### Abstract

‘The laws of algebra’ explores the three laws that govern arithmetic operations and explains how these rules are extended so that they continue to be respected as we pass from one number system to a greater one that subsumes the former. The associative law of addition shows that that *(a + b) + c = a + (b + c)*, and the associative law of multiplication is *a(bc) = (ab)c*. The distributive law tells us how to multiply out the brackets: *a(b + c) = ab + ac*. The commutative law of addition is *a + b = b + a*, a law that holds equally well for multiplication: *ab = ba*.