What are the Multiplication Properties of 0 and -1?

For multiplying by 0, n is a variable standing for any number
Multiplying any number by 0 gives us 0 back
As you can see, no matter what we multiply by 0, the result is 0
For multiplying by -1, n is a variable standing for any number that is not zero!
Multiplying a number by -1 flips the sign of that number
Multiplying 0 by -1 doesn't flip 0's sign since it doesn't have one!

1. In other words, multiplying anything by zero will get us zero again!
1. For example, 10,428,141,246 times 0 is still 0
1. 5•0=0
2. -3•0=0
3. 0•0=0
4. x•0=0
5. (3x+2)•0=0
6. x is a variable, so it can be any number, but since it's being multiplied by 0 that doesn't matter
1. In other words, multiplying by -1 flips the sign of the other number
1. In other words, multiplying by -1 flips the sign of the other number
1. Multiplying by -1 flips the sign of positive 5 to give us negative 5
1. Multiplying by -1 flips the sign of negative 3 to give us positive 3
1. The two negative signs cancel out and give us a positive 1!
1. We got -x, which means that whatever we plug into x gets its sign flipped
2. For example, plugging in -7 would give us 7, and plugging in 15 would give us -15
1. We have two rules referring to this situation, but which one do we use?
2. Since 0 is not a non-zero number, we can't use the Multiplication Property of -1
1. Since 0 is not a non-zero number, we can't use the Multiplication Property of -1
2. But we can use the Multiplication Property of 0, because there n can be any number!
3. 0 times anything is still 0
4. So in this case, n would be -1, since we multiply it by 0 to get 0

Definition: Multiplication properties of 0 and -1