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Post by Progenitor A on Sept 12, 2010 17:23:49 GMT 1
Why is (-1)x(-1) = +1
Posed in the Spectator
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Post by abacus9900 on Sept 12, 2010 17:54:05 GMT 1
Why is (-1)x(-1) = +1 Posed in the Spectator That is just the normal rule of signs, naymissus. In division and multiplication like signs are always a positive result while unlike signs are always a negative result. It's just a convention but one that works. For example: (+3)*(+3) = +9; ( -3)*(+3) = -9; ( -3)*( -3) = +9; (+3)/(+3) = +1; ( -3)/(+3) = -1; ( -3)/(- 3) = +1. There is something called an 'imaginary number' where this rule is violated, but that is another branch of maths. |
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Post by olmy on Sept 13, 2010 8:58:23 GMT 1
It's because of the distributive law. Basically, if we want to do arithmetic with negative numbers then this law must hold, so, for any numbers, a(b + c) = ab + ac, e.g. 2x7 = 2(5+2) = 2x5 + 2x2 = 10 + 4 = 14. Putting a=-1, b=1 and c=-1, we get -1(1+(-1)) = ((-1)x1 + ((-1)x(-1)) so -1x0 = -1 + (-1)x(-1) so 0 = -1 + (-1)x(-1) so (-1)x(-1) = 1. |
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Post by Progenitor A on Sept 13, 2010 14:43:32 GMT 1
It's because of the distributive law. Basically, if we want to do arithmetic with negative numbers then this law must hold, so, for any numbers, a(b + c) = ab + ac, e.g. 2x7 = 2(5+2) = 2x5 + 2x2 = 10 + 4 = 14. Putting a=-1, b=1 and c=-1, we get -1(1+(-1)) = ((-1)x1 + ((-1)x(-1)) so -1x0 = -1 + (-1)x(-1) so 0 = -1 + (-1)x(-1) so (-1)x(-1) = 1. You illustrate the point that the Spectator was attempting to make quite well. Other mathematical operations involving positive and negative numbers are intuitive, whereas when negatives are multiplied and divided, the RULE is the justification, intuitio is absent e.g. 2 x 4 = two sets of 4 added together 2 x -4 = two sets of (-4) added together 4/2 = the number of times 2 can be subtracted from 4 4/-2 =(minus) the number of times 2 can be subtracted from 4 Try telling a primary schol child that (-1) x (-1) = 1 because of the distributive law |
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Post by olmy on Sept 14, 2010 8:24:24 GMT 1
Try telling a primary schol child that (-1) x (-1) = 1 because of the distributive law Why? I didn't realize that a primary school level answer was what you wanted............ |
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