Properties of arithmetic operations

The basic laws of addition and multiplication are the commutative law (a + b = b + a, ab = ba), the associative law ((a + b) + c = a + (b + c), (ab)c = a(bc)) and the distributive law a(b + c) = ab + ac. They make computing easier: 48 + 29 + 52 + 11 is simple to add as (48 + 52) + (29 + 11). Subtraction reduces to addition: a - b = a + (-b), and division to multiplication by the reciprocal: a : b = a · (1/b), b ≠ 0. Terms that differ only in their coefficients are called like terms, for example 4b and 9b; to combine them we add the coefficients: 4b + 9b = 13b. Simplifying an expression first and substituting numbers afterwards makes the calculation much lighter.