Performing a String of Operations in Correct Order

One of the most important mathematical concepts to understand is the order of operations. Order of operations is what allows you to perform a long string of operations like this in the correct order to arrive at the correct answer. The mnemonic that most people use to remember the correct order of operations is PEMDAS (Parentheses Exponents Multiplication Division Addition Subtraction).

This is most commonly remembered by the phrase “Please Excuse My Dear Aunt Sally.” The important thing to understand with this is that multiplication and division have the same priority level and addition and subtraction have the same priority level. If you have a string of operations that have both multiplication and division, you work the multiplication and division from left to right in whatever order they happened to come in.

It’s the same thing with addition and subtraction. Let’s look at the example here. First thing we’re going to look for is parentheses. We have two sets of parentheses, and so we need to resolve them first. 8 minus 5 equals 3. 9 plus 3 equals 12. We resolved our parentheses. Next, we have exponents. We only have one exponent here.

It’s 4 to the second power, which is 16. We’ve resolved exponents. Next is multiplication and division, but first let’s rewrite this to see what’s left. We have 3 times 6 plus 16 divided by 2 times 12 divided by 3. Now we’ll work from left to right on multiplication individually.

3 times 6 is 18. 16 divided by 2 is 8. I’ll rewrite the rest of this on here so that we have it. 8 times 12 is 96. 96 divided by 3 is 32. You see we had a string of operations here with division and multiplication and we just work from left to right. What we have left now is 18 plus 32. That’s just one operation. We’ll add these two up and we get 50.