Why -1×-1=+1? Why the product of two negative numbers is a positive number?
Srilekha , 6 Years ago
Grade 12
6 grade maths> Why -1×-1=+1? Why the product of two nega...
1 Answers
Arun
Last Activity: 6 Years ago
Dear student...
I am giving its prrof by another approach-
let's take ,
x=ab+(-a)b+(-a)(-b)
so x=ab+(-a)(b+(-b)
But, (b+(-b))=0.
so, x=ab ....result1
so x=b(a+(-a))+(-a)(-b).
buts
(a+(-a))=0.
x=(-a)(-b) ....result2
From result1 and result2 x=ab=(-a)(-b)
x=ab+(-a)b+(-a)(-b)
- now lets consider factor of (-a),
so x=ab+(-a)(b+(-b)
But, (b+(-b))=0.
so, x=ab ....result1
- lets consider factor of b,
so x=b(a+(-a))+(-a)(-b).
buts
(a+(-a))=0.
x=(-a)(-b) ....result2
From result1 and result2 x=ab=(-a)(-b)
The fact that the product of two negatives is a positive is therefore related to the fact that the inverse of the inverse of a positive number is that positive number back again.
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