Order of Operations
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PEMDAS
The term order of operations refers to the way one should calculate equations containing many different functions (such as addition, subtraction, multiplication, and division.)
For example, if my equation is:
How do I know what to take care of first? Use PEMDAS! It tells me the order in which to solve the separate functions of the equation. Specifically it tells me that I should calculate anything that's inside of Parenthesis first, take care of any Exponents next, then do all Multiplication followed by Division, Addition, and lastly Subtraction.
Importance of PEMDAS/Example
Let's say Angie must calculate the problem above but she isn't familiar with the order of operations. She might do the problem this way:
Angie didn't do PEMDAS, she did DPSEAM, which, in my book stands for Don't Produce Sophisticated Equation Answers Mindlessly!
Here's how to solve for p the correct way:
Who would have thought that following one silly rule would give such a lower (and more correct) answer?
What if...?
You may have realized that IF your equation doesn't have all parts of PEMDAS (is missing one or more of: parenthesis, exponents, multiplication, division, addition, and subtraction,) just skip whatever parts aren't in your equation.
With an equation that's simply: r = 7 + 4 * 3, you only use the M and A. The only thing that matters is that you do them in the right order.
IF the same function is done multiple times in one equation, simply work to solve it from right to left.
For example, here's my equation:
(8 + 14) – 7 – 94 – 9
Following order of operations, first solve what’s inside the parenthesis:
(22) – 7 – 94 – 9
Then go from left to right subtracting what needs subtracted:
(22 – 7) – 94 – 9
22 – 7 = 15
15 –94 – 9
(15 – 94) – 9
15 – 94 = -79
-79 – 9
(-79 – 9) = -88
IF there is more than just one function inside the parenthesis—such as (8 + 5 * 6³)—use PEMDAS for that, too. For example, to solve (8 + 5 * 6³), do the exponent, multiplication, and then addition.
6³ = 216
(8 + 5 * 216)
5 * 216 = 1080
(8 + 1080)
8 + 1080 = 1088
(1088)
It's Hard to Remember That Long Acronym!
The most widely-known way to remember PEMDA is saying Please Excuse My Dear Aunt Sally. However, you may want to spice things up a bit and think of your own little phrase. One I thought of was Paul Eats Many Doritos After School. Let your imagination run wild.
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