TIPS IN MULTIPLYING DIFFERENT DIGITS ENDING IN 5 MENTALLY
E.g. 75*45
Find the difference between 7 and 4. If it is ODD, the last two digits is automatic 75. If it is EVEN, the last two digits is automatic 25. In our example, 7-4=3 , 3 is odd, so the last two digits of 75*45 is 75.
To find the other digits, add 1 to the larger digit, then multiply by the smaller digit, then add the floor[difference/2]
In our example, 7 is the larger digit, so (7+1)(4) = 32. Remember that our difference is 3, so add floor[3/2] which is floor[1.5] or 1. 32+1 = 33.
Thus, 75*45 = 3375
Another example: 115*35
11 - 3 = 8. 8 is an even number, thus the last two digits is automatic 25. (11+1)(3) = 36. 36 + floor[8/2] = 36 + 4 = 40
Thus, 115*35 = 4025
Last example: 445*255
44 - 25 = 19. 19 is an odd number, thus the last two digits is automatic 75. (44+1)(25) = 45*25. We will notice that this can be shortcut too. 4-2 = 2, thus, the last two digits is 25. (4+1)(2) = 10. 10 + floor[2/2] = 11.
Thus, 45*25 = 1125. But we have to add floor[19/2] also. 1125 + 9 = 1134
Thus, 445*255 = 113475
Hope it helps :)
#MMBLTutorial
-shinnichi
