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.
You may also like:
- Vedic Multiplication of two numbers close to Hundred
- Multiplying Two Numbers when Sum of their Unit Digits is 10
- The Criss-Cross Method: An Alternative Form of Multiplication
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I am Vineet Patawari - PGDM (IIM Indore), ACA, B.Com(H). My passion for Mathematics, specially Vedic Maths encouraged me to start QuickerMaths
I believe that if trained properly using powerful tools like Vedic Maths, the immense intellect of human mind can be ignited instantly - find out more
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April 22nd, 2013 - 11:53
Awesome tricks..thanx a lot.
January 25th, 2013 - 17:22
As per trick I tried to solve 78*729 and I ended up with 567|162 so what should be the next step because answer is 56862 and this we can get only by adding 7+1 56862…Is this correct???
January 16th, 2013 - 11:26
35×35= 3 x4 and 5 x5= 12 25
now 35 x37= 3×4 and 5 x7 PLUS 30X2= 12 and 35 + 60= 12 and 95
????why + 60
reason is 7+ 5 = 10 + extra 2
so 30 x 2
January 10th, 2013 - 11:32
theres an equation sorta rule for this that i came up with idk if anyone knows anythin about that…?
June 24th, 2012 - 14:02
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. ??
June 23rd, 2012 - 22:48
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.
June 24th, 2012 - 09:12
What you have explained here is the criss-cross method of multiplication. Check out this post –
http://www.quickermaths.com/the-criss-cross-method-an-alternative-form-of-multiplication/
June 13th, 2012 - 20:41
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 !
June 13th, 2012 - 20:26
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 !
June 13th, 2012 - 20:16
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 !
June 9th, 2012 - 08:24
28 * 50 = 28 *100/2 = 28/2 * 50 = 14 *50 = 700 .
March 3rd, 2012 - 13:24
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
March 3rd, 2012 - 13:03
plz send easy tricks of data interpretation on my e-mail id
March 1st, 2012 - 11:28
I imprised you for this mathematic.
February 28th, 2012 - 11:03
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.
February 28th, 2012 - 11:28
small correction : it is practice not progress.
February 28th, 2012 - 13:48
Please read forget forgetting on http://forgetforgetting.wordpress.com
February 28th, 2012 - 14:39
Dear Yash,
Thanks a lot for your encouraging comment. I would try to include more of practice exercises in the future.
Vineet
February 24th, 2012 - 08:46
???? ?????: ??? ?????? ?? ???? ???, ??? ??? ??? ?? ??? ?????
????? ?????? ???? ???, ???? ???? ?? ????? ????
????? ?? ??? ????
??? ????? ?? ???? ???? ???? ??? ???? ????? ? ??????: 4 / (½) = 4 * (2/1) = 8
???????? ???????? (Binomial) ?? ?????
????, ?????, ????, ??????
(?+?) (?+?) =??+??+??+??
????? ????
??????? ‘??’ ?? ???? ????, ???? ??? ??? ???? ????
???? ????? ??? ??? ,?? ???? ?? ???? ??? ????
” ????? ??? ????? ?? ???? ???? ?? “
February 20th, 2012 - 20:54
thanx…………….
January 2nd, 2012 - 00:38
245*320? as it takes 0 at unit place
January 2nd, 2012 - 00:28
245*320?
November 24th, 2011 - 10:05
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…
November 11th, 2011 - 12:57
how to find the product of 104*105
November 12th, 2011 - 00:13
104+5 | 4*5
=10920
November 13th, 2011 - 20:43
i’m not able to understand what is the base taken here 100 or 110
November 14th, 2011 - 15:32
The base taken is 100. Please have a look at this post to have a clear understanding -
http://www.quickermaths.com/vedic-mathematics-multiplication-of-two-numbers/
December 25th, 2011 - 23:04
sir,pl tell me how to solve the following equations
root x+y=11
x+root y=7
December 6th, 2011 - 22:57
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
December 6th, 2011 - 23:06
Very nicely explained Farooqi!!
December 25th, 2011 - 23:27
your explanation is very nice sir, pl tell me how to solve the following equations
root x+y=11
x+root y=7
October 13th, 2011 - 13:02
Hi Diana!
28 * 25 = 7 * 4 * 25 = 7 * 100 = 700 .
regards!
June 9th, 2012 - 08:15
Hi mathemagican , You are Perfectly Right but I can say 28 * 100/4 = 2800/4 =700 may also Right !
October 12th, 2011 - 20:08
thanx 4r giving me dis easiest multiplication
October 12th, 2011 - 12:00
@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
November 24th, 2011 - 21:24
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.
December 20th, 2011 - 11:42
Please explain the preocedure for 53 x 22 @ vineet
December 20th, 2011 - 11:44
47 x 78 also
October 12th, 2011 - 11:09
pls let me know how would you multiply 25 x28 by the above vedic method
October 12th, 2011 - 12:14
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
December 6th, 2011 - 23:11
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.)
December 6th, 2011 - 23:17
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