# 5x5-5÷5+5=?

#### giorgiopin

##### New member
Hello. I came across the above sum, the other day, in one of those Facebook puzzle posts. I don't normally look at this sort of thing, but I had a quick glance at this one and am still trying to get to the bottom of things. The way I was taught, the answer to this sum is 9. But there appears to be another school of thought where the answer is 29. At first, I thought it was a wind up, but it seems there are some genuine people, teachers even, who insist the answer is 29. Can someone please explain how there can be two schools of thought to solving this sum. If I do the calculation on one of my personal calculators or on the Windows 10 calculator, the answer is 9. Obviously!! But if I do the calculation on my mobile phone, the answer is in fact 29!! How can this be? I find this very worrying. Can someone please explain how this can be and how long ago the second method came about and which method came first and who, on earth, is right etc etc. Many thanks.

#### Subhotosh Khan

##### Super Moderator
Staff member
Hello. I came across the above sum, the other day, in one of those Facebook puzzle posts. I don't normally look at this sort of thing, but I had a quick glance at this one and am still trying to get to the bottom of things. The way I was taught, the answer to this sum is 9. But there appears to be another school of thought where the answer is 29. At first, I thought it was a wind up, but it seems there are some genuine people, teachers even, who insist the answer is 29. Can someone please explain how there can be two schools of thought to solving this sum. If I do the calculation on one of my personal calculators or on the Windows 10 calculator, the answer is 9. Obviously!! But if I do the calculation on my mobile phone, the answer is in fact 29!! How can this be? I find this very worrying. Can someone please explain how this can be and how long ago the second method came about and which method came first and who, on earth, is right etc etc. Many thanks.
5x5-5÷5+5 = 25 - 5÷5 + 5 = 25 - 1 + 5 = 29
There are no "separate" schools of thought - only the way "some" calculators handle the "input" operation. My calculator (Casio - 30X) gives the correct answer.

Now, If the problem was:

[{(5x5) - 5} ÷ 5] + 5 = 9

Insertion of these brackets forced the operation to be conducted in the order operators were inserted (instead of conducting multiplication and/or division ahead of addition and/or subtraction.

Without those parentheses, 29 is the correct answer.

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#### pka

##### Elite Member
Hello. I came across the above sum, the other day, in one of those Facebook puzzle posts. I don't normally look at this sort of thing, but I had a quick glance at this one and am still trying to get to the bottom of things. The way I was taught, the answer to this sum is 9. But there appears to be another school of thought where the answer is 29. At first, I thought it was a wind up, but it seems there are some genuine people, teachers even, who insist the answer is 29. Can someone please explain how there can be two schools of thought to solving this sum. If I do the calculation on one of my personal calculators or on the Windows 10 calculator, the answer is 9. Obviously!! But if I do the calculation on my mobile phone, the answer is in fact 29!! How can this be? I find this very worrying. Can someone please explain how this can be and how long ago the second method came about and which method came first and who, on earth, is right etc etc.
Have a look HERE. I simply copies & paste into WolframAlpha.
It followed the rule of doing multiplication and divisions first then addition or subtractions after thoses.

#### giorgiopin

##### New member
5x5-5÷5+5

= 25 - 5÷5 + 5

= 25 - 1 + 5 = 29

There are no "separate" schools of thought - only the way "some" calculators handle the "input" operation. My calculator (Casio - 30X) gives the correct answer.

Now, If the problem was:

[{(5x5) - 5} ÷ 5] + 5 = 9

Insertion of these brackets forced the operation to be conducted in the order operators were inserted (instead of conducting multiplication and/or division ahead of addition and/or subtraction.

Without those parentheses, 29 is the correct answer.
I am afraid there are. Everyone I speak to knows the answer as 9. Maybe that is because we were taught in London, I don't know. Are you saying that your calculator is right and any calculator that says 9 (including Windows 10) is wrong? Mmmm. I would prefer to know what is going on.

#### tkhunny

##### Moderator
Staff member
If I just enter the keystrokes, left-to-right, in my Windows 7 Enterprise V6.1 calculator, I get 29.

