How Zero Affects Positive and Negative Numbers
It isn’t too tricky to perform operations using positive and negative numbers with zero. You follow normal addition and subtraction rules, and what zero does to the final sign depends on where the zero is. When you multiply or divide using zero, that zero just wipes out the numbers and leaves you with zero.
Here are some general guidelines about zero:
Adding with zero: 0 + a is just a. Zero doesn’t change the value of a. (This is also true for a + 0.)
Subtracting with zero: 0 – a = –a. Use the rule for subtracting signed numbers: Change the operation from subtraction to addition and change the sign of the second number. Likewise, a – 0 = a. It doesn’t change the value of a to subtract zero from it.
Multiplying by zero: a × 0 = 0. If you’re in a club with a bunch of friends and none of you has anything, multiplying what each of you has yields nothing: Likewise, 0 × a = 0.
Multiplying any number by zero always yields zero.
Dividing zero by a number: 0 ÷ a = 0. Take you and your friends: If none of you has anything, then dividing that nothing into shares just means that each share has nothing. And you can’t use zero as the divisor because if you have a things, you can’t divide them into zero parts.