Maths Tricks and Fun 15-digital sum

 Maths Tricks and Fun 15-digital-sum

Hello friends today we will study how multiplication becomes easy by the use of digital sum.What is 

digital sum? It is the sum of the digits of a number 

. Here its use in multiplication of big same digit

 numbers ,their squaring and cubing are discussed.

 Here use of digital sum in squaring of 4digit number 

is shown the digit is 4 ie (4444) are to be squared..so 

first we multiply the two outer fours 4×4 is 16. We will write 1 then a gap and 6.Digital sum of 16 is 7 . So we have totally 8 digits in the answer.and outer digits we

 have written and three digits each from either side we have to fillup.For this we will add 7 from either side 

and progress Arithmetically .so 1+7 is 8,8+7 is15, 

15+7is 22 stop here we have finished 4 digits on this 

side .we will add 7 to the other side. 6+7 is 13, 13+7

 is 20, 20+7 is 27.Now will add the carry overs and we 

get 19749136.

 Here multiplication of four digit number is shown but

 with a difference.4 fours are multiplied by 4 twos. Here also procedure is the same .Outer one digit each taken and multiplied.4×2 =08.we will write 0 on left side and 8 on the right . Then add 0+8= 8, 8+8 16, 16+8 24 stop 

 and start from right side 8+8 16, 16+8%= 24, 24+8 is 32.then adding the carry overs we get 09874568.

Similar one more multiplication is shown.4444×3333 , 

4×3 is 12, 1+2 is 3 so digital sum 3 is added from either side after putting 1 on left side 6 dots in the middle and 

2 on the lateral side we get the answer 14811852

Here also similar multiplication is shown in the third 

One ,7777×4444 , 7×4 is 28,2+8 is 10 we will use this 

for adding After putting 2 on left and then 6 dots

 followed by 8. The add 10 to 12, 12+10is 22, then

 22+10 is 32.then from right side 8+10 is 18, 

18+10 is 28, 28+10 is 38, Adding carry overs we get 34560988

 Here how to find cube of a same digit number using digital sum is shown.cube of 7777.cube of 7 is 343

we take 34 on left side and gap and 3 onthe right side.Now 34+3 is 37. We will add 37 from both sides total8 digits 34 is counted as single digit .Adding carry overs we get 

423372103.now using this we will get the cube totally 

12 digits should be there.we will add from side 4 digits separately like bring down 4 then 4+2 is 6 write 6 then

 6+3 is 9, then 9+3 is 13 like that from the other side similarly written .following this we will add 4 digits 

from either side after skipping outer one digit.middle 

2 digits we get by this.they will be put on either side .

now central 2 digits we have to find out. Exclude 2

 digits

 and add 4 digits each from both sides.finally adding

 the carry overs we get the answer 4703 6640 6433. 

In the coming class we will discuss on Tesla code-369

 and related calculations..Thank you