# calculators giving different answers
**URL:** https://boards.straightdope.com/t/calculators-giving-different-answers/469325
**Category:** Factual Questions
**Created:** [October 24, 2008, 9:34am UTC](https://boards.straightdope.com/t/calculators-giving-different-answers/469325 "2008-10-24T09:34:04Z")
**Posts on this page:** 20
**Page:** 1
### Author:  [@shijinn](https://boards.straightdope.com/u/shijinn)
#### Post date: [October 24, 2008, 9:34am UTC](https://boards.straightdope.com/t/calculators-giving-different-answers/469325/1 "2008-10-24T09:34:04Z")
are the answers the same for these two questions?
8/2\*(5-3)
vs
8/2(5-3)
two different calculators gave conflicting answers to the second question.
---
### Author:  [@Jragon](https://boards.straightdope.com/u/Jragon)
#### Post date: [October 24, 2008, 9:39am UTC](https://boards.straightdope.com/t/calculators-giving-different-answers/469325/2 "2008-10-24T09:39:52Z")
It’s probably interpreting the latter as 8/[2\* (5-3)], as a general rule it’s best to use signs rather than parenthesis with calculators as they can be rather finicky like that, in my experience at least.
ETA: An even BETTER way to ensure you’re getting the answer you want is to write it as
(8/2)(5-3) or (8/2) \* (5-3) to be absolutely certain.
---
### Author:  [@chrisk](https://boards.straightdope.com/u/chrisk)
#### Post date: [October 24, 2008, 9:41am UTC](https://boards.straightdope.com/t/calculators-giving-different-answers/469325/3 "2008-10-24T09:41:44Z")
How are you punching the second one in? I’d sort of expect a calculator to drop the previous part if you don’t punch an operation button, and thus just give you (5-3)
---
### Author:  [@Jragon](https://boards.straightdope.com/u/Jragon)
#### Post date: [October 24, 2008, 9:43am UTC](https://boards.straightdope.com/t/calculators-giving-different-answers/469325/4 "2008-10-24T09:43:49Z")
> [@chrisk](#):
>
> How are you punching the second one in? I’d sort of expect a calculator to drop the previous part if you don’t punch an operation button, and thus just give you (5-3)
That actually brings up another question:
Are you using a graphing calculator (i.e. a higher end Casio, or a TI-84/89 etc), or a scientific calculator, or are you using a standard calculator? The advice above was assuming a calculator that handles parenthesis like a TI-84 for example.
---
### Author:  [@shijinn](https://boards.straightdope.com/u/shijinn)
#### Post date: [October 24, 2008, 9:53am UTC](https://boards.straightdope.com/t/calculators-giving-different-answers/469325/5 "2008-10-24T09:53:37Z")
i keyed it in exactly as shown. it’s a Casio (i forget the model, but it’s new) where you’re supposed to key in the entire question before you get an answer.
so “2” is simply wrong right? i was told it is correct and the calculator shown as prove. :dubious:
---
### Author:  [@Mangetout](https://boards.straightdope.com/u/Mangetout)
#### Post date: [October 24, 2008, 9:57am UTC](https://boards.straightdope.com/t/calculators-giving-different-answers/469325/6 "2008-10-24T09:57:54Z")
It’s not unheard of for calculators to operate differently from each other - I remember there being two distinct methods for using the percent button on different brands.
I also remember in one of the first maths lessons at college, the teacher told us to perform some specific sequence of operations to work out whether we had a calculator that was compliant with the expected standard for the course. The pupils who had a non-standard calculator were taken outside and shot - kids have it easy these days.
---
### Author:  [@Derleth](https://boards.straightdope.com/u/Derleth)
#### Post date: [October 24, 2008, 10:22am UTC](https://boards.straightdope.com/t/calculators-giving-different-answers/469325/7 "2008-10-24T10:22:15Z")
> [@mangetout](#):
>
> the pupils who had a non-standard calculator were taken outside and shot - kids have it easy these days.
Down with Fascist CORDIC!
(Not all CORDIC, only Fascist CORDIC.)
---
### Author:  [@DSYoungEsq](https://boards.straightdope.com/u/DSYoungEsq)
#### Post date: [October 24, 2008, 11:07am UTC](https://boards.straightdope.com/t/calculators-giving-different-answers/469325/8 "2008-10-24T11:07:52Z")
> [@shijinn](#):
>
> i keyed it in exactly as shown. it’s a Casio (i forget the model, but it’s new) where you’re supposed to key in the entire question before you get an answer.
