1467 * 2531 = 3712977

Requires 16 single mutiplicative steps

Karatsuba’s method reduces this to 9 single mutiplicative steps

My method ive used for years taught to me by my father for adding stacks of random numbers together quickly modified by me to do high powered multiplication.

Start by rounding each number to the nearest whole number and remember that number

1467 + 533 = 2,000

2531 + 469 =3,000

2k x 3k = 6m (or viewed as 3k +3k x 1k)

Step 2:

realize that we have a larger number and remove the offset diffrence by both sides inflation rates

533 x 3k (1599k) (viewed as 533 + its self 3 times)

469 x 2k ( 938k) (viewed as 469 + its self twice)

Add these together = 2537k

Step 3 :

Relise that step 2 over offsets and add that of set back on

533x469 = 249977

Repeat steps 1 - 3 on step 3. For each mutipler part thats not a power of 10.

For this example:

(469+31)*(533+67) - (31*600) - (67*500) + (67*31)

(67 +3) * (31*9) - (9*40) - (3*70) + (9*3)

Results in no multiplication like this .

3m+3m - (533k +533 k +533k) - (469k + 469k) +(60k+60k+60k+60k+60k) - (3100+3100+3100+3100+3100+3100) ( 6700+6700+6700+6700+6700) +( 700+700+700+700) - (90+90+90+90) - (70+70+70) + (9+9+9)

6m - 2537k + 249977 = 3,712,977