Base Method of Multiplication

Base method of multiplication derived from Vedic Mathematics can be applied for multiplication of two numbers close to 100.

This post in is in continuation of an earlier post named “Vedic Multiplication of two numbers close to hundred“. Though you can understand this post stand alone, yet I’ll recommend you to read the linked post before reading this one.

In this post I’ll explain how to multiply two numbers lesser than the base (in this case 100). In the earlier post it was about both numbers more than 100.

Multiplication where both numbers are lesser than 100

Rule: Still remains the same as earlier. Here you go –

You will get the answer in two parts

First part, to get left hand side of the answer: Add the difference between 100 and either of the numbers to the other number

Second part, to get right hand side of the answer: multiply the difference from 100 of both the numbers

Example

93 x 94

First part: 93 – 100 = – 7; Add this to the other number, thus 94 + (- 7) = 87

Or you can start with the other number 94;

94 – 100 = – 6; Add this to the other number, thus 93 + (- 6) = 87

Result will be same in both the cases

Second part:

Multiply the difference from 100 of both the numbers.

Hence, (93 – 100) x (94 – 100) = -7 x -6 = 42

Combined effect:  87  | 42 = 8742

*| is just a separator.

 

Example

92 x 86

Step 1: 92 + (86 – 100) = 78

Step 2: (92 – 100) x (86 – 100) = -8 x -14 = 112

Combined effect will look like this: 78 | 112

Step 3: Add the 1 (digit at 100s place) of 112 to 78

Answer: 78 + 1 | 12 = 79 | 12 = 7912

 

When One number is lesser than 100 and the other is more than 100

Same Rule as Above

Example

96 x 103

First part: 96 – 100 = – 4; Add this to the other number, thus 103 + (- 4) = 99

Or you can start with the other number 103;

103 – 100 = 3; Add this to the other number, thus 96 + 3 = 99

Result will be same in both the cases

Second part:

Multiply the difference from 100 of both the numbers.

Hence, (96 – 100) x (103 – 100) = -4 x 3 = – 12

Combined effect:  99 | -12 = 8742

Now to remove negative sign from the right side, we have to take one from the left hand side. 1 when shifted from left to right becomes 100. Thus we’ll have:

Combined effect:  99 – 1 | 100 – 12 = 9888

*| is just a separator.

Example

89 x 113

= 89 + 13  | -11 x 13

= 102  |  -143

In this case, right side number is greater than 100, so we need to subtract it from next higher 100, i.e. 200. Hence, we’ve to take 2 from left hand side, so that we get 200 on the right hand side.

= 102 – 2 | 200 – 143

= 100 | 57

= 10057

Does this method makes such multiplications simpler for you? Leave a comment below to express your opinion.

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Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

51 thoughts to “Base Method of Multiplication”

  1. Sir tell me short cuts to solve the digits that one is greater than base and other is smaller than base.
    Eg:11*998.

  2. Sir tell me short cuts to solve the digits that one is greater than base and other is smaller than base.
    Eg:11*998.

  3. xcuz me sir please give me the answer of this qustn
    ..statmnts: some highways are roads
    All roads are streets
    concln: All highways are being streets is a possibility
    Some streets are not highways

    sir cncln 1 is A type or I type. ??

    1. manjusha – didn’t get your question…what do you mean by A type or I type.

      moreover, this is an article on multiplication trick, hence you can post it here – quickermaths.com/questions

  4. 35*37
    First of all multiply the last digits of both the numbers, i.e 5*7=35 and keep 3 as a carry(base=5)
    Then multiply the last digit and the first digit of both the numbers, i.e 5*3=15
    Then multiply the first digit and the last digit of both the numbers, i.e 3*7=21
    Now add both the multiplication, i.e 15+21=36
    Remember to add the carry 3, i.e 36+3=39 and keep 3 as carry(base 9)
    Now multiply the first digit of both the numbers, i.e 3*3=9 and add the carry 3, i.e 9+3=12(base12)
    At last arrange the bases
    The first base 5 then the second base 9 and then the last base 12
    On arranging from backwards we get 1295
    Thus 35*37=1295.

    Sir, please let me know whether this method of multiplication is easy or not and also that whether any blunder may be created in this method or not.
    Regards.

