I really don't get this. Why is it that -2*-2*-2 = -8, but -2*-2=4?
- Thread starter Dukhara
- Start date
D
Deleted member 4993
Guest
(-2) * (-2) = 4
This is true by definition:
Two negative numbers - when multiplied by each other - produces a positive number.
- Joined
- Feb 4, 2004
- Messages
- 16,582
If -2 * -2 = -4, then -4/-2 = (-2*-2)/(-2) = (-2/1)*(-2/-2) = (-2/1)*(1) = -2/1 = -2.
Is it true that -4 divided by -2 equals -2? So that the product (or quotient) of two negative numbers is another negative number?
This is a crude analogy, and it might be super confusing. So I apologize if it doesn't make any sense. But, here goes...
Imagine yourself standing in a field. For this example, you can only walk forward or walk backward, and only in increments of 1 meter. If you wanted to travel 2 meters, you'd simply walk forward two meters, easy. But what would you do if you wanted to travel (-2) meters? Well, that's really the same as traveling backwards for two meters, right? So we can infer that the negative sign means to turn around before walking. Then, if you wanted to walk (-2)*2 meters... that could be written as -(2*2). So you'd turn around and walk 4 meters.
But, what if you wanted to travel (-2)*(-2) meters? There are two negative signs in the problem, so we can rewrite that as -[-(2*2)]. Since a negative sign means to turn around, and there are two negative signs, you'd have to turn around twice. But, after turning around twice, you'd be facing the same way you were originally facing, right? In the end you'd have moved forward 4 meters.
Imagine yourself standing in a field. For this example, you can only walk forward or walk backward, and only in increments of 1 meter. If you wanted to travel 2 meters, you'd simply walk forward two meters, easy. But what would you do if you wanted to travel (-2) meters? Well, that's really the same as traveling backwards for two meters, right? So we can infer that the negative sign means to turn around before walking. Then, if you wanted to walk (-2)*2 meters... that could be written as -(2*2). So you'd turn around and walk 4 meters.
But, what if you wanted to travel (-2)*(-2) meters? There are two negative signs in the problem, so we can rewrite that as -[-(2*2)]. Since a negative sign means to turn around, and there are two negative signs, you'd have to turn around twice. But, after turning around twice, you'd be facing the same way you were originally facing, right? In the end you'd have moved forward 4 meters.
pka
Elite Member
- Joined
- Jan 29, 2005
- Messages
- 11,983
In number theory \(\displaystyle -2 \) is just notation for the additive inverse of \(\displaystyle 2\) or \(\displaystyle (2)+(-2)=0 \)
It should be written as \(\displaystyle (-1)(2) \), so \(\displaystyle (-2)\cdot (-2)=[(-1)\cdot(2)]\cdot[(-1)\cdot(2)] \).
That becomes \(\displaystyle (-2)\cdot (-2)=[(-1)\cdot(-1)]\cdot[(2)\cdot(2)]=4 \). Surely \(\displaystyle [(-1)\cdot(-1)]=1] \)
Now \(\displaystyle (-2)\cdot (-2)\cdot(-2)=[(-1)\cdot(-1)\cdot(-1)]\cdot[(2)\cdot(2)\cdot(2)]=-8 \) because \(\displaystyle [(-1)\cdot(-1)\cdot(-1)]=-1 \)