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## Multiplication by series of 1’s to any number

Here we apply Easy Vedic method for specific multiplication by series of 1 i.e.  multiply by 11,111,1111 etc. by fast & easy way. I have explain first example of each type  step by step to understand the method, so read it 2 or 3 time carefully. once you got the trick you can solve such specific multiplication in 9 to 10 time faster than regular method.

#### a) Two digit in multiplicand

Ex. i) 62 x 11

step 1: First write the right-hand side of multiplicand as it is in right hand side of the answer

Step 2: Now we add both digit of multiplicand i.e. 6 + 2 = 8, this is middle digit of our answer,

Step 3: Finally write left hand side digit of multiplicand as it is in LHS of answer,

Answer, 62 x 11 = 682

Ex. ii) 43 x 11

Answer,  43 x 11 = 473

Ex. iii) 95 x 11

9145 = 1045

Answer, 95 x 11 = 1045

#### b) 3- digit in multiplicand

Ex. iv) 432 x 11

Step 1: we write 2 as it is in left hand side

Step 2: Now we add 2 & 3 for next digit of ans.

Step 3: Now add 3 & 4 for the next digit of the ans.

Step 4: Now write 4 as it is in right hand side of the ans.

Answer,  432 x 11 = 4752

v) 629 x 11

Answer, 629 x 11 = 6919

Similarly,

vi) 2463 x 11

Note: As two 1’s in multiplier i.e. 11 so, we add maximum 2-digit at time from right to left. if multiplier will be 111 then we add maximum 3-digit at a time & so on …..as explained below.

#### Case 2: Vedic method of Multiplication when multiply by 111

vii) 402 x 111

Step 1: write 2 as it is in RHS

Step 2: Add 0 & 2 for next digit of the ans.

Step 3: now add 2, 0 & 4 for next digit of the ans (As three 1 in multiplier so we add 3 digit at a time)

Step 4: Add 0 & 4 for next digit of the ans.

Step 5: Now write 4 as it is in LHS

Answer, 402 x 111 = 44622

Ex. viii) 263127 x 111

Step 1: write 7 as it is in RHS

Step 2: add 2 & 7, = 9

Step 3: add 1,2 & 7 = 10, so write 0 & carryover 1

Step 4: now add 2, 1 & 3 = 6 & add carryover 1 =7

Step 5: add 1, 3 & 6 =10, so write 0 in ans & carryover 1

Step 6: add 3, 6 & 2 = 11 + carryover 1 = 12, write 2 in the ans & carryover 1

Step 7: add 6 & 2 = 8 + carryover 1 = 9

Step 8: write 2 as it is in LHS

Answer,  263127 x 111 = 29207097

Similarly,

Ex. ix) 120423 x 111

Ex. x) 231051 x 1111

#### Case 3: Multiply a number by series of same digits

This technique is basically a extension of previous technique.  Here we multiply a number by series of other numbers like 2 series, 3 series, 4 series….

Ex. xi)  341 x 222

We know the method of how to multiply by 111 but we don’t know how to multiply by other number series.  But here we can easily convert the number 222 in 111 by applying simple logic.

341 x 222

=341 x 2 x 111 (222= 2 x 111)

= 682 x 111 (341 x 2 = 682)

Now here by applying simple logic our sum is converted into previous method sum, now we can easily solve this by 1 series.

Ex. xii)  112 x 44

= 112 x 4 x 11 (4 x 11 =44)

= 448 x 11  (112 x 4 = 448)

Now solve by 1 series method,

Try This:

i)61 x 11   ii)92 x 11  iii) 142 x 11

iv) 635 x 111 v) 7123 x 111  vi) 7462 x 111

viii) 2153 x 1111

Also find the following link to study more-

Base method of multiplication