Despite being an honor/AP student in grade school I never grasped long division mental math, but I have two young kids that will broach this subject in a few years and I want to be able to teach them if they need help.
In: Mathematics
Well first, dont do long division menially. Get your self a piece of graph paper for it. If you want to do mental division, use a different method.
Now that you have your graph paper, write the number you want to divide by (divisor) on the second line, and then put a line and write the number you want to divide (dividend) next to it, 1 digit per cell, and overline it. The lines are just to keep things organized. Lets use an example of 89326145061531432/1958, so it gets set up as
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___________________
7958|89326145061531432
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Next, copy down 1 digit from the dividend in the same column
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___________________
1958|89326145061531432
8
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check if that number is bigger than the divisor, if it isnt, write a 0 above that number, and copy the next digit until it is.
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0
___________________
1958|89326145061531432
89
“`
“`
00
___________________
1958|89326145061531432
893
“`
“`
000
___________________
1958|89326145061531432
8932
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Now that its bigger, find the largest single digit number where divisor*digit is still < the number. In this case its 4. You can figure it out with trial and error, there are only 9 options after all. It can be helpful to write these all down as we will be frequently using them (or write them down as you calculate them naturally).
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1958*1= 1958
1958*2= 3916
1958*3= 5874
1958*4= 7832
1958*5= 9790
1958*6=11748
1958*7=13706
1958*8=15664
1958*9=17622
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Then write the digit above the number, and write divisor*digit under the number you have been making
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0004
___________________
1958|89326145061531432
8932
-7832
“`
Now subtract those 2 numbers. remember to stay in the correct columns
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0004
___________________
1958|89326145061531432
8932
-7832
1100
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Now using the result of the subtraction, start bringing down numbers again
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0004
___________________
1958|89326145061531432
8932
-7832
11006
“`
And repeat until you are out of digits
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000456211
___________________
1958|89326145061531432
8932
-7832
11006
-9790
12161
-11748
4134
-3916
2185
-1958
312
“`
If it gets to long, and you have the space, feel free to shift up into the unused space under the number, just be careful when you do to keep everything lined up
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000456211
___________________
1958|89326145061531432
8932 312
-7832
11006
-9790
12161
-11748
4134
-3916
2185
-1958
227
-1958
312
“`
Then continue dropping digits as normal
“`
00045621115966052
___________________
1958|89326145061531432
8932 3126 5532
-7832 -1958 -1958
11006 11681 1616
-9790 -9790
12161 18915
-11748 17622
4134 12933
-3916 11748
2185 11851
-1958 11748
2270 10343
-1958 -9790
312 553
“`
when you run out of digits, you can either just take the result of the last subtraction, and call that the remainder (in this case 45621115966052 R 1616), or you can add a decimal point and keep going. Do the exact same steps, but keep adding 0s to the number. If you do this long enough, it will either stop or you will recognize you are repeating operations. if this happens, overline the repeating decimal, it is the repeating part.
(for example 1/3, is
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0.3333
______
3|1.0000
10 10
-9 -9
10 1 #etc, it keeps doing this exact same 10-3*3 sequence
-9
10
-9
“`
Do you mean HOW it works or WHY it works?
The how is quite simple, you start from the front of the number and divide with remainder, but write down the remainder in front of the next number.
1234 / 4
1 / 4 is 0 remainder 1
12 / 4 is 3 remainder 0
03 / 4 is 0 remainder 3
34 / 4 is 8 remainder 2
Decimal point
20 / 4 is 5 remainder 0
Final result 308.5
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