Mix 5

Q. Can anyone make 3 using two 2's ?

Sol. Yes anyone can write it 
2 + 2⁰ = 2 + 1 = 3

Or

2/2 + 2 = 2 + 1 = 3

Multiply by 5: 

Multiply by 10 and divide by 2.

Multiply by 6: 

Sometimes multiplying by 3 and then 2 is easy.

Multiply by 9: 

Multiply by 10 and subtract the original number.

Multiply by 12: 

Multiply by 10 and add twice the original number.

Multiply by 13: 

Multiply by 3 and add 10 times original number.

Multiply by 14: 

Multiply by 7 and then multiply by 2

Multiply by 15: 

Multiply by 10 and add 5 times the original number, as above.

Multiply by 16: 

You can double four times, if you want to. Or you can multiply by 8 and then by 2.

Multiply by 17: 

Multiply by 7 and add 10 times original number.

Multiply by 18: 

Multiply by 20 and subtract twice the original number (which is obvious from the first step).

Multiply by 19: 

Multiply by 20 and subtract the original number.

Multiply by 24: 

Multiply by 8 and then multiply by 3.

Multiply by 27: 

Multiply by 30 and subtract 3 times the original number (which is obvious from the first step).

Multiply by 45: 

Multiply by 50 and subtract 5 times the original number (which is obvious from the first step).

Multiply by 90: 

Multiply by 9 (as above) and put a zero on the right.

Multiply by 98: 

Multiply by 100 and subtract twice the original number.

Multiply by 99: 

Multiply by 100 and subtract the original number.

TO FIND SQUARE OF 3-DIGIT NUMBER

LET THE NUMBER BE ABC

SQ (ABC) is calculated like this

STEP 1. Last digit = last digit of SQ(C)
STEP 2. Second Last Digit = 2*B*C + any carryover from STEP 1.
STEP 3. Third Last Digit 2*A*C+ Sq(B) + any carryover from STEP
2.
STEP 4. Fourth last digit is 2*A*B + any carryover from STEP 3.
STEP 5 . In the beginning of result will be Sq(A) + any carryover
from Step 4.


EXAMPLE :

SQ (431)

STEP 1. Last digit = last digit of SQ(1) =1
STEP 2. Second Last Digit = 2*3*1 + any carryover from STEP
1.= 6
STEP 3. Third Last Digit 2*4*1+ Sq(3) + any carryover from STEP
2.= 2*4*1 +9= 17. so 7 and 1 carryover
STEP 4. Fourth last digit is 2*4*3 + any carryover (which is 1) . =
24+1=25. So 5 and carry over 2.
STEP 5 . In the beginning of result will be Sq(4) + any carryover
from Step 4. So 16+2 =18.

So the result will be 185761.

You are writing an algorithm of ordinary multiplication in a different way

431 * 431
      431
    1293
 + 1724
185761

431 * 431 = 185761