By Shakuntala Devi

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For example, to check that 8216 X 4215 = 34630440: 8 + 2 + 1 + 6 = ^ = 1 1 , casting out the nines, leaves 8 as the check number. 4 + 2 + 1 + 5 = 12, casting out the nines, leaves 3 as the check number. 3 + 4 + 6 + 3 + 0 + 4 + 4 + 0 = 24, casting out the nines, leaves 6 as the check number. 3 x 8 = 24, 2 + 4 = 6 which was the check number of the original product. Therefore, the multiplication is correct. However, I must mention here that this system of casting out the nines is not infallible, but if the answer you have obtained checks out as correct when you have used it, the chances of your being wrong are very slim.

60 x 100 = 18760 1 ^ 0 = 4690 4 4690 X 3 = 14070 To multiply by 9, just remember that 9 is one less than 10, so all that is necessary is to add a zero and then subtract the original multiplicand. Take 9 X 84 10 X 84 = 840 840 - 84 = 756 This can be extended, if asked to multiply by 18. All that is necessary is to multiply by 9 and double the product. For example, 448 X 18 448 x 10 = 4480 4480 - 448 = 4032 4032 X 2 = 8064 Alternatively, you can start from the fact that 18 is 20 less 2, in which case the sequence is: 448 x 2 = 896 896 x 10 = 8960 8960 - 896 = 8064 This method can be used for all numbers which are multi pies of 9.

For example: 165 divided b,- 5 = 'V;. Jc by 15. vidend by 2 and divide by l - ' .

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