Let us discuss a few

*Multiplication by 11*It is the simplest of all next to multiplication by zero.

For eg.

960403 x 11 = 10564433

How this is done in single line.

Start from right and approach left while adding the current digit to the preceeding digit and at the extremes the two numbers come as they are with carry anywhere if applicable is to be added.

960403 x 11

Step1 ) ________3 last digit as it is

Step 2) _______33 Added 0 to previous digit 3 of original no.

Step 3) ______433 Added 4 to the previous digit 0

Step 4) _____4433 Added 0 to thee previous digit 4

Step 5) ____64433 Added 6 to previous digit 0

Step 6) ___564433 Addded 9 to previous digit 6. this becomes 15. Write 5 and take 1 as carry for next step

Step 7) 10564433 Added the carry 1 to 9. After this there is no more digit to the left so the process completes and the answer is 10564433

*Squaring of number ending in 5*To square a number which ends in 5 is very easy. For eg to square a number 25,35,15,85 or any other

The last two digits will always be 25 because both 5 will multiply to give 25.

What will come before 25 ? Take the digits ahead of 5 in the original number and multiply it with one more.

That means for a number say 85

The last digits will be ____25

And before that will come 8 x (8+1) = 8 x 9 =72

So the answer is 725

You can check this with 25 .

Last digit ____25

Before will come 2 x (2+1) = 2 x 3 =6

So the answer is 625

This will work with bigger numbers also

For eg 115

Last digit ______25

Before will come 11 x (11+1) = 11 x 12 = 132

So the answer is 13225

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