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 Fast & easy Multiplication of number with series of 9 By Vedic Method 

This method is useful for multiplication of number with series of 9  by very  fast & easy way.  Here multiplier is 9 or series of 9 & multiplicand is any digits. Sub-sutra Ekanyuneva purvena is useful to solve this type of multiplications. Read first example very carefully as I have explained it step by step.  Once you understand the steps you can do any multiplication from this topic in one line.

We will solve sum in 3 different cases-

Case 1: Multiplying a number with equal number of   9

Ex. i) 8 x 9

step 1: Divide answer in 2 parts LHS & RHS

Step 2: Apply formula,

Put the values in formula,

  LHS = 8 – 1 = 7

Step 3: Apply formula,

Put the values in formula,

 RHS = 9 – 7 = 2

So,

Answer, 8 x 9 = 72

Ex. ii) 23 x 99

LHS = 23 – 1 =22

RHS = 99 – 22 = 77

Answer,   23 x 99 = 2277

Ex. iii) 322 x 999

LHS = 322 – 1 =321

RHS = 999 – 321 = 678

Answer 322 x 999 = 321678

Case 2: Multiply a number with higher number of 9–

Case 2 is same as case 1, only we need to add 0 in left side of multiplicand

Ex. iv) 62 x 999

As we see the number of 9 in multiplier is more than the number of digit in multiplicand so, we add one 0 in left side of multiplicand

Now example is, 062 x 999

Now solve like case 1:

LHS = 062 – 1 =061

RHS = 999 – 061 = 938

Answer 62 x 999 = 061938 = 61938

As we see the method is very easy so, now we try to solve sum directly,

Ex. v) 141 x 9999

Answer 141 x 9999 = 1409859

 Once we understand the steps, Within 3 sec. we get the solution of such big multiplication.

(Explanation: Ans = LHS / RHS

LHS = 0141 – 1= 0140 & RHS = 9999 – 0140 = 9859)

Similarly,

vi) 223 x 99999 = 00222/99777 = 22299777

vii) 1265 X 99999 = 01264/98735 = 126498735

Case 3: Multiply a number with lesser number of nine-

Case 3 is different than case 1 & case 2. We will understand the steps while solving the problem…

viii) 54 x 9

Step 1: Divide answer in LHS & RHS

Ans = LHS / RHS

Step 2:  Divide the multiplicand in two parts by slash line.

Number of digit in right hand side of slash is equal to number nine in multiplier.

So, we divide 54 as,

5/4          (only one 9 in multiplier)

Step 3:  Apply formula

Here our Multiplicand is 54 and LHS of multiplicand is 5

Put the values in above formula,

LHS = 54 – (5+1) = 48

Step 4: Apply formula,

As multiplier is 9, so base = 10 (nearest power of 10 digit)

RHS of multiplicand is 4

Put the values in RHS formula,

RHS = 10-4 = 6

So, Ans = LHS/RHS =486

Answer 54 x 9 = 486

Ex. viii) 325 x 99

Step 1: Ans = LHS / RHS

Step 2:  Multiplicand 325 = 3/25 (as two 9 in multiplier, so number of digit in RHS of slash equal to 2)

Step 3:  LHS = Multiplicand – (LHS of multiplicand +1)

=325-(3+1)

= 321

Step 4: RHS =Base of multiplier – (RHS of multiplicand)

As multiplier = 99, so base =100

= 100 – 25 = 75

Answer 325 x 99 = 32175

  OR

But, applying Vedic method is complicated here, so instead of this method you can apply simple logic-

325 x 99 =325 x (100-1)

= 32500-325 = 32175

ix) 13456 x 999 = 13456 x (1000-1)

=13456000-13456 = 13442544

Find this link to study more-

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