As mathematical expressions get more and more complicated, we need to develop a set of rules that tell us which operations to do first, second, and so on. This is known as the Order of Operations. Oftentimes, to help people remember, you'll see acronyms such as PEMDAS and BEDMAS.
Question
What is the Order of Operations? And what do PEMDAS and BEDMAS stand for?Answer
The Order of Operations is like grammar for math. It tells us in what order we should do the operations that are written. It helps to make sure that the person writing an expression and the person reading it get to the same answer - the one intended by the writer.Analysis
The order in which we work expressions is:
- P = Parentheses (also known as Brackets)
- E = Exponentials
- M = Multiplication (same weight as Division)
- D = Division (same weight as Multiplication)
- A = Addition (same weight as Subtraction)
- S = Subtraction (same weight as Addition)
Now let's talk about why we order in this way.
- P = Parentheses (also known as Brackets)
We use brackets to group terms - they let us know that a group of terms needs to be calculated first before moving on.
- E = Exponentials
Exponentials are a combination of parentheses (we're doing an operation that is grouped) and multiplication (a certain number being repeatedly multiplied).
- M = Multiplication (same weight as Division)
- D = Division (same weight as Multiplication)
Multiplication and Division are essentially the same operation but are inverses of each other, and so they carry the same weight in the Order of Operations. Unlike Parentheses and Exponentials, they aren't specifically grouped and so come after those two.
- A = Addition (same weight as Subtraction)
- S = Subtraction (same weight as Addition)
Addition and Subtraction are essentially the same operation bur are inverses of each other, and so just like with Multiplication and Division above, they carry the same weight in the Order of Operations.
- Read from Left to Right
The last rule, which isn't part of the acronym, is to read the expression being evaluated from Left to Right. It helps to clarify something like this:
If we do the division first, we get
If we do the multiplication first, we get
Which should we do first? The Order of Operations says it doesn't matter!
This is where the rule of reading Left to Right comes into play. We do the division first and the multiplication second to get to 6.
Where might you have come from?
Fact-orials Index
Operations:
Where might we go?
Operations:
Operations with different kinds of numbers:
- Addition, Subtraction, and Whole Numbers - Practice Problems
- Multiplication, Division, and Whole Numbers
- Addition, Subtraction, and Integers - Practice Problems
I noticed that the 'Answer' and the 'Analysis' sections contain the exact same paragraph. I'd say that you can break it up into two parts and have one in the 'Answer' section and one in the 'Analysis' section, just to keep the reader from having to go over the same paragraph two times.
ReplyDeleteAlso, would a full stop work better than a colon here, especially since you have that paragraph in between 'Analysis' and the explanation of the acronym?
"See below for the acronym meaning: "
Great couple of points - I've edited appropriately. Thanks for the suggestions!
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