Algebra and order of operations

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Nanette Bülow

2019. október 11. 14:36

Hi there

Im re-learning some basic algebra, and I am having a bit of trouble with the order of operation.

Copied from Khan Academy's own learning material: We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

However, when trying to solve the exercises in two-step equations and I keep getting them wrong. The worked solutions vary so much in which order they solve the equation. Sometimes they seem to follow the PEMDAS, but they just as often dont, making it seem completely random how they are solved. I'm not sure if I'm missing something, but I dont understand how I ought to solve them in this case.

Hope this makes sense

Thank you

Nanette

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Allison F.

2019. október 11. 15:26
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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

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