In the example, in order to avoid the going back you could take 70 instead of 60. In that case you always subtract too much, so the correction is always an addition:

Let’s just do this:

235813 divided by 64. Use 70. Correction is now with a factor of 6 instead of 4.

235/70 = 3. 3X70 =210. 235-210 = 25

3X6 = 18. 25+18 = 43.

438/70 = 6. 6X70 = 420. 438-420 = 18

6X6 = 36. 18 +36 = 54

541/70 = 7. 7X70 = 490. 541-490 = 51

7X6 = 42. 51+42 = 93. Now we have an issue the other way round.

The remainder of 93 is bigger than 64. ‘7’ needs to become ‘8’.

The correction is easier now though. 93 - 64 = 29 and we use 8 instead of 7 in this step.

In other words: 7R93 = 8R29.

293/70 = 4. 4X70 = 280. 293 -280 = 13.

6X4 = 24. 13+24 = 37

Again, the answer is: 3684R37

Drawback is that when you have to divide by 61 and you use 70, the corrections become a lot greater than when you use 60.

I have talked about it a lot but imho the nine and eleven proof is great for strengthening those muscles.

Let’s do the eleven proof this time, and let’s do it in a way that keeps your brain calculating (there is a shorter way of doing the modulo 11).

So 235813 divided by 64 = 3684 R 37.

In other words: 3684 X 64 + 37 = 235813

We do a modulo 11 on all numbers by subtracting multiples of 11, so chosen that the numbers become smaller with each step:

3,684 - 3,300 = 384

384 - 330 = 54

54 - 44 = 10

64 - 55 = 9

37 - 33 = 4

We do the multiplication and addition again. However, now with the modulo 11 numbers:

10X9+4 = 94

Aain, do a modulo 11 on 94:

94 - 88 = 6

Now see if the answer also brings us back to 6:

235,813 - 220,000 = 15,813

15,813 - 11,000 = 4,813

4,813 - 4,400 = 413

413 - 330 = 83

83 - 77 = 6

6=6, so the answer is probably correct.

As always, it is a lot to type out.

If you get a little proficient in doing this, it is easier than it looks now.

9 proof using repeated subtraction (there is a way quicker method, but stick with me):

3,684 X 64 + 37 = 235,813

3,684 - 3,600 = 84

84 - 81 = 3

64 - 63 = 1

37 - 36 = 1

Do the calculation again:

3X1+1 = 4

Now the big one:

235,813 - 180,000 = 55,813

55,813 - 54,000 = 1,813

1,813 - 1,800 = 13

13 - 9 = 4

4 = 4, the calculation is correct.

By working so intensely with numbers you are sharpening your brain to work with bigger and bigger numbers.

In order to do one calculation you will be doing a lot of mental work and since you are going back to your original numbers a couple of times you will strengthen your memory for numbers.

Don’t try to work with big numbers too soon. Start small, get proficient, then move to bigger numbers.