The Order of Mathematical Operations

You may know the sentence "Please Excuse My Dear Aunt Sally" and what it means in relation to mathematics operations, but if you don't read on to get familiar with this memory device. In addition to this memory device, this article is more designed to consider the order of mathematical operations when applied to computer formulas in spreadsheets.

When we were young children math textbooks and our teachers were not as likely to cover this concept or to give us math problems that would require the use of this concept. If we look at a problem such as: 2 + 3 * 3 -1 = ; we might come up with an answer of 14 or an answer of 10. The correct answer is 10 and if you apply the order of mathematical operations you should get that result.

Each letter that starts a word in the sentence becomes the key to know what mathematical operation is done first, second, third, etc. The "Please" stands for parentheses; The ":Excuse" stands for exponents; The "My" stands for multiplication; The "Dear" stands for division; The "Aunt" stands for addition; and the "Sally" stands for subtraction. This means that if there are any parentheses, then everything mathematical is completed inside the parentheses before any math outside the parentheses is completed. The entire rule applies inside a set of parentheses, so it would be applied even if there were double or triple sets of parentheses inside parentheses.

After parentheses, then Exponents would be computed, then any multiplication, then any division, then any addition, then any subtraction. Computers follow this rule, so formulas used in cells will apply this rule and if you are not aware of how this rule is applied you may be surprised at the results.

In our example, 2 + 3 * 3 -1 = ; the multiplication is completed first with this computation now changing our equation to: 2 + 9 -1 = . At this point the addition is completed which changes the equation to: 11 -1 = . At this point the subtraction is computed with the result of an answer of 10.

If you actually wanted the answer to be 14 then the problem should be written like this: (2 + 3) * 3 -1 = ; which would have required that the mathematics in the parentheses would be computed first.

Computers do not use the "X" for multiplication, but instead use the "*" symbol. Because "X" is used in algebra it was felt that this would create less confusion in computer calculations. Computers also do not list "powers" in the same manner as typical written math. Computers use the symbol "^" for the powers function. This means that 2 to the 3 power; which is 2 * 2 * 2 would in a spreadsheet be written as 2^3.

Very large and very small numbers are sometimes handled differently by computers, basically converting numbers to "scientific notation" or rounding to a specified decimal place. Scientific notation and rounding are important mathematical concepts, but different issues than the order of mathematical operations. It is important not to jump to a mathematical conclusion just because the problem seems relatively easy to solve as demonstrated by the example.

You might want to look at: Kathy Reed, published Jun 11, 2007 for the viewpoint from a mathematics teacher on the same subject.