# How To Evaluate Mathematical Expressions by T E Miller BSc

During the years I was teaching mathematics, both privately and in schools, I found that many students and even teachers struggled with evaluation of expressions. The use of BODMAS (means evaluate first brackets, then Of then Division, then Multiplication, then Addition, then Subtraction) caused considerable confusion, even amongst teachers.
Now there is one advantage of studying computer science (which I did) and that is that you have to tell the computer what to do step by step. The computer scientists therefore took pains to tell us how to evaluate mathematical expressions so we would be able to write programs that could  calculate expressions.
Now if one uses BODMAS on 5 – 2 + 3 we might think that A (addition) comes before S (subtraction) and we might therefore say that 5 – 2 + 3 is 5 – 5 (we did the addition of 2+3)
This is NOT correct. In fact 5 – 2 + 3 is equal to 3 + 3 (we correctly did S before A)
In fact 5 – 2 + 3 = 3 + 3 = 6 (use a scientific calculator to verify that this is correct).
In fact the correct rules are:
1) First do brackets
2) Then Exponents
3) Then multiplication and division