this:

Step 7: The Final Division

Finally, we figure out how many times 25 goes into 145. Let's see... if we try 5, we get 5 times 25 equals 125. If we try 6, we get 6 times 25 equals 150, which is slightly too big. So, 5 is the correct number. We write "5" next to the "147" in our quotient above the 5 in the original number. Then, we write 125 (which is 5 times 25) underneath the 145 and subtract. The result of 145 minus 125 is 20.

Our problem now looks like this:

The Answer and the Remainder

We've reached the end! We have a quotient of 1475 and a remainder of 20. This means that 36895 divided by 25 is 1475 with 20 left over. In other words, 25 fits into 36895 a total of 1475 times, and after taking out all those groups of 25, we still have 20 left. So, the remainder is 20. The result of 36895 divided by 25 is 1475 with a remainder of 20.

So, our final answer is:

Quotient: 1475

Remainder: 20

Verification

To verify our result, we will multiply the quotient (1475) by the divisor (25) and add the remainder (20) to the result. This should equal the dividend (36895).

1475 * 25 = 36875

36875 + 20 = 36895

This confirms our calculation, the final result is correct!

Conclusion

There you have it! We've successfully divided 36895 by 25 using the long division method. It might seem like a lot of steps, but once you get the hang of it, it becomes much easier. The key is to break the problem down into smaller, manageable chunks and take it one step at a time. Keep practicing, and you'll be a long division pro in no time! Remember, math is like any other skill – the more you practice, the better you get. So, keep those pencils moving and those numbers crunching! You got this! And if you ever get stuck, just remember this step-by-step process and you'll be able to tackle any division problem that comes your way.