secrets-of-mental-math-malestrom

The Tough Stuff Made Easy: Advanced Multiplication 167
Without repeating all the detailed steps as we did in the last
problem, I will point out some of the highlights of this problem.
After doing the 8 8,862 70,896, note that 896 is above 750,
so a carry is possible. In fact, since 431 2 is greater than 400 2
160,000, there definitely will be a carry when you do the addition
to the number 896,000. Hence we can safely say aloud,
“Seventy-one million . . .” at this point.
When you square 431, you get 185,761. Add the 185 to the
896 to get 1,081, and say the rest of the answer. But remember
that you already anticipated the carry, so you just say, “. . . 81
thousand . . . 761.” You’re done!
We illustrate one more fine point with 2,753 2 :
247 3,000 “Light off”
2,753 2
247
2,506
7,518,000
61,009
7,579,009
(3,000 2,506)
(247 2 )
47 294
247 2
47
200
58,800
2,209
61,009
(294 200)
(47 2 )
Since you are rounding up to 3,000, you will be multiplying
3,000 by another number in the 2,000s. You could subtract
2,753 247 2,506, but that’s a little messy. To obtain the last
three digits, double 753 to get 1,506. The last three digits of this
number, 506, are the last three digits of the 2,000 number:
2,506! This works because the two numbers being multiplied
must add to twice the original number.
Then proceed in the usual manner of multiplying 3,000
2,506 7,518,000, convert 518 to the words light off, and say