5
x
5
- (This subtraction tells the calculator to go ahead and perform the multiplication - giving the intermediate value 25)
/
5
+ (This addition tells the calculator to go ahead and perform the division, followed by the subtraction - giving the intermediate value 24)
5
[Enter] (and we're done)
29

If I enter that line in my primary programming language, evaluating strictly right to left, I get

5*5-5/5+5
5*5-5/10
5*5-(1/2)
5*(9/2)
45/2

If I boldly perform operations as I encounter them, left to right, we see:

5*5-5/5+5
25 - 5/5+5
20/5+5 (This has clearly performed subtraction before division - a violation of the convention to which PKA was referring)
4+5
9

In any case, There is NO substitute to knowing what you are doing. The keys you press on a calculator may make a difference. The intermediate values you encounter along your way will absolutely make a difference. It helps to have a convention. Otherwise, there is only very difficult communication. We can't be saying 9 in the UK and 29 in the US for the very same expression, well, unless the US owes $29 trillion USD. I think we would gladly pay$9 trillion USD to expunge the debt.

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#### Subhotosh Khan

##### Super Moderator
Staff member
I am afraid there are. Everyone I speak to knows the answer as 9. Maybe that is because we were taught in London, I don't know. Are you saying that your calculator is right and any calculator that says 9 (including Windows 10) is wrong? Mmmm. I would prefer to know what is going on.
What brand of calculator is giving you the answer "9"?

#### giorgiopin

##### New member
What brand of calculator is giving you the answer "9"?
Does it matter? Casio, in this instance but I suspect there are a whole bunch of others. I also stated that W10 comes up with 9 as well.

#### giorgiopin

##### New member
I note that there is an option in the Windows calculator to switch it to, 'Scientific', mode, giving 29. 'Standard', mode gives 9.
I don't want to argue whether it's 9 or 29. I'm trying to find out what's going on. Clearly, no one seems to know.

#### tkhunny

##### Moderator
Staff member
Does it matter? Casio, in this instance but I suspect there are a whole bunch of others. I also stated that W10 comes up with 9 as well.
Yes, it does matter. But, it also matters EXACTLY what keys you pressed and in what order.

HP 12C

5[ENTER]5*5-5/5+ gives 9
5[ENTER]5*5[ENTER]5/-5+ gives 29

Same calculator. Different attitude.

What keystroke tells the calculator to do what? This is the question.

#### tkhunny

##### Moderator
Staff member
Clearly, no one seems to know.
Why is that clear? Which convention is followed?

If you just want to add up a bunch of numbers, then Standard Mode is fine.
If you want to evaluate a more complicated expression, you should use Scientific Mode.

#### giorgiopin

##### New member
Yes, it does matter. But, it also matters EXACTLY what keys you pressed and in what order.

HP 12C

5[ENTER]5*5-5/5+ gives 9
5[ENTER]5*5[ENTER]5/-5+ gives 29

Same calculator. Different attitude.

What keystroke tells the calculator to do what? This is the question.
It does not matter. I told you Casio (or a bunch of others) anyway - what's your point? I don't know what you mean with your other point.....Obviously I'm pressing the same keys every time in the same order, just different answers.

#### giorgiopin

##### New member
Why is that clear? Which convention is followed?

If you just want to add up a bunch of numbers, then Standard Mode is fine.
If you want to evaluate a more complicated expression, you should use Scientific Mode.

I don't know what's going on here. I said there were two schools of thought. Someone replied there aren't. Now you're saying, 'which convention?' I don't know anything about, 'Standard Mode' or 'Scientific Mode'. If someone would have read my first post and volunteered that information in the first place, we would have saved a lot of time.

#### tkhunny

##### Moderator
Staff member
It does not matter. I told you Casio (or a bunch of others) anyway - what's your point? I don't know what you mean with your other point.....Obviously I'm pressing the same keys every time in the same order, just different answers.
Nope. Not obvious. You pushed the same keys but used a different mode, and got a different result. One can do this in one's brain, too. Without an explicit understanding of ALL the intermediate values, there isn't anything obvious about it.

#### giorgiopin

##### New member
Nope. Not obvious. You pushed the same keys but used a different mode, and got a different result. One can do this in one's brain, too. Without an explicit understanding of ALL the intermediate values, there isn't anything obvious about it.
'Without an explicit understanding of ALL the intermediate values, there isn't anything obvious about it.'

What? All the intermediate values were given. If I say I am getting different results on different calculators, it is obvious I am pressing the same keys in the same order. If I wasn't, it wouldn't be the same sum, would it? That's why it's obvious.

#### tkhunny

##### Moderator
Staff member
You are not