Confused by long division? By the end of this article you'll be able to divide 405 by 360 using long division and be able to apply the same technique to any other long division problem you have! Let's take a look.
Want to quickly learn or show students how to solve 405 divided by 360 using long division? Play this very quick and fun video now!
Okay so the first thing we need to do is clarify the terms so that you know what each part of the division is:
- The first number, 405, is called the dividend.
- The second number, 360 is called the divisor.
What we'll do here is break down each step of the long division process for 405 divided by 360 and explain each of them so you understand exactly what is going on.
405 divided by 360 step-by-step guide
Step 1
The first step is to set up our division problem with the divisor on the left side and the dividend on the right side, like we have it below:
| 3 | 6 | 0 | 4 | 0 | 5 |
Step 2
We can work out that the divisor (360) goes into the first digit of the dividend (4), 0 time(s). Now we know that, we can put 0 at the top:
| 0 | ||||||||||
| 3 | 6 | 0 | 4 | 0 | 5 |
Step 3
If we multiply the divisor by the result in the previous step (360 x 0 = 0), we can now add that answer below the dividend:
| 0 | ||||||||||
| 3 | 6 | 0 | 4 | 0 | 5 | |||||
| 0 |
Step 4
Next, we will subtract the result from the previous step from the second digit of the dividend (4 - 0 = 4) and write that answer below:
| 0 | ||||||||||
| 3 | 6 | 0 | 4 | 0 | 5 | |||||
| - | 0 | |||||||||
| 4 |
Step 5
Move the second digit of the dividend (0) down like so:
| 0 | ||||||||||
| 3 | 6 | 0 | 4 | 0 | 5 | |||||
| - | 0 | |||||||||
| 4 | 0 |
Step 6
The divisor (360) goes into the bottom number (40), 0 time(s), so we can put 0 on top:
| 0 | 0 | |||||||||
| 3 | 6 | 0 | 4 | 0 | 5 | |||||
| - | 0 | |||||||||
| 4 | 0 |
Step 7
If we multiply the divisor by the result in the previous step (360 x 0 = 0), we can now add that answer below the dividend:
| 0 | 0 | |||||||||
| 3 | 6 | 0 | 4 | 0 | 5 | |||||
| - | 0 | |||||||||
| 4 | 0 | |||||||||
| 0 |
Step 8
Next, we will subtract the result from the previous step from the third digit of the dividend (40 - 0 = 40) and write that answer below:
| 0 | 0 | |||||||||
| 3 | 6 | 0 | 4 | 0 | 5 | |||||
| - | 0 | |||||||||
| 4 | 0 | |||||||||
| - | 0 | |||||||||
| 4 | 0 |
Step 9
Move the third digit of the dividend (5) down like so:
| 0 | 0 | |||||||||
| 3 | 6 | 0 | 4 | 0 | 5 | |||||
| - | 0 | |||||||||
| 4 | 0 | |||||||||
| - | 0 | |||||||||
| 4 | 0 | 5 |
Step 10
The divisor (360) goes into the bottom number (405), 1 time(s), so we can put 1 on top:
| 0 | 0 | 1 | ||||||||
| 3 | 6 | 0 | 4 | 0 | 5 | |||||
| - | 0 | |||||||||
| 4 | 0 | |||||||||
| - | 0 | |||||||||
| 4 | 0 | 5 |
Step 11
If we multiply the divisor by the result in the previous step (360 x 1 = 360), we can now add that answer below the dividend:
| 0 | 0 | 1 | ||||||||
| 3 | 6 | 0 | 4 | 0 | 5 | |||||
| - | 0 | |||||||||
| 4 | 0 | |||||||||
| - | 0 | |||||||||
| 4 | 0 | 5 | ||||||||
| 3 | 6 | 0 |
Step 12
Next, we will subtract the result from the previous step from the fourth digit of the dividend (405 - 360 = 45) and write that answer below:
| 0 | 0 | 1 | ||||||||
| 3 | 6 | 0 | 4 | 0 | 5 | |||||
| - | 0 | |||||||||
| 4 | 0 | |||||||||
| - | 0 | |||||||||
| 4 | 0 | 5 | ||||||||
| - | 3 | 6 | 0 | |||||||
| 4 | 5 |
So, what is the answer to 405 divided by 360?
If you made it this far into the tutorial, well done! There are no more digits to move down from the dividend, which means we have completed the long division problem.
Your answer is the top number, and any remainder will be the bottom number. So, for 405 divided by 360, the final solution is:
1
Remainder 45
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Extra calculations for you
Now you've learned the long division approach to 405 divided by 360, here are a few other ways you might do the calculation:
- Using a calculator, if you typed in 405 divided by 360, you'd get 1.125.
- You could also express 405/360 as a mixed fraction: 1 45/360
- If you look at the mixed fraction 1 45/360, you'll see that the numerator is the same as the remainder (45), the denominator is our original divisor (360), and the whole number is our final answer (1).
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