secrets-of-mental-math-malestrom

Divide and Conquer: Mental Division 89
57
Answer: 7 62
Actually, there’s a nifty trick to make problems like this easier.
Remember how you first tried multiplying 62 8, but
found it came out a little high at 496? Well, that wasn’t a
wasted effort. Aside from knowing that the answer is 7, you
can also compute the remainder right away. Since 496 is 5 more
than 491, the remainder will be 5 less than 62, the divisor.
Since 62 5 57, your answer is 7 57
62. The reason this trick
works is because 491 (62 8) 5 62 (7 1) 5 (62
7 62) 5 (62 7) (62 5) 62 7 57.
Now try 380 39 using the shortcut we just learned. So 39
10 390, which is too high by 10. Hence the answer is 9 with a
remainder of 39 10 29.
Your next challenge is to divide a two-digit number into a
four-digit number:
3657 54
Since 54 100 5400, you know your answer will be a
two-digit number. To arrive at the first digit of the answer, you
need to figure how many times 54 goes into 3657. Since 54
70 3780 is a little high, you know the answer must be 60
something.
Next, multiply 54 60 3240 and subtract 3657 3240
417. Once you say the 60, your problem has been simplified to
417 54. Since 54 8 432 is a little too high, your last digit
is 7 with the remainder 54 15 39.