>
> so “2” is simply wrong right? i was told it is correct and the calculator shown as prove. :dubious:
As a math teacher, I cannot tell you how many times students show me calculator output as “proof” of some obviously incorrect answer, where the issue is one of GIGO (garbage in, garbage out). We are starting our unit in my Algebra II class on quadratic functions, and as such the students are going to be squaring numbers regularly. I have made my standard demonstration of how the TI-83+ will not produce a correct answer if you key in -3^2 when what they want is -3 squared (it’s an order of operations thing). Nevertheless, I know that for the next three weeks, I’ll be shown all sorts of answers where they have done just that, gotten a negative value as the result of squaring something, and when challenged by me as to the validity of that answer, will say that that’s what the calculator said! :smack:
In answer to your question: your original posting is not sufficiently precise to allow us to answer your question. If you are intending to take the fraction 8/2 and multiply it by (5-3), then the answer should be 8 (4\*2 = 8). But if the problem is asking us to divide 8 by the product of 2(5-3), then the answer is, of course, 2 (8 divided by (2 times 2) is equal to 2). The trouble with using the / symbol as a division operator is that, unlike the horizontal fraction bar, you can’t easily tell what is intended to be “under” the bar (in the denominator of the fraction). The calculators are giving different answers based upon how they are handling order of operations. Which one is “correct” depends upon what you really meant by the expression in your OP. 🙂
---
### Author:  [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)
#### Post date: [October 24, 2008, 11:10am UTC](https://boards.straightdope.com/t/calculators-giving-different-answers/469325/9 "2008-10-24T11:10:08Z")
> [@DSYoungEsq](#):
>
> As a math teacher…
Oh. For some reason (well, some obvious reason), I thought you were a lawyer, though one with a marked interest in math.
---
### Author:  [@chrisk](https://boards.straightdope.com/u/chrisk)
#### Post date: [October 24, 2008, 11:24am UTC](https://boards.straightdope.com/t/calculators-giving-different-answers/469325/10 "2008-10-24T11:24:40Z")
Interestingly, I’ve tried the second example on two ‘calculators’ by punching it in one element at a time:
8 / 2 ( 5 - 3 ) =
Both on my Casio scientific fx-250d, and the windows XP scientific calculator mode, I get a result of 4, which puzzled me. At first, I thought that it had dropped off the 8/ and was working 2 \* (5 - 3), but a bit of experimenting showed me that what was actually happening was that it was dropping the 2 and working 8 / (5 - 3)
8 / 8 (5 - 3), 8 / 4 (5 - 3), and 8 / 1 (5 - 3) all gave the same answer of 4.
---
### Author:  [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)
#### Post date: [October 24, 2008, 11:26am UTC](https://boards.straightdope.com/t/calculators-giving-different-answers/469325/11 "2008-10-24T11:26:24Z")
Presumably, your calculator does not take entering quantities in sequence to implicitly denote multiplication, and just ignores all but the last one.
---
### Author:  [@shijinn](https://boards.straightdope.com/u/shijinn)
#### Post date: [October 24, 2008, 12:55pm UTC](https://boards.straightdope.com/t/calculators-giving-different-answers/469325/12 "2008-10-24T12:55:33Z")
> [@DSYoungEsq](#):
>
> … The calculators are giving different answers based upon how they are handling order of operations. Which one is “correct” depends upon what you really meant by the expression in your OP. 🙂
iinm, “8/2(5-3)” was simply intended to be another way to write “8/2\*(5-3)”. perhaps this is the mistake in the first place? or can i blame the calculator for following a different order of operations? especially since it is able to display fractions with the horizontal bar?
oh btw, when i keyed the question in Google it forced the question to display as (8/2)\*(5-3). heh.
---
### Author:  [@CurtC](https://boards.straightdope.com/u/CurtC)
#### Post date: [October 24, 2008, 1:51pm UTC](https://boards.straightdope.com/t/calculators-giving-different-answers/469325/13 "2008-10-24T13:51:34Z")
Works fine for me - I keyed in:
[8][Enter][2][/][5][Enter][3]
---
### Author:  [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)
#### Post date: [October 24, 2008, 2:04pm UTC](https://boards.straightdope.com/t/calculators-giving-different-answers/469325/14 "2008-10-24T14:04:20Z")
> [@Indistinguishable](#):
>
> Oh. For some reason (well, some obvious reason), I thought you were a lawyer, though one with a marked interest in math.
