Don’t Break the Laws of Math! Learn the Order of Operations

Why? Why do we need an order of operations? Consider the following problem:

There are two ways to solve this! The order of operations tells us which way is correct. We even have a good way to remember the order of operations. (next…)

Judge Judy Please Excuse My dear Aunt Sally

Do this first! ‘Please’ stands for parentheses and other grouping symbols. Parentheses ( ) Brackets [ ] Braces { } The fraction bar (groups the problem into a top and a bottom)

Then do these ‘Excuse’ stands for exponents. Exponents are a shorthand for repeated multiplication of a number by itself.

Next come this pair ‘My Dear’ stands for: Multiply and divide IN ORDER from left to right. Multiply is not more important – do whichever comes first as you go from left to right.

Last but not least! ‘Aunt Sally’ stands for: Add and subtract IN ORDER from left to right.

Let’s try it! Please excuse my dear Aunt Sally Since parentheses come first, it seems as if we should do something with the 5. But what? Trick #1 Parentheses can be used 2 different ways As a grouping symbol (that’s what Please means) As a multiplication sign (that’s what this is) How can you tell which way it’s being used? (next…)

Parentheses as a grouping symbol If the parentheses are being used as a grouping symbol, there will be some action going on inside. By action, I mean Addition ( 5 + 4) Subtraction ( 7 – 3) Multiplication ( 6 x 4 ) Division ( 10 / 2 )

Parentheses as a multiplication symbol Once we start algebra and use x to mean the unknown number that we’re trying to find, we can’t also use x to mean multiply. One way to indicate multiplication is with a number followed immediately by parentheses. 5 ( ) means 5 times whatever is inside the parentheses 2 of the most popular alternate multiplication signs are parentheses 4 ( 5 ) and a raised dot

S M A M Identify your operations and them perform them in the correct order. Multiply first – from left to right. Then add and subtract in order.

A D M E Identify your operations and them perform them in the correct order. Exponents first, then multiply and divide, in order, from left to right. Add last.

D P M P Identify your operations and them perform them in the correct order. Parentheses first, then multiply and divide, in order, from left to right. The parentheses around the 5 in line 2 are optional.

M A M Identify your operations and them perform them in the correct order. Multiply first and then add.

P E D M Identify your operations and them perform them in the correct order. Parentheses first, then exponents, then multiply and divide in order.

Order is important in court . . and in math! Please excuse my dear Aunt Sally.