Algebraic equalities and formulas

A formula is an equality written with letters that links quantities, for example S = ab and P = 2(a + b) for a rectangle, and s = vt for motion. Letters also help us record the laws of arithmetic briefly: a - (b + c) = a - b - c, (a + b)c = ac + bc, (a + b) : c = a : c + b : c with c ≠ 0. An even number is divisible by 2, so we write it as a = 2n; an odd number leaves remainder 1 when divided by 2 and is written as b = 2n + 1 (odd natural numbers can also be written as 2k - 1). To express a required quantity from a formula we use properties of equalities: from s = vt we get t = s : v. When we substitute numbers into a formula, we also keep track of the units.