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## MAP Recommended Practice

### Course: MAP Recommended Practice>Unit 17

Lesson 11: Order of operations

# Order of operations example

The order of operations tells us the order to solve steps in expressions with more than one operation. First, we solve any operations inside of parentheses or brackets. Second, we solve any exponents. Third, we solve all multiplication and division from left to right. Fourth, we solve all addition and subtraction from left to right. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• Hello, I had two questions in regards to order of operations. 1. I was wondering where does the order of operations come from? In my limited google research :), I have found that no one really knows this, but we see it being used in history back in the 1500s or so.

2. Is there a mathematical reason why this works? Or, does this just seem to be the historical standard or traditional way to perform equations based on history or precedence?

Thanks!
• i dont know. i'm guessing mathmaticians were finding several different ways to do the same problem and argued over which way is right so they came up with the traditional, modern, Order of Operations.
• Should there be a multiplication sign between the 5 and 4?
• If there is no sign in the question let’s say (6)(5) it be multiplication so the answer is 30
• How come you didn't distribute the negative sign within the parenthesis?
• You have to take care of everything in the parentheses first: 6+10/2
There weren't any variables inside the parentheses, so it could be simplified right to 11, and the negative sign just tells us to subtract that 11. If there were variables involved, then we would need to distribute a negative sign. However, in this case it was just straight subtraction.
Does that help?
• At the end, when there was 28-11+44, wouldn't you add 11 and 44 first because adding comes before subtracting?
• Nope. You do the addition and subtraction in the same step, always moving from left to right and doing the addition/subtraction in the order that you see them.

Here we have: 28 - 11 + 44
See how the subtraction comes first?

You want to work through the all the addition/subtraction in left to right order.

28 - 11 + 44
17 + 44
61

(You might notice that for this problem you get the same answer either way you do it. This doesn't always happen, though, especially when you have more complicated problems.)

Hope this helps!
• When dividing, for example, 8^2bc-b^2? b=4 c=16 how would u do it?
• You can use PEMDAS to solve this expression:
P = parentheses
E = exponents
MD = multiplication / division

First, plug in the given values for b and c
8²bc - b²
b=4, c=16
= 8²⋅4⋅16 - 4²

P = parentheses
There aren't any parentheses, so we can go on to the next step.

E = exponents
Next, calculate the exponents from left to right:
8²⋅4⋅16 - 4²
= 64⋅4⋅16 - 4²
= 64⋅4⋅16 - 16

MD = multiplication / division
Now, going from left to right, work out any multiplication or division:
64⋅4⋅16 - 16
= 256⋅16 - 16
= 4096 - 16

Finally, do any remaining addition or subtraction in left to right order:
4096 - 16
= 4080

So (given the values b=4 and c=16):
8²bc - b² = 4080

Hope this helps!
• hi ,I'm having a doubt that why we we can't follow the order of operations,why can't it be correct when we do it in some other way
• Hello! I have two questions with the order of operations. What if a problem has parentheses, brackets, and exponents? What is the order then?

Thanks!
• If there is both brackets and parentheses, it indicates to do them first in PEMDAS, they just added brackets so they don't have two sets of parentheses. Using the example Kim gave, [15-(3+6)^2] You would add 3+6 first which would add up to 9. Then you would do the exponent next with 9^2 then with that answer you subtract it from 15
• So im stuck in a problem 5(2-4+1)+2/3(6)= and i know im going to end up with -5+2/3(6)= put from there i dont know how to work it out can i get some help??...
• Why does the order have to be the way it is? Why couldn't we just read it left to right? It would make more sense.
• But it wouldn't be the wrong answer if everyone did it that way. It would be right because that would be the rule. PEMDAS is much more confusing.
• 6/2(1+2)
Can anyone clear up this for me?
i have two answers, 1 or 9.
• Using PEMDAS:

6 / 2 (1 + 2)
= 6 / 2 (3)
= 6 / 2 x 3
= 3 x 3
= 9

I'm assuming that you got 1 by solving 6 / (2 x 3)

That would be incorrect because multiplication and division are given the same preference in PEMDAS, so you solve from left to right.

Hope I helped :)