# math

### BEDMAS 101

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It has always been a pet peeve for me when there are people around me who still do not know the BEDMAS rule. But then I always think this over the moment I hear that someone beside me in the library would argue with all their might to their friend that that 2 + 8 x 3 is 30 and not 26. But hey, I would then understand that Math is a tricky subject and that anything Math-related especially these types of problems can be quite confusing. Nevertheless, rather than being mad at that guy over at the library, it would be better if I teach them the ways of the BEDMAS.

Now BEDMAS, which stands for Brackets, Exponents, Division/Multiplication and Addition/Subtraction, represents the order of operations. It is a very handy mnemonic to easily remember the precedence among operations. There are other names for BEDMAS and one in particular would be PEMDAS, which is Parentheses, Exponents, Multiplication/Division and Addition/Subtraction. Both work the same way, as long as the order of operations is still followed.

So how does this work? The rule states that any operation found within brackets or parentheses must be worked out first. It is also important to note that the innermost grouping symbol has to be operated first before the outermost grouping. For instance, in calculating 3 x [2 – (4 + 5)], we solve first for 4 + 5 to get 9. Replace the  (4 + 5) in the original expression as 9 to make the expression much simpler by reducing the number of grouping symbols. So we then have 3 x [2 – 9]. Solving the operation inside the brackets which is 2 – 9 = -7. Replace [2 – 9] with -7, which leaves us with 3 x -7 and therefore can easily be solved to get -21.

The next precedence would be Exponents. After getting rid of the grouping brackets, then it is time to attack exponents. For instance, calculate 40 / (6 – 2^2)^3. Note here that “/” means division and “^” means an exponent raised to the power of. So here we start solving for the bracket which is 6 – 2^2. Here we see an exponent, which we should solve first. 2^2 is 4 and it should replace 2^2 here. Therefore 6 – 4 = 2. This was initially part of the bracket in the original expression and we should replace this with the number we got which is 2. Our simplified expression would thn be 40 / 2^3. Now recall that Exponents must go before any Multiplication, Division, Addition or Subtraction. Therefore 2^3, which is also equal to 2 x 2 x 2, is 8. Replace 2^3 with 8 to get 40 / 8, which is 5.

Now always keep mind to solve for bracketed operations first, beginning from the innermost operation to the outermost. Then any exponents found must be solved immediately before solving for any operation with Division, Multiplication, Addition or Subtraction. Division and Multiplication have interchangeable precedences, meaning that the first operation that appears after reading the expression from left to right has to be performed first. A simple example, for instance, would be 6 / 3 x 2. Here we first operate 6 / 3 to get 2 before multiplying it to 2 to get 4. If we have 3 x 9 / 27, therefore we first solve 3 x 9 before dividing the result by 27, which is equal to 1. Addition and subtraction, however have lower precedences than Division and multiplication; thus, division and multiplication would have to be performed first before operating addition and subtraction, while of course keeping the interchangeable precedence premise among division and multiplication. Moreover, like division and multiplication, addition and subtraction also have interchangeable precedences, performing first the operation that appears when the expression is read from left to right.

Here’s a recap of the rules of BEDMAS:

1. Begin performing bracketed operations in an expression, starting from the innermost going to the outermost brackets (or parentheses or braces or any other grouping symbol for that matter).
2. Simplify exponents whenever possible.
3. Solve for division and multiplication operations. Precedences are interchangeable.
4. Finish up with addition and subtraction. Precedences are also interchangeable.
5. Repeat back to step 1 if there are any other further brackets and continue performing the cycle.

Now go and test yourself if you can calculate the final result of the following expressions using BEDMAS rule, and then check your answers:

1. (2^7 – 1 x 5) + 3^4
2. 1 + 1 + 1 + 1 + 1 x 0
3. 180 / [2 + (8 x 1/2)]^2