# Why do we need negative one?

In terms of algebraic structures, it is to ensure that the set of integers forms a group: that is, the elements of the set have an additive inverse.

For the same reason we need all the other negative numbers. Negative numbers are regularly used whenever there are two opposites - in which case, one of the opposites is assigned to positive numbers, the other to negative numbers. For example:* Height above (or below) sea level

* Having (or owing) money

* Gaining (or losing) money

* Electrical charges

* Moving forward (or moving backward) - along a line

* Etc.

### What are the factors that will equal negative ten?

factors are the numbers you multiply together to get a product in a multiplication problem. a positive times a positive = a positive a positive times a negative = a negative a negative times a negative = a positive since you are looking for negative 10, you need one factor to be positive and one to be negative. this could be: -1*10 -10*1 -2*5 -5*2