  5. 96 x 103 = 96 ( -4 ) x 103 ( + 3 )
    =(96 + 3 ) / ( – 4 x 3 ) = 99 / ( -12 )
    = 99 / ( -100 + 88 )
    = (99 – 1) /88 = 9888 .

    Please let me know am I right !

  6. 35 x 37 = 3 x ( 35 + 7 ) l ( 5 x 7 )
    = 3 x 42 l (35 )= 126 l 35
    = 126 +3 l 5 = 1295 .

    Please tell me whether I am right or to wright !

  7. 96 x 103 = 96 ( -4 ) x 103 ( + 3 )
    =(96 + 3 ) / ( – 4 x 3 ) = 99 / ( -12 )
    = 99 / ( -100 + 88 )
    = (99 – 1) /88 = 9888 .

    Please tell me know am I right !

  8. 104*105 =?
    ==========
    Here base =100
    Our first No. is 104. Subtract from base i.e. 100 from this No. i.e. 104-100=4 (i)
    Our 2nd No. is 105. Subtract from base i.e. 100 from this No. i.e. 105-100=5 (ii)
    In first No. i.e. 104 add the balance of second No. i.e. 5
    104+5= 109
    Multiply (i) and (ii) 4×5=20
    Write both result together
    Ans. 109 20 i.e. 10920
    {Note:-
    (x)The multiplication of above balance i.e. (i) and (ii) will be in two digit.
    In case of multiplication of three digit like 109×106
    In this case it is 20 no problem. But if in any case suppose produce of
    multiplication is 6 then write it as 06 (102×103).
    (y) Suppose in a case product of multiplication become in three digit then first
    digit from left side will be treated as carry to add in next No.
    (e.g. 115×110)
    ============
    Second example
    Multiply 112×113
    ============
    Our first No. is 112. Subtract from 100 from this No. i.e. 112-100=12 (a)
    Our 2nd No. is 113. Subtract from 100 from this No. i.e. 113-100=13 (b)
    In first No. i.e. 112 add the balance of second No. i.e. 13
    112+13= 125
    Multiply (a) and (b) 12×13=156
    for 156 we can say product of multiplication is 56 with carry 1 (explained in (x)).
    Write both result together
    Ans 125 156 (In 156 one is carry which will be add in next No.
    = 126 56 (i.e. 125+1=126)
    =12656
    I want to know that my explanation method is easy or not. If anyone feel problem to understand it then plz. call me on 90 4142 43 22 I will again explain on phone and try to improve the method to explanation method.
    Good Night

    1. 1) 104*105 = ?
      4,5 —– Difference of both numbers from 100
      4*5= 20
      104+5 =109
      Answer 10920

      2) 106*109 = ?
      6, 9 — Difference from 100
      6*9= 54
      106+9 =115
      Answer = 11554

      3) 112* 113 = ?

      12, 13 — Difference from 100
      12*13 = 156
      112+13= 125

      125
      +156
      ———-
      12656 Answer

  9. Wow!! You are awesome. Hope to get an awesome college like yours. Thanks for these fine methods.

    But the problem remains – ‘We have great material and methods but forget them in time because of lack of progress.’

    Hope to see some exercises also in your site or some suggestions of the same.

  10. ???? ?????: ??? ?????? ?? ???? ???, ??? ??? ??? ?? ??? ?????
    ????? ?????? ???? ???, ???? ???? ?? ????? ????
     ????? ?? ??? ????
    ??? ????? ?? ???? ???? ???? ??? ???? ????? ? ??????: 4 / (½) = 4 * (2/1) = 8
    ???????? ???????? (Binomial) ?? ?????
    ????, ?????, ????, ??????
    (?+?) (?+?) =??+??+??+??
    ????? ????
    ??????? ‘??’ ?? ???? ????, ???? ??? ??? ???? ????
    ???? ????? ??? ??? ,?? ???? ?? ???? ??? ????
    ” ????? ??? ????? ?? ???? ???? ?? “

  11. This is interesting, but the fact remains that we would have studied most of the things without trying to apply them in real life.

