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let's play with algorithm :)
The computation 37×23=851
Thus 37×23 corresponds to the area of a 37-by-23 rectangle.
Exercise: What if we thought of 37 as 10+10+10+7 and 23 as 10+10+3 (as most friends first want to do)? Draw the 37-by-23 rectangle subdivided into twelve pieces, compute the areas of the individual pieces, and verify that they have total sum 851.
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EXAMPLE: 15×17.
Answer: 15×17=100+70+50+35=255.
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EXAMPLE: 371×42.
Answer: Subdivide a rectangle into six pieces.
371×42=(300+70+1)×(40+2)=12000+600+2800+140+40+2=15582
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EXAMPLE: The computation (4+5)(3+7+1) corresponds to subdividing a rectangle into how many pieces?
Answer: Six pieces.
We have (4+5)(3+7+1)=4×3+4×7+4×1+5×3+5×7+5×1=12+28+4+15+35+5=99.
Comment: This was a very complicated way of computing 9×11=99!
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EXAMPLE: What does the computation (a+b+c+d)(e+f+g) mean geometrically?
Answer: It corresponds to subdividing a rectangle into 12 pieces.
With patience one could write this out:
(a+b+c+d)(e+f+g)=ae+af+ag+be+bf+bg+ce+cf+cg+de+df+dg.
Comment: One usually omits the multiplication sign “×” or “⋅” when multiplying two quantities represented by symbols.
#idoja
