You can put this solution on YOUR website! One multiplied by any number is equal to that number.
For example:
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When a negative number is multiplied by another negative number, the negative signs cancel out and make the result positive.
Examples:
The other tutor did not prove it.
We assume that the distributive, identity and inverse principles hold.
First we must prove that (-1)(0) = 0
[You might already accept that anything times 0 is 0,
but even that must be proved!]
Start with:
(-1)(0)
Since 0 = 0 + 0 we can replace the 0 by (0 + 0):
(-1)(0) = (-1)(0 + 0)
We use the distributive principle on the right side:
(-1)(0) = (-1)(0) + (-1)(0)
We subtract (-1)(0) from both sides:
0 = (-1)(0)
So we have proved that (-1)(0) = 0:
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Now start with
(-1)(-1) + (-1)
Since (-1) = (-1)(1), we can substitute (-1)(1) for the second term (-1),
and the above becomes:
(-1)(-1) + (-1) = (-1)(-1) + (-1)(1)
We factor (-1) out of both terms:
(-1)(-1) + (-1) = (-1)(-1 + 1)
We know that (-1 + 1) = 0 so we have
(-1)(-1) + (-1) = (-1)(0)
and we have proved above that (-1)(0) = 0, so we have proved
(-1)(-1) + (-1) = 0
and we know that 1 + (-1) = 0, so we replace the 0 on the right
by 1 + (-1)
(-1)(-1) + (-1) = 1 + (-1)
We subtract (-1) from both sides:
(-1)(-1) = 1
Edwin
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