Preferred double digit divisor mental approach

I find that I often have have to divide by 2 digit numbers mentally. Division still gives me more problems than other operations. My working memory is stretched trying to remember all the individual parts of the quotient.
My question is what is your preferred technique for dividing mentally when you have eg:
1234/73
894/37

Do you use a Vedic method, a short division method?

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Here is how I do this.

73 is a bit over 70, so try 70 and correct as follows.
12/7 = 1 remainder 5, so start by taking 10 times 73 off:
1234 - 730 = 504.

7 times 7 is 49 of course, so Try 7 times 73 = 490 + 21 = 511.
511 is 7 over 504, so the answer is: 10 + 7 (- 7/73).
7/73 is a little less than 0.1, so I would answer this as 16.9…

37 is close to 40 and 89 / 40 = 2 remainder 9, so try 20 times 37 = 740:
894 - 740 = 154.

154 / 40 is almost 4 and since we are actually working with 37 (instead of 40), let’s try 4:
4 times 37 can be calculated as 4 times 40 = 160 minus 4 times 3 is 12.
160 - 12 = 148 and 154 - 148 = 6.
In short:
154/37 = 4 with a remainder of 6.

So the answer is: 24 + 6/37

We continue with 6/37.
6/37 is close to 6/40 and 6/4 i s 1.5, so 6/40 = 0.15
The difference of 37 to 40 is 3 and since 3/4 is 0.75, so 3/40 is 0.075.
This means we can guestimate the answer by adding about 7.5%:
Round 7.5 % to 8% for easy calculation. 8% of 0.15 is 0.12 so add that to 0.15 and get: 0.162.

So the answer is: 24 + 6/37 = 24.162…

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Thank you Kinma for sharing your method. I see a combination of simplification and then some guesttimating in an efficient manner.
Just wondering, do you use this technique when dividing by a 3 digit divisor?

Hi Tiger. Great to see you back!
You and I have discussed division in the past a lost. Starting in 2017.

I use a lot of techniques and here is a list of them:

Yes, in two steps usually.
I think I wrote about it in the past, but could not find it, so let’s do it again.

Let’s divide 1000 by 323.
Here goes. 1000/333 = 3.
323 is lower, so try 3 times.

Now let’s find the remainder in two steps.
1: 3 times 300 is 900. Subtract from 1000 to get 100.
2: 23 times 3 is 69. Subtract from 100 = 31.

If we divide by a number close to a multiple of 100, we can do this slightly different and work with negative numbers.

Let’s divide 1000 by 378.
Here goes. 1000/333 = 3.
378 is higher, so try 2 times.

Now let’s find the remainder in two steps.
1: 2 times 300 is 600. Subtract from 1000 to get 400.
2: 78 is 22 from 100. Subtract 2 times 100 = 200 from 400 and then add 2 times 22 = 44 to get 244.
(We will get back to this remainder later.)

Let’s continue working. We now have 2R244.
Add a zero: 2440.
Try to find a multiple using 400 instead of 378.
2440 goes into 400 about 6 times or 6 time 400 is 2400 and fits in 2440.

2 steps again:
1: 2240 - 6 times 400 =2400 = 40.
2: Add 6 times 22 = 132 to get 172.

Add a zero:1720

1720 goes into 400 4 times.
1720 - 1600 = 120. 120 + 4*22 = 208
Etc, etc.

You might want to experiment with switching 2 steps. Saves one digit in short term memory.

Starting from the remainder of 244:
Instead of adding a zero, do the subtraction of the hundreds first.
But since we have not added the zero yet, the 400 is now 40
Try to find a multiple using 40.
244 goes into 40 about 6 times or 6 time 40 is 240 and fits in 244.

244 - 240 = 4.
Now add the zero. 4 => 40.
Step 2 is the same as above:
2: Add 6 times 22 = 132. Add to 40 of the previous step to get 172.

This can be done in the 323 case as well as above.

The remainder is now always 3 digits.
Subtract the hundreds first, not forgetting that 378 => 400 => 40 or that 323 => 300 => 30.

Try this on random numbers and see if it works for you.

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Hi Kinma,

Hope you’re keeping well in these unusual times.
Thank you for your tips, they make great reading! I will give this division method a try, I have started going back through some of your old posts, the multiplication ones are very useful and I’ve put them to good use.

Writing about 3 digit division got me thinking about 4 digit division.
I’ll write soon how I do this mentally.

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Look forward to it Kinma. Your posts are always worth reading.

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Thank you!
It’s here: Four digit division

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