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# Intro to order of operations

This example shows the steps and clarifies the purpose of order of operations: to have ONE way to interpret a mathematical statement. Created by Sal Khan.

## Want to join the conversation?

• Did mathematicians choose arbitrarily the particular order of operations or there is an innate logic into it? Why did not they opt for left to right operations or exponents first then addition/subtraction, subsequently parentheses, finally multiplication/division or whatever, provided that a stable pattern was to be followed?
• Yes, Mathematicians just chose to do it the way it's done. Everyone had to agree on some format, so that everyone would always get the same answer when they did the same problem. Here's a link to some information you might find interesting:
http://mathforum.org/dr.math/faq/faq.order.operations.html
• I have always thought that within the same level of priority that the specific order (left to right, right to left, jumping around, etc.) wasn't important. At Sal says that you have to do things from left to right when you have multiple operations at the same level. At this point in the video, the problem is: 10 x 4 / 2 - 5 x 6

Sal solves left to right: 40 / 2 - 5 x 6 = 20 - 30 = -10

But if I don't do it in the same order I get the same answer: 10 x 2 - 5 x 6 = 20 - 30 = -10

Thoughts?
• This confused me when Sal first said it too, but it can make a difference. For example, if the question were rearranged to:

10 / 2 x 4 - 5 x 6

Then you can't do 2 x 4 first i.e:

10 / (2 x 4) - 5 x 6

Otherwise you would get:

10 / 8 - 5 x 6

1.25 - 30

-28.75

Similarly, in the example at , you can not do:

1 + 2 - 3 + 4 - 1 = (1 + 2) - (3 + 4) - 1 = 3 - 7 - 1 = -5
• The practice questions expect you to accept that a fraction bar is the equivalent of putting parentheses around the whole numerator and the whole denominator. Did Sal cover this in either of the order of ops vids? I can't find it but maybe I missed it. If not, would be a good addition to the vids.
• I'm not sure that he covered this in the video, but when you have multiple operations over a fraction bar, with more operations or a single number underneath, the implication is that you are dividing the entire operation by the number underneath the fraction bar (fractions are essentially saying "the numerator divided by the denominator"). You cannot divide the operation until you have solved it, of course, so it is implied in the layout of the equation itself that you need to solve the numerator and/or denominator before dividing.
• I have been taught BODMAS which is
Bracket
Of
Division
Multiplication
Subtraction .
This is mostly the same as brackets and parentheses are the same and exponents is a different thing but then am I supposed to do multiplication first or division ??
I have been taught that I have to divide first but here they have explained something else . What do I have to do ?
All help appreciated😊
• The way I have been taught is with PEMDAS; parenthesis, exponent, multiplication, division, addition, and subtraction. When it comes to multiplication and division, you do whichever comes first in a left to right order, same goes for addition and subtraction.
• i'm a bit confused... :?
I live in england and my teacher told us to do:
Brackets (parentheses)
Indices (exponents)
Division
Multiplication
Subtraction
...so i dont do add and sub in the same group and if they are together go from left to right coz i would do the addition then the subtraction... is it different over in the US???? plz i am going mad thinking about it, which one is right????????
• PEMDAS = BIDMAS = BODMAS

BIDMAS brackets (parentheses); indices (exponents); div/mult (mult/div); add/sub

BEDMAS brackets (parentheses); exponents; div/mult (mult/div); add/sub

They're all the same way of order of operations. It's just that people use other words to tell the same thing.
• Could you do order of operations with fractions?
• You can and should do it with everything from integers to decimals to fractions.
• PEMDAS is what it would be for short
• Uhm hi uhh I wanna know, uhh what is the meaning of "Exponents" It is a hard word to remember and spell. Can't they just eliminate it?
Thanks, Sal
- Lexi! <3
• Hi Lexi! I am not Sal, but I can still help you understand exponents if you want to.
Exponents are numbers like this: 10⁵
The big number is the base while the smaller number floating is the number of times you multiply a base by itself. For example, in the exponent "10⁵", the expanded sentence is 10*10*10*10*10, which is 100,000. A trick only in exponents when 10 is the base is the number of 0's in the value is the small number. Like in the example, 10⁵, 5 is the small number or the exponent. So there will be 5 0's in the answer, 100,000. in exponents when 2 is the base, you just double the number the amount of times the small number, or the exponent is. For example, if the problem is 2⁵, I double 2, 4 times to get 32 (The first time doesn't count because 2¹ is just 2). also if 1 is the base, no matter what the small number is, the answer is always 1. and if the small number is 1, then the answer or value is always the base.
Hope this helps!