7/27/2019 Vedic Maths - Multiplications With 9

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Vedic Mathematics

Shortcuts for Multiplication

with numbers9, 99, 999and9999

-Hareesh Kumar

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MULTIPLICATION WITH 9

We do have a very simple method and very fast technique to multiply any number with

9. This is one of the techniques in Vedic Mathematics. To be perfect in this technique one

should be perfect in subtractions and even with the 9 table. Let us see some examples:

i) 12*9 = (12-2) | (Units digit of 2*9) = 108ii) 29*9 = (29-3) | (Units digit of 9*9) = 261iii) 63*9 = (63-7) | (Units digit of 3*9) = 567iv) 157*9 = (157-16) | (Units digit of 7*9) = 1413And so on

From the above examples, we can observe a pattern as follows:

Let us consider that the multiplier is: XY. For the numbers in the range XY to (X+1)0, the

product would be: (XY K) | (Units digit of Y * 9)

Where: X = {0, 1, 2, 3.} and Y = {0, 1, 2, 3..} and K = {1, 2, 3, 4,..}

i.e. For 1 10 K = 1

11 20 K = 2

21 30 K = 3

31 40 K = 4 and so on

Some more examples:

v) 43 * 9 = (43 5) | (UD of 3*9) = 387vi) 96 * 9 = (96 10) | (UD of 6*9) = 864vii) 254 * 9 = (254 26) | (UD of 4*9) = 2286viii) 1234 * 9 = (1234 124) | (UD of 4*9) = 11106ix) 756 * 9 = (756 76) | (UD of 6*9) = 6804x) 72 * 9 = (72 8) | (UD of 2*9) = 648

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MULTIPLICATION WITH 99, 999, 9999

We have already seen the multiplication with 9. Now we are going to see the multiplication

with 99. This is also a unique method and based on the principles from Vedic Mathematics.

Let us see some examples after which we will see the pattern of the multiplication:

i) 43 *9 9 =?Solution: 0 | 43

-1 | -43

42 | 57 (100 43)

Hence, 43*99 = 4257

The procedure is simple,

Step 1: Separate the number into two parts: one before the 10s digit and the other after it. If

there is no digit before 10s digit, replace it by a zero as we did in the above example.

Step 2: Add one to the number before the 10s digit and subtract it from the second part. This

forms the first part of the resultant.

Step 3: For the second part of the resultant, subtract the 10s and the unit digit from 100.

Step 4: Combine the first and the second resultants to form the final product!

SOME MORE EXAMPLES:

ii) 123 * 99Sol: 1 | 23

-2 | -23

1 | 21 | 77 123*99 = 12177

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iii) 786*99Sol: 7 | 86

-8 | -86

7|78|14 786*99 = 77814

iv) 1123*99Sol: 11 | 23

-12 | -23

11|11|77 1123*99 = 111177

v) 7864*99Sol: 78 | 64

-79 | -64

78|-15|36 (7800 15)|36 = 778536

vi) 4321*99Sol: 43 | 21

-44 | -21

43|-23|79 (4300-23)|79 = 427779

WITH 999:

vii) 236*999Sol: 0 | 236

-1 | -236

0|235|(1000-236) 236*999 = 235764

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viii) 7536*999Sol: 7 | 536

-8 | -536

7|528|464 7536*999 = 7529464

WITH 9999:

ix) 5648*9999Sol: 0 | 5648

-1 | -5468

5647|4532 5648*9999 = 56474532

x) 896523*9999Sol: 89 | 6523

-90 | -6523

89|6433|3477 896523*9999 = 8964333477

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