Prove (Verify) or disprove the following division algorithm:

Here is a trick I learned as a child which I think is worth documenting for eternity in cyberspace. It is how to multiply the numbers six through ten using only your fingers.

First assign numbers in the following way to the fingers of both hands

pinky = 6

ring finger = 7

middle finger = 8

index finger = 9

thumb = 10

Fine, you have just constructed a simple 'digital' computer.

Now keep your hands in front of you, palms facing you, thumbs up.

Let's say we want to multiply 6 x 7.

Touch and hold the pinky of the left hand (6) to the ring finger of the right hand (7). Now with your hands in this position, fingers touching, hands in front of you, palms facing you and thumbs up:

count any touching fingers as ten each. (10 for left pinky plus 10 for right ring finger = 20)

count any fingers below the touching fingers as ten each.(ten for the right pinky which is below the touching fingers = 10)

multiply the number of fingers above the touching fingers on the left hand by the number of fingers above the touching fingers on the right hand. (there are four non-touching fingers above the touching fingers on the left hand and three on the right so 4 x 3 = 12).

So now add the numbers obtained from steps 1, 2, and 3. You get 20 + 10 + 12 = 42 and of course the original problem 6 x 7 = 42

Another example? Let's try an easy one. 7 x 8. Hands in position. Touch and hold the left ring (or 7) finger to the right middle (or 8 finger)

count the two touching fingers as 10 each = 20.

count any non-touching fingers below the two touching fingers as ten each (in this case the left pinky plus the right pinky and ring total up to = 30).

count up the non-touching fingers above the touching fingers on the left hand and the non-touching fingers above the touching fingers on the right hand (in this case there are three on the left and two on the right) and multiply them. 3 x 2 = 6

So now add the numbers obtained from steps 1, 2, and 3. 20 + 30 + 6 = 56 and the original problem was 7 x 8 and the answer of course proves to be 56.

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## BMAD 65

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Prove (Verify) or disprove the following division algorithm:

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