Algebra 1A - Canon Mac

Although the first set of rules for dealing with negative numbers was stated in the 7th century by the Indian mathematician Brahmagupta

It was not until the 19th century when British mathematicians like De Morgan, Peacock, and others, began to investigate the 'laws of arithmetic' in terms of logical definitions that the problem of negative numbers was finally sorted out.

In 200 BCE the Chinese number rod system (see note1 below) represented positive numbers in Red and Negative numbers in black

Laws of Exponents

Number Line Imagine a number line on which you walk. Multiplying x*y is taking x steps, each of size y. Negative steps require you to face the negative end of the line before you start walking and negative step sizes are backward (i.e., heel first) steps. So, -x*-y means to stand on zero, face in the negative direction, and then take x backward steps, each of size y.