Algebra and order of operations

Hi Nanette,

When you are solving a basic math problem, you are correct in saying you will use PEMDAS. Here's an example problem of using PEMDAS to solve a problem:

2 * 4 + (7 - 2)

First, you would solve the expression inside the parentheses- 7 - 2 is 5. Now you have 2 * 4 + 5. Next is multiplication, so you would solve 2 * 4, which is 8. Finally, 8 + 5 equals 13. So, 2 * 4 + (7 - 2) = 13.

However, when you first begin to solve equations with variables, or unknown factors, you need to solve this backwards, using SADMEP (the opposite of PEMDAS). This allows you to backtrack to isolate the variable.

Here's an example problem when using SADMEP is appropriate:

2x + 6 = 16 (solving for x)

Using SADMEP, what can you do to get rid of the 6? You would first subtract 6 from each side (being the opposite of + 6), because whatever you do to one side of the equation needs to be done to the other. Now you have 2x = 10. Since x is being multiplied by 2, we will want to divide by 2 on each side. Dividing 10 by 2 results in 5, meaning that x is equal to 5. We can then recheck our answers by plugging 5 in wherever you see x. Does 2 * 5 + 6 = 16? Yep!

This video and this article may provide better detail for each step.

Hope this helps!

Allison