## Tuesday, August 28, 2018

### [pofovqxy] Multiplication up to product 100

Most people memorize a square portion of the multiplication table up to 10*10.  Beyond that, the obvious thing to try is a larger square, like up to 12*12 or 20*20.  However, instead of a square, consider memorizing the area under a hyperbola, numbers whose products are less than or equal to 100.  This requires memorizing the following 59 additional products:

2*15=30 2*16=32 2*17=34 2*18=36 2*19=38 2*25=50 2*26=52 2*27=54 2*28=56 2*29=58 2*35=70 2*36=72 2*37=74 2*38=76 2*39=78 2*45=90 2*46=92 2*47=94 2*48=96 2*49=98
3*14=42 3*15=45 3*16=48 3*17=51 3*18=54 3*19=57 3*24=72 3*25=75 3*26=78 3*27=81 3*28=84 3*29=87
4*13=52 4*14=56 4*15=60 4*16=64 4*17=68 4*18=72 4*19=76 4*23=92 4*24=96 4*25=100
5*12=60 5*13=65 5*14=70 5*15=75 5*16=80 5*17=85 5*18=90 5*19=95
6*12=72 6*13=78 6*14=84 6*15=90 6*16=96
7*12=84 7*13=91 7*14=98
8*12=96

We have omitted as trivial products which don't require a carry so break down into independent multiplications of the tens and ones places, e.g., 3*23=69, x*11.  We've also omitted duplicates by commutativity.

Incidentally, the square multiplication table up to 10*10 has 36 nontrivial products:

2*2=4 2*3=6 2*4=8 2*5=10 2*6=12 2*7=14 2*8=16 2*9=18
3*3=9 3*4=12 3*5=15 3*6=18 3*7=21 3*8=24 3*9=27
4*4=16 4*5=20 4*6=24 4*7=28 4*8=32 4*9=36
5*5=25 5*6=30 5*7=35 5*8=40 5*9=45
6*6=36 6*7=42 6*8=48 6*9=54
7*7=49 7*8=56 7*9=63
8*8=64 8*9=72
9*9=81

However maybe 2*X can be omitted assuming you've already learned single digit addition, leaving 24 products.