Common Errors in MDAS Operations

The order of operations of multiplication, division, addition, and subtraction (MDAS) seems a very basic concept, but it is one of the source of misconceptions. The two errors below are very common.

Error 1: Addition must be performed before subtraction.

This is not always the case.  If addition and subtraction are adjacent operations, the operations must be performed from left to right. For example, although addition and subtraction are both present in

5 - (-2) + 7

subtraction must be performed first. Performing the operation, we have

5 - (-2) + 9 = 7 + 9 = 16.

Error 2: Multiplication must be performed before division.

Similar to addition and subtraction, if multiplication and division are adjacent operations, the operation which comes first must be performed. For example, in

6 \div 2 ( 1 + 2) .

you must divide 6 by 2 first, before multipying it by (1 + 2).

Therefore,

6 \div 2 (1 + 2)= 6 \div 2 (3) = 3(3) = 9.

For my Filipino readers, Sipnayan, a math blog written in Filipino, has a more extensive explanation about MDAS, PEMDAS, and order of operations.

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