## Derek’s Maths Tip – Dividing with the Japanese abacus

Let’s divide 5376 by 7. We start by entering 5376 in the middle of the abacus. The exact position depends on the fact that there are 3 more digits in the dividend than in the divisor, but that’s beyond the scope of this article.

Then we ask ourselves how many times 7 goes into 53, answer 7, but 7 x 7 is 49, so there’s some left over. Enter the 7 immediately to the left of 5376. Remember to pinch it between the thumb and first finger as indicated by the blue arrows.

Now we have to subtract the 49 from the 53, take away 50 (green 5 up) and add 1 back (orange 1 up). Whatever is left, in this case, 476 remains as the new dividend.

Now, how many times does 7 go into 47? Answer 6, but 6 x 7 is 42, so there’s some left over. Enter the 6 immediately after the 7. Again it’s a pinch between the thumb and first finger as indicated by the blue arrows.

Next we have to subtract the 42 from the 47, take away 40 (green 4 down) and take away 2 (orange down). Again, whatever is left, in this case, 56 is the new dividend.

Finally, how many times does 7 go into 56. Answer 8. Enter the 8 to the right of the 6. 8 x 7 is 56 so now we take away the 56 from the dividend -50 (green 5 up) followed by – 6 (reverse pinch orange). Leaving 0, so 768 is the exact answer to the sum.

If the result had not been zero, there would be a remainder. You could either have disclosed the remainder, or carried on dividing, in which case your final answer would contain decimals.

That’s it. We won’t be tackling square roots until I’ve learned how to do them which won’t be for a while.

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