Brackets (parentheses) in formulas

Abstract

Each year, new health sciences postgraduate students in York are given a simple maths test. Each year the majority of them fail to calculate 20 – 3 × 5 correctly. According to the conventional rules of arithmetic, division and multiplication are done before addition and subtraction, so 20 − 3 × 5 = 20 − 15 = 5. Many students work from left to right and calculate 20 − 3 × 5 as 17 × 5 = 85. If that was what was actually meant, we would need to use brackets: (20 − 3) × 5 = 17 × 5 = 85. Brackets tell us that the enclosed part must be evaluated first. That convention is part of various mnemonic acronyms which indicate the order of operations, such as BODMAS (Brackets, Of (that is, power of), Divide, Multiply, Add, Subtract) and PEMDAS (Parentheses, Exponentiation, Multiplication, Division, Addition, Subtraction).1 Schoolchildren learn the basic rules about how to construct and interpret mathematical formulas.1 The conventions exist to ensure that there is absolutely no ambiguity, as mathematics (unlike prose) has …