# How to Divide

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Division is a core life skill. Calculating the fraction someone is owed or should receive — for instance when splitting a check or dividing the costs of a trip — is a mathematical challenge you are likely to encounter on an almost daily basis.

Long division sounds scary, but it’s not. This instructable will teach you how to find the answer to a division problem, also known as the quotient. It will also teach you how to solve division problems that have remainders. You won’t need a calculator, and you will be able to show your work. You’ll not only be able to complete any worksheet for school, you’ll always be prepared and confident when you have to split a check three ways.

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## Step 1: Things You'll Need

There are three different "methods" that I will be teaching you. To learn all of the methods you will need a pencil and lots of paper. You may also want to have a calculator to double-check your answers.

## Step 2: Simple Division

The first method is simple division. Your answer will come out as a whole number.

1) Setup the division problem (84/7).
2) Divide 8 by 7 to get 1. Place this on top of the 8 and the division sign.
3) Multiply 1 and 7 to get 7. Place this under the 8.
4) Subtract 7 from 8 to get 1.
5) Carry down the 4.
6) Divide 14 by 7 to get 2. Place this on top of the 4 and the division sign.
7) Multiply 2 by 7 to get 14.
8) Subtract 14 from 14 to get 0.

## Step 3: Simple Division With Remainder

This is the same as simple division except we add in the remainder.

1) Setup the division problem (10/3).
2) Divide 10 and 3 to get 3. Place this on top the 0 and the division sign.
3) Multiply 3 by 3 to get 9. Place this under the 10.
4) Subtract 9 from 10 to get 1. That is the remainder.

The answer is 3 r 1!

## Step 4: Long Division With Decimal

This is similar to dividing with a remainder except you go a step further and have a decimal.

1) Setup the division problem (127/4).
2) Divide 12 and 4 to get 3. Put this on top of the 12 and the division sign.
3) Multiply 3 and 4 to get 12. Place this under the 12.
4) Subtract 12 and 12 to get 0.
5) Carry down the 7.
6) Divide 7 and 4 to get 1. Put this on top of the 7 and the division sign.
7) Multiply 4 and 1 to get 4. Place this under the 7.
8) Subtract 7 and 4 to get 3.
9) Add a 0 and a decimal point. Carry down as before. Dividing to a decimal, you can add as many zeroes as the problem requires.
10) Divide 30 and 4 to get 7.
11) Multiply 4 and 7 to get 28. Place this under the 30.
12) Subtract 30 and 28 to 2.
13) Add another 0 and a decimal point. Carry down as before.
14) Divide 20 by 4 to get 5.
15) Multiply 4 and 5 to get 20. The remainder is 0, therefore you have completed the division problem.

## Step 5: Divide With More Than One Digit

Last method! Dividing when the divisor is more than one digit, like 63.

1) Setup the division problem (2856/84).
2) Divide 285 by 84 to get 3. Place this on top of the 5 and the division sign.
3) Multiply the 3 and 84 to get 252. Place this under the 285.
4) Subtract 285 and 252 to get 33.
5) Carry down the 6.
6) Divide 336 by 84 to get 4. Place this on top of the 6 and the division sign.
7) Multiply 4 and 84 to get 336.
8) Subtract 336 and 336 to get 0.

## Step 6: Conclusion

Now you know how to divide!

Remember that you can't divide by zero.

First Prize in the
Burning Questions: Round 6

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## 104 Discussions

I am going into 7th grade, but I am still awful at this! Especially the two digit ones.

Thanks Y'all

and how do you do 13 ÷ 3?
it goes on forever

how do you do it if the dividend has a decimal

In the problem 84/2856 devided how did you get you get the number 3. If you don't know the answer how do you multiply?

It's a guess. Actually, every choice for a new digit in the quotient, is a guess. In each step, you guess at that part of the quotient. Then use multiplication, followed by subtraction, to confirm your guess was correct.

At this point you're probably thinking you have to be clairvoyant to do long division, i.e. see into the future, to correctly find the digits for each new guess, but it is not as bad as that.

This guesswork was easy in the case in Step 4, where the divisor was just one digit wide.

(?) .................trial multiplication: too low, correct, too high
4 into 12? Answer: 3R0, since 4*2= 8, 4*3=12, 4*4=16
4 into 07? Answer: 1R3, since 4*0= 0, 4*1= 4, 4*2= 8
4 into 30? Answer: 7R2, since 4*6=24, 4*7=28, 4*8=32
4 into 20? Answer: 5R0, since 4*4=16, 4*5=20, 4*6=24

The reason why it is easy is because you have, in your memory, the answer to every 1-digit by 1-digit multiplication problem. I mean, that is why you memorized a multiplication table, and that's why you likely did that before trying to tackle long division.

Moving on to Step 5: How do we best guess at a 2-digit into 3-digit division problem, like:

84 into 285?

Well, one way is to divide by 10 and round, both divisor and dividend, to get a 1-digit divisor division problem, that approximates the actual division problem.

round(84/10)= 8, round(285/10)=29

(?) .................trial multiplication: too low, correct, too high
8 into 29? Answer: 3R5, since 8*2=16, 8*3=24, 8*4=32

And it turns out, 3 is the correct guess. And this can be shown by computing the more precise 84*n products.

(?) .................trial multiplication: too low, correct, too high

84 into 285? Answer: 3R33, since 84*2=168, 84*3=252, 84*4=336

So, rounding before guessing, is probably the best way for a human to tackle this problem.

Another way to tackle this problem is to just compute the complete 84*n table, for n={0...9}, in advance.

84*0= 0
84*1= 84
84*2=168
84*3=252
84*4=336
84*5=420
84*6=504
84*7=588
84*8=672
84*9=756

Although, that's more the brute force way, that a computer, or rather a computer programmer, might use. However this is instructive, because it shows us the problem is not insolvable. The number of choices for the guess for the next digit, is not infinite, nor crazy huge. Rather it is, at most, 10 choices, the numbers in the set, {0...9}

Thanks, in 7th grade and forgot how to divide, but managed to skim through skool till' now, thanks again!