My dear friends,
try to do some simple calculations given below within a second…
1)83 multiplied by 87 2)24 multiplied by26 3)72 multiplied by 78 4)99 multiplied by 91 5) 65 multiplied by 65
Tell me how much time did you take to solve them correctly. Let me analyze your reply & then I’ll tell you the trick to calculate it within a second!
If you know already don’t disclose it here, send me a message.
You only need seconds if you use and automate the use of the binomic formulas:
(x-y)(x+y) = x2 – y2 and (x+y)2 = x2 + 2xy + y2
then, e.g. : 83 * 87 = (85-2)(85+2) = (80+5)2 – 22 = (6400+800+25) – 4 = 7221
automated: take the square of the tens, add 10 time the tens, add 25, subtract the square of difference to the number with the ending five (i.e. 85-83=2), voila.
this is the trick exclusively applicable to the multiplications of 2 numbers whose digits at unit’s place add up to 10 as well as whose digits at tenth’s place are same. both of these conditions should be satisfied.
e.g.1)in product of 83 & 87, digit at tenth’s place is same i.e.8 & sum of 3 & 7 is 10.
now, follow the rules—-
a)firstly, find product of digits at unit’s places i.e. here 3 * 7=21.
b)secondly, multiply tenth’s place digit by next consecutive number i.e. here 8 * 9=72.
c)now your answer is the outcome in second step i.e.72 followed by outcome in first stepi.e.21
d) hence, your answer is 7221.
In example 3, answer is 7 * 8=56 followed by 2 * 8=16 i.e. 5616.
You should take care that when digits at unit’s places are 1 & 9, you must write their product as 09.
considering example 4, answer is 9 * 10=90 followed by 9 * 1=09 i.e. 9009.
now, you can do such specific multiplications orally within a second!
Here is the math behind that wonderful trick:
(10x + y)(10x + 10 – y)=100x2 +100x – 10xy +10xy +10y -y2 = 100x2 +100x + 10y – y2 = 10x * 10(x+1) + (10-y) * y
You showed me what to look for – after that it was simple.
Thanks to both of u sir for the great disscussion..
83 * 87 = Multiply last and first digit ( 38 = 24) , Multiply First & First Digit ( 88 = 64 ), Multiply Last & last digit (37 = 21), Multiply First & last digit ( 87 =56)
64 & 21 if joined – 6421
7221
24
what about this When you multiply two numbers in the 90’s together, in parenthesis next to each number put how far that number is away from 100. Since 92 is 8 away from 100 and 94 is 6 away from 100, the problem 92×94 would look like this: 92(8) x 94(6) Example: 93(7) x 96(4) Step 1: Add up the numbers in parenthesis 7 + 4 = 11 and subtract that number from 100. 100 – 11 = 89 Step 2: Multiply the two numbers in parenthesis together and tack that on to the number from Step 1. 7×4 = 28 Answer: 93×96 = 8928
One more simple trick!
83
x 871) find out 100 – 83=17 2) find 100 – 87=13 3) multiply 17 and 13 which gives 221 Thus you have got units place 4) But here we have taken base as 100 which has two 0’s so we will take 2 from 221 as carry over 5) either subtract 83 – 13 or 87 – 7=80 + carry over(2) =82 So we have got the final answer 8221.
Post Comments
zwitten said – Mon, 14 Jul 2008 20:42:06 -0000 ( Flag Edit Link )
sir, one should need more than 5 seconds to calculate by the method you stated. a good X th standard student in India knows this trick. But, i have a trick by which it really takes less than a second to do it! These are some special tricks which you will learn in the subject VEDIC MATHS FOUND in vedas. I’ll tell about vedas afterwards.
I’m posting this trick separately in this discussion.
mitesh137 said – Wed, 30 Sep 2009 14:25:38 -0000 ( Flag Edit Link )
89=72 & 37=27 THEREFORE 7227
manu1684 said – Thu, 22 Oct 2009 02:10:19 -0000 ( Flag Edit Link )
pls solve 59 multiply by 56 through ur trick