    (ax+b)*(cx+d) = acx^2 + (ad+bc)x + bd

    in case of numbers close to 100, x = 100 and a=c=1
    this simplifies to: x^2 + (d+c)x + bd
    which is (x+d+c)*x + bd
    which is (100+d+c)100 + bd…

    Talking about this, also explore (10n+k)^2…

    1. 104*105 =?
      ==========

      Here base =100

      Our first No. is 104. Subtract from base i.e. 100 from this No. i.e. 104-100=4 (i)
      Our 2nd No. is 105. Subtract from base i.e. 100 from this No. i.e. 105-100=5 (ii)

      In first No. i.e. 104 add the balance of second No. i.e. 5
      104+5= 109

      Multiply (i) and (ii) 4×5=20

      Write both result together

      Ans. 109 20 i.e. 10920

      {Note:-
      (x)The multiplication of above balance i.e. (i) and (ii) will be in two digit.
      In case of multiplication of three digit like 109×106
      In this case it is 20 no problem. But if in any case suppose produce of
      multiplication is 6 then write it as 06 (102×103).
      (y) Suppose in a case product of multiplication become in three digit then first
      digit from left side will be treated as carry to add in next No.
      (e.g. 115×110)

      ============
      Second example
      Multiply 112×113
      ============

      Our first No. is 112. Subtract from 100 from this No. i.e. 112-100=12 (a)
      Our 2nd No. is 113. Subtract from 100 from this No. i.e. 113-100=13 (b)
      In first No. i.e. 112 add the balance of second No. i.e. 13
      112+13= 125

      Multiply (a) and (b) 12×13=156
      for 156 we can say product of multiplication is 56 with carry 1 (explained in (x)).

      Write both result together

      Ans 125 156 (In 156 one is carry which will be add in next No.
      = 126 56 (i.e. 125+1=126)
      =12656

      I want to know that my explanation method is easy or not. If anyone feel problem to understand it then plz. call me on 90 4142 43 22 I will again explain on phone and try to improve the method to explanation method.
      Good Night

    2. shad Farooqi – January 5th, 2016 at 17:30 none Comment author #24931 on Base Method of Multiplication by Quicker Maths
      1) 104*105 = ?
      4,5 —– Difference of both numbers from 100
      4*5= 20
      104+5 =109
      Answer 10920

      2) 106*109 = ?
      6, 9 — Difference from 100
      6*9= 54
      106+9 =115
      Answer = 11554

      3) 112* 113 = ?

      12, 13 — Difference from 100
      12*13 = 156
      112+13= 125

      125
      +156
      ———-
      12656 Answer

    1. Hi mathemagican , You are Perfectly Right but I can say 28 * 100/4 = 2800/4 =700 may also Right !

  12. @Diana – For multiplying 28×25, the base is 20.

    (28+5)*2 | 8×5
    (For base 20 multiply 2. For base 30, multiply by 3 and so on )
    =66 | 40
    (Since the base is single digit, r.h.s part will have only 1 digit, hence 4 will be carried over to l.h.s and added to 66)
    =66+4 | 0
    =700

    1. Quoted: “Since the base is SINGLE digit, r.h.s part will have only 1 digit, hence 4 will be carried over to l.h.s and added to 66”.

      If Base is 20. How it is single digit… Pls explain with some more examples for numbers below 50.

    1. hi…. this method is for the conditioned no..

      but, u can solve it another method
      25 * 28
      step 1- u hav to, add the unit place digit.. to the others no…25+8=33
      put a zero & multiply it by 2, as it is the ten’s place,
      330*2=660
      step 2- multiply the unit digit’s of both the no.. 8*5= 40

      step 3- adding both results
      660+40=700

      1. Example :- 35 * 37

        (i) 35+7 = 42
        (ii) 420 (place 0 on RHS)
        (iii) 420*3=1260 (Base is 30)
        (iv) 5*7= 35
        (v) Add (iii) and (iv)
        1260+35= 1295 (Ans.)

      2. One more thing is to clear is that after addition in next step is to multiply it with the base
        In 25*25 , base is 20
        25+8=33
        so 33*20=660
        To make it easy another way :- place 0 on RHS i.e. 33=330 multiply
        it with 2 , 330*2= 660

      3. 35 *37 = ?
        5, 7 ——- difference from 30
        35+7 = 42
        42*30 = 1260 — Base is 30
        5*7 =35

        Answer = 1260+35 = 1295

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