Fermat? Is that you? If so, could you explain that marginal note of yours…
---
### Author:  [@UncleRojelio](https://boards.straightdope.com/u/UncleRojelio)
#### Post date: [October 24, 2008, 2:06pm UTC](https://boards.straightdope.com/t/calculators-giving-different-answers/469325/15 "2008-10-24T14:06:13Z")
[quote=“CurtC, post:13, topic:469325”]
Works fine for me - I keyed in:
[8][Enter][2][/][5][Enter][3][/QUOTE]
Hurray for RPN!!
---
### Author:  [@Chronos](https://boards.straightdope.com/u/Chronos)
#### Post date: [October 24, 2008, 4:48pm UTC](https://boards.straightdope.com/t/calculators-giving-different-answers/469325/16 "2008-10-24T16:48:43Z")
> [@](#):
>
> As a math teacher, I cannot tell you how many times students show me calculator output as “proof” of some obviously incorrect answer, where the issue is one of GIGO (garbage in, garbage out).
Likewise, in physics classes. Except the one I most often encounter is when students are dividing something by 2pi. If they have a diameter as 8, say, and they want to find the radius, they’ll enter 8/2pi, which the calculator then interprets as (8/2)\*pi. It’s gotten to the point that whenever I see an answer that’s off by a factor of almost ten, I ask them if they had parentheses around their (2pi). If they’re off by a factor of _exactly_ ten, of course, it’s usually a matter of someone entering 10[sup]8[/sup] as 10e8.
> [@](#):
>
> Fermat? Is that you? If so, could you explain that marginal note of yours…
The title Esq. (Esquire) after a name usually indicates a lawyer, in the US at least.
---
### Author:  [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)
#### Post date: [October 24, 2008, 5:21pm UTC](https://boards.straightdope.com/t/calculators-giving-different-answers/469325/17 "2008-10-24T17:21:49Z")
> [@DSYoungEsq](#):
>
> I have made my standard demonstration of how the TI-83+ will not produce a correct answer if you key in -3^2 when what they want is -3 squared (it’s an order of operations thing).
WADR if you key in “-3^2” and get -9, then it \*is \*giving you the correct answer, to what you actually keyed in. The students just don’t understand order of operations and key in something different than what they really mean. I mention this because it sounds like you’re criticizing the calculator.
---
### Author:  [@KneadToKnow](https://boards.straightdope.com/u/KneadToKnow)
#### Post date: [October 24, 2008, 5:27pm UTC](https://boards.straightdope.com/t/calculators-giving-different-answers/469325/18 "2008-10-24T17:27:04Z")
> [@Chronos](#):
>
> The title Esq. (Esquire) after a name usually indicates a lawyer, in the US at least.
Perhaps in this case it stands for “E, squared.”
---
### Author:  [@Tenebras](https://boards.straightdope.com/u/Tenebras)
#### Post date: [October 24, 2008, 5:37pm UTC](https://boards.straightdope.com/t/calculators-giving-different-answers/469325/19 "2008-10-24T17:37:58Z")
> [@shijinn](#):
>
> iinm, “8/2(5-3)” was simply intended to be another way to write “8/2\*(5-3)”. perhaps this is the mistake in the first place? or can i blame the calculator for following a different order of operations? especially since it is able to display fractions with the horizontal bar?
>
> oh btw, when i keyed the question in Google it forced the question to display as (8/2)\*(5-3). heh.
I don’t know what iinm means, but the entire first sentence is completely ambiguous to me. What is “8/2(5-3)” supposed to mean? There are two possibilities, either one of which could be intended.
```auto
8
--- * (5-3) = 4*2 = 8
2
```
or
```auto
8 8
----------- = ----- = 2
2*(5 - 3) 2*2
```
I would argue that both of these interpretations are valid, and that the latter is the more likely looking of the two. If you really wanted the expression to be equal to 8, why wouldn’t you write 8\*(5-3)/2?
---
### Author:  [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)
#### Post date: [October 24, 2008, 6:09pm UTC](https://boards.straightdope.com/t/calculators-giving-different-answers/469325/20 "2008-10-24T18:09:50Z")
> [@Tenebras](#):
>
> I don’t know what iinm means
If I’m not mistaken
> [@](#):
>
> but the entire first sentence is completely ambiguous to me. What is “8/2(5-3)” supposed to mean? There are two possibilities…
There is only one correct possibility based on order of operations, the way this is actually written. Your first example is the only way to interpret it and that’s how any programming language would do it (although they need an explicit multiplication symbol). If it had been written as in your second example, the result would be different, but that’s not how it was written.
[Next page](https://boards.straightdope.com/t/calculators-giving-different-answers/469325.md?page=2)