secrets-of-mental-math-malestrom

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Secrets of Mental Math
To see how factoring makes multiplication easier, consider the
following problem:
46
42
7 6
Previously we solved this problem by multiplying 46 40
and 46 2 and adding the products together. To use the factoring
method, treat 42 as 7 6 and begin by multiplying 46 7,
which is 322. Then multiply 322 6 for the final answer of
1932. You already know how to do 2-by-1 and 3-by-1 multiplication
problems, so this should not be too hard:
46 42 46 (7 6) (46 7) 6 322 6 1932
Of course, this problem could also have been solved by reversing
the factors of 42:
46 42 46 (6 7) (46 6) 7 276 7 1932
In this case, it is easier to multiply 322 6 than it is to multiply
276 7. In most cases, I like to use the larger factor in solving
the initial 2-by-1 problem and to reserve the smaller factor
for the 3-by-1 component of the problem.
Factoring results in a 2-by-2 multiplication problem being
simplified to an easier 3-by-1 (or sometimes 2-by-1) multiplication
problem. The advantage of the factoring method in mental
calculation is you do not have to hold much in memory. Let’s
look at another example, 75 63:
75 63 75 (9 7) (75 9) 7 675 7 4725