Usually we have a number of operations (operations are like adding, subtracting, multiplying, dividing and using exponents) together, we need to know what order to do them (which ones to do first). Don’t worry whywe perform the operations in these orders; this is just something you have to memorize and not worry about.
This section is very important, since you’ll use this all through Calculus and college. Another thing that’s quite interesting with learning the order of operations is that your calculator will automatically perform the correct order if you type in the numbers correctly (including with parentheses).
I like to use the mnemonic “Please Excuse My Dear Aunt Sally” or PEMDAS to remember the order. The order is Parentheses, Exponents, Multiplication and Division (either one, in order from left to right), and then Addition and Subtraction (either one, in order from left to right) – PEMDAS.
My Dear Aunt Sally
PEMDAS stands for:
So you’ll do the math left to right, like you’re reading a book, but you must pay careful attention and perform some operations before others.
Note that with embedded parentheses (parentheses within parenthesis), you always perform operations inside out; do the math on the inside before the outside.
Note that if you have an absolute value | | sign (which means take the positive value only of a number inside), you treat it like a parenthesis – so do that math first.
Also, if you have a fraction, and there are operations in the numerator or denominator, it’s almost like there are parentheses around them, so you do those first.
Also note that when you start working with variables in Algebra, you have to do the same order of operations.
Here are some examples:
Learn these rules, and practice, practice, practice!
Click on Submit (the arrow to the right of the problem) to solve this problem. You can also type in more problems, or click on the 3 dots in the upper right hand corner to drill down for example problems.
If you click on “Tap to view steps”, you will go to the Mathway site, where you can register for the full version (steps included) of the software. You can even get math worksheets.
You can also go to the Mathway site here, where you can register, or just use the software for free without the detailed solutions. There is even a Mathway App for your mobile device. Enjoy!
On to Introduction to Statistics and Probability – you are ready!