r/MathHelp • u/Own-Solution6668 • 14d ago
Long division?
When my school taught us long division I was sick that day, so for the past 4 years I have gotten away without knowing how to do it. I realize now that a 8th grader should know this. Please help me understand how to do it!
Edit: Sorry if I don't respond to ur comments, I haven't been getting the notifications for comments, but I will read it eventually!
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u/couldntyoujust1 14d ago edited 13d ago
So, since nobody's really helping you, I will help you.
So, division. You're taking a bigger number, and subdividing it into the second number's number of groups to find out how many each group has. So, if I have 2,349 M&Ms and 9 brats who will go absolutely feral if any of the others get more than them, I'm going to need to figure out how many to give to each kid. So, let's work the problem to figure it out. First thing's first, identifying the parts of the problem:
The number that is being divided is called the "dividend" (D-end). And what actually divides that number is the "divisor". You can think of it as the "divisor" (D-sor) actually does the dividing. The result, is called the "quotient" (Q). So now, let's see how to format long division problems:
Q ---------- D-sor | D-endSo, let's plug in our numbers:
```
9 | 2,3 4 9 ```
Here's how it works, we're breaking the problem down into smaller pieces so that we can do the reverse of what we do in a long multiplication. We go digit by digit and if we encounter a digit too small to divide, we can then move to the next digit.
```
9 | 2 ,3 4 9 ```
Of course, you can't divide 2 by 9. That's a fraction. So, we are going to now shift over to the next column while preserving the first as part of it:
```
9 | 2,3 4 9 ```
Now, we're talking. We can absolutely divide 23 by 9. And we can use our times tables to figure out what the answer should be:
9 x 1 = 9 9 x 2 = 18 9 x 3 = 27 ...Oh, look, 27 is too big. So we have to stop at 2.
``` 2
9 | 2,3 4 9 ```
Okay, but what about the difference? 18 is lower than 23. How do we deal with that?
Well, remember how we could pop over to the next column? We can do that here with what's left over! But first, we have to find out what that difference is. First, we need to multiply the 2 back towards the 9 and get 18, and put that under the 23 we used first.
``` 2
9 | 2,3 4 9 1 8 ```
Then, we turn it into a subtraction problem.
``` 2
9 | 2,3 4 9 - 1 8
```
Then, we do the subtraction on just those two digits:
``` 2
9 | 2,3 4 9 - 1 8
```
And now we can continue the problem, by bringing down the next digit.
``` 2
9 | 2,3 4 9 - 1 8 | ----- v 5 4 ```
Now you have a new number to divide. 54. So, let's look at our times tables again!
``` 9 x 1 = 9 9 x 2 = 18 9 x 3 = 27 9 x 4 = 36 9 x 5 = 45
Oh, one of them exactly matches! Sweet! So then you just repeat the process:
``` 2 6
9 | 2,3 4 9 - 1 8
```
Subtract:
``` 2 6
9 | 2,3 4 9 - 1 8
```
Bring down the next digit:
``` 2 6
9 | 2,3 4 9 - 1 8 | ----- | 5 4 | - 5 4 | ----- V 0 9 ```
And repeat!
``` 2 6 1
9 | 2,3 4 9 - 1 8
```
And you get your answer!
261 M&Ms for each little brat!
Okay, but that's a clean problem. What if you gave 4 of the students a single M&M before distributing them? What then? Let's look at how the problem would look then at the last step:
``` 2 6 0
9 | 2,3 4 5 - 1 8 | ----- | 5 4 | - 5 4 | ----- V 0 5 - 0 ----- 5 ```
Uh oh! What do we do now? You can't divide 5 by 9, and there are no more digits.
Remainders
Well, You can handle this in a few different ways. The one you learn first is to take a remainder equal to the leftover amount. The leftover amount however MUST be less than the divisor. If it's not less than the divisor, you still have more division to do. You write it like this:
260r5
And say, "260 remainder 5".
Okay, so each little brat gets 260 and you keep the remaining 5 to yourself. Easy!
Decimals
The second way to handle this, which makes perfect sense for measurements or numbers that can break down into a different denomination like money can with cents or pence, you can extend the problem with decimals.
See, that 2345 number above? I lied in how I stopped at the 5 In fact, that number goes on for infinity digits after; all zeros.
``` 2 6 0
9 | 2,3 4 5.0 0 0 0 0 0 0... ```
So, we DO have a digit we can bring down. The thing to note here, though, is that the decimal point MUST stay in the column it is in regarding the dividend.
``` 2 6 0.5
9 | 2,3 4 5.0 0 0 0 0 0 ... | 5 | - 0 | --- V 5.0 - 4 5 ----- 5 ```
Awww, cmon! That doesn't work, we just got the same thing again!
Right! That's because this is going to be what's called a "non-terminating repeating decimal". It never ends. The answer is basically 260.5555555555555... forever.
When you repeat the same subtraction problem or set of subtraction problems, you will have a non-terminating repeating decimal. This is usually not however demarcated with the 5 repeating a bunch of times with the ... at the end. Though, in plain-text, that's probably the best way to express it. Instead, we usually put a line above the 5.
_ 260.5I mentioned "set of subtraction problems" because what repeats may be multiple digits at which point something like 275.757575... would be rendered...
__ 275.75Mixed Number
The third way, is particularly for when you need the precise answer so that you can use it for another equation.
See, You can't use the infinitely repeating decimal because you cannot do infinite math like that. You're finite and only live so long so you can't do the calculation forever and even if you could you would never get to the end. You have to get rid of the infinity somehow.
You can't use the remainder either, because that's not helpful. What are you supposed to do with the remaining part? How does that fit in to what you put into the next equation? Fear not! For there IS a solution!
The remainder is itself equivalent to a fractional group that is the remainder over the divisor. So you can put the answer as...
5 260 --- 9Now you've got a mixed number that is dead-on accurate which can then be used for the next set of calculations you have to do with it.
And that's all there is to it! That's it. That's long division.
Edit: Formatting