Secrets of Mental Math

Mental Calculation, Mathematics, and Puzzles
26

I still following this post by analyzing the chinese book and found some ways of calculation. The most exciting point of this method is it will calculate from left to right (vs the traditional way of right to left).
For short explanation, i take the short number to be multiplied only. But it does not a matter how long you like.
Plz share with you as below:

  • General rule: Before the first digit of the multiplicand add a zero
  1. Multiply by 2
    Ex: 67394 x 2 ==> 067394 x 2
  • Each figure of result = unit digit of left most figure multiple 2, plus 1 if the “neighbour” is “>” or “=” 5
  • Step 1: 0 x 2 = 0, its neighbour is 6 that bigger than 5 ==> first digit of result = 0 + 1 = 1
  • Step 2: 6 x 2 = 12, taking only its unit digits is 2. The neighbour of 6 is 7 (>5) so the next digit of result = 2 + 1 = 3
  • Step 3: 7 x 2 = 14, taking 4 only. The neighbour of 7 is 3 (<5) so will not plus 1. the next digit of result = 4
  • Step 4: 3 x 2 = 6, the neighbour of 3 is 9 (>5) ==> plus 1. The next digit of result = 6 + 1 = 7
  • Step 5: 9 x 2 =18, taking 8. The neighbour of 9 is 4 (<5), not plus any. The next digit of result = 8
  • Final step: 4 x 2 = 8. Taking 8 as the final digit of result.
    ==> The result is: 134788
    For further, plz visit the site that Josh suggests: welcome to shifengshou.com
  1. Multiply by 5
    Ex: 475 x 5 ==> 0475 x 5
    Rule:
  • If the neighbour from the left is 0, 1 ==> plus nothing
  • If the neighbour is 2, 3 ==> plus 1
  • If the neighbour is 4, 5 ==> plus 2
    …
  • If the neighbour is 8, 9 ==> plus 4
  • I guess the number added here is the ten unit of 5 x the neighbour itself. Now here we go
  • Step 1: 0 x 5 = 0. The neighbour of 0 is 4 ==> plus 2. The first digit of result is: 0 + 2 = 2
  • Step 2: 4 x 5 = 20, taking its unit digit 0 only. The neighbour of 4 is 7 => plus 3: The next digit of result: 0 + 3 = 3
  • Step 3: 7 x 5 = 35, taking the unit digit 5. The neighbour of 7 is 5 => plus 2. The next digit of result: 5 + 2 = 7
  • Final step: 5 x 5 = 25. Taking the unit digit 5 only. The next digit of result is 5
    ==> The result is: 2375

Other cases i not know, i am still studying… and finding someone know chinese to translate but not available yet :slight_smile:

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