# Equation: Order of operations
**URL:** https://boards.straightdope.com/t/equation-order-of-operations/1012088
**Category:** Factual Questions
**Tags:** science-math
**Created:** [December 24, 2024, 2:38am UTC](https://boards.straightdope.com/t/equation-order-of-operations/1012088 "2024-12-24T02:38:25Z")
**Posts on this page:** 20
**Page:** 1
### Author:  [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)
#### Post date: [December 24, 2024, 2:38am UTC](https://boards.straightdope.com/t/equation-order-of-operations/1012088/1 "2024-12-24T02:38:25Z")
6 ÷ 2(1+2)
I would solve it like this:
- 6 ÷ 2(3)
- 6 ÷ 6
- = 1
The calculator on my iPhone solves it like this:
- (6 ÷ 2) x 3
- 3 x 3
- = 9
PEMDAS: Parentheses, Exponent, Multiplication, Division, Addition, Subtraction.
So:
- Parenteses = 1 + 2 = 3
- (No exponents)
- Multiplication - 2 x 3 = 6
- Division = 6 ÷ 6 = 1
Am I right, or is my phone right?
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### Author:  [@beowulff](https://boards.straightdope.com/u/beowulff)
#### Post date: [December 24, 2024, 2:40am UTC](https://boards.straightdope.com/t/equation-order-of-operations/1012088/2 "2024-12-24T02:40:05Z")
What makes you think that the iPhone calculator knows anything about the order of operations?
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### Author:  [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)
#### Post date: [December 24, 2024, 2:40am UTC](https://boards.straightdope.com/t/equation-order-of-operations/1012088/3 "2024-12-24T02:40:48Z")
I would assume people much smarter than I am wrote the program.
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### Author:  [@Seanette](https://boards.straightdope.com/u/Seanette)
#### Post date: [December 24, 2024, 2:47am UTC](https://boards.straightdope.com/t/equation-order-of-operations/1012088/4 "2024-12-24T02:47:42Z")
If I recall high school math classes correctly (it’s been about 40 years so no guarantee 🙂 ), you’re correct and your iPhone is exhibiting artificial unintelligence.
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### Author:  [@Princhester](https://boards.straightdope.com/u/Princhester)
#### Post date: [December 24, 2024, 2:48am UTC](https://boards.straightdope.com/t/equation-order-of-operations/1012088/5 "2024-12-24T02:48:46Z")
The calculator is correct.
You are solving 6 divided by (2 x (1+2)). The equation does not say that the 6 is divided by the (1+2).
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### Author:  [@ASL\_v2.0](https://boards.straightdope.com/u/ASL_v2.0)
#### Post date: [December 24, 2024, 2:48am UTC](https://boards.straightdope.com/t/equation-order-of-operations/1012088/6 "2024-12-24T02:48:53Z")
Multiplication is division. Addition is subtraction. PEMDAS is really PEMA.
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### Author:  [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)
#### Post date: [December 24, 2024, 2:49am UTC](https://boards.straightdope.com/t/equation-order-of-operations/1012088/7 "2024-12-24T02:49:01Z")
> [@Johnny\_L.A](#):
>
> 6 ÷ 2(1+2)
I just plugged the equation into my (Safari) search bar, and it also says 9.
> [@Princhester](#):
>
> The equation does not say that the 6 is divided by the (1+2).
The equation says it is divided by the product of 2 x 3.
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### Author:  [@Northern\_Piper](https://boards.straightdope.com/u/Northern_Piper)
#### Post date: [December 24, 2024, 2:50am UTC](https://boards.straightdope.com/t/equation-order-of-operations/1012088/8 "2024-12-24T02:50:24Z")
The purpose of parentheses is to indicate: « do this first ».
Once you do that step the parentheses are done and then it’s a division followed by a multiplication.
No need to add parentheses to (6 / 2), because multiplication and division are done in the order of the equation.
So, 6 / 2 \* 3 = 9
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### Author:  [@Princhester](https://boards.straightdope.com/u/Princhester)
#### Post date: [December 24, 2024, 2:50am UTC](https://boards.straightdope.com/t/equation-order-of-operations/1012088/9 "2024-12-24T02:50:49Z")
We can all agreed that the (1+2) is just 3. This is not controversial.
Now write it like this
6 ÷ 2 x 3
Why do you think you would do the 2 x 3 first?
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### Author:  [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)
#### Post date: [December 24, 2024, 2:51am UTC](https://boards.straightdope.com/t/equation-order-of-operations/1012088/10 "2024-12-24T02:51:16Z")
> [@Princhester](#):
>
> Why do you think you would do the 2 x 3 first?
Because M comes before D in PEMDAS.
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### Author:  [@Telemark](https://boards.straightdope.com/u/Telemark)
#### Post date: [December 24, 2024, 2:51am UTC](https://boards.straightdope.com/t/equation-order-of-operations/1012088/11 "2024-12-24T02:51:49Z")
Which is why it isn’t taught like that anymore.
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### Author:  [@Princhester](https://boards.straightdope.com/u/Princhester)
#### Post date: [December 24, 2024, 2:52am UTC](https://boards.straightdope.com/t/equation-order-of-operations/1012088/12 "2024-12-24T02:52:02Z")
> [@Johnny\_L.A](#):
>
> The equation says it is divided by the product of 2 x 3.
No it doesn’t. There is no rule that due to the convention of leaving out the implied “x” it means that the “x” is prioritised.
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### Author:  [@ASL\_v2.0](https://boards.straightdope.com/u/ASL_v2.0)
#### Post date: [December 24, 2024, 2:52am UTC](https://boards.straightdope.com/t/equation-order-of-operations/1012088/13 "2024-12-24T02:52:45Z")
And as I said, multiplication is not really before division in the OOO, it’s equivalent to it. Thus the operations are performed literally in the order they appear. Like the calculator says.
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### Author:  [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)
#### Post date: [December 24, 2024, 2:53am UTC](https://boards.straightdope.com/t/equation-order-of-operations/1012088/14 "2024-12-24T02:53:58Z")
> [@Telemark](#):
>
> Which is why it isn’t taught like that anymore.
Well, I wasn’t notified!
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### Author:  [@Snarky\_Kong](https://boards.straightdope.com/u/Snarky_Kong)
#### Post date: [December 24, 2024, 2:54am UTC](https://boards.straightdope.com/t/equation-order-of-operations/1012088/15 "2024-12-24T02:54:38Z")
How many times can we do this?
Both are fine. It’s just a convention, not a law of mathematics. I prefer your answer, but your reasoning is incorrect.
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### Author:  [@Princhester](https://boards.straightdope.com/u/Princhester)
#### Post date: [December 24, 2024, 2:55am UTC](https://boards.straightdope.com/t/equation-order-of-operations/1012088/16 "2024-12-24T02:55:58Z")
It was in Memo 323.45 of 1989 Annex B at Chapter 6 section 5 paragraph 7(xii)(a) at the third dot point. On page 1248.
If you aren’t going to keep up with the Memos, you really can’t blame us.
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### Author:  [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)
#### Post date: [December 24, 2024, 2:59am UTC](https://boards.straightdope.com/t/equation-order-of-operations/1012088/17 "2024-12-24T02:59:49Z")
Is it in a filing cabinet that has a sign that says ‘Beware of the leopards’?
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### Author:  [@TriPolar](https://boards.straightdope.com/u/TriPolar)
#### Post date: [December 24, 2024, 3:11am UTC](https://boards.straightdope.com/t/equation-order-of-operations/1012088/18 "2024-12-24T03:11:03Z")
What does your phone say it uses for the order of operations? If your phone does it the way it says it does then it’s right.
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### Author:  [@Stranger\_On\_A\_Train](https://boards.straightdope.com/u/Stranger_On_A_Train)
#### Post date: [December 24, 2024, 3:15am UTC](https://boards.straightdope.com/t/equation-order-of-operations/1012088/19 "2024-12-24T03:15:36Z")
> [@Telemark](#):
>
> Which is why it isn’t taught like that anymore.
This is why Polish Notation (or better yet, Reverse Polish Notation) is superior to PEMDAS; no ambiguity because the “order of operations” is defined by the order in which operations are applied.
Stranger
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### Author:  [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)
#### Post date: [December 24, 2024, 3:21am UTC](https://boards.straightdope.com/t/equation-order-of-operations/1012088/20 "2024-12-24T03:21:51Z")
> [@beowulff](#):
>
> What makes you think that the iPhone calculator knows anything about the order of operations?
I can’t speak to iPhones but my Android gets PEMDAS. Notably, it does not resolve each button push before going on to the next bit (well, actually it does but it re-evaluates the answer as the equation is typed in so, 1+2 and you see 3…when you add x 3 it resolves to 7). The whole equation is evaluated to produce an answer. (NOTE: This is the built in Android calculator and it is set at its most basic function and not scientific mode or whatever else it has).
[ ](https://i.imgur.com/Bgs464Y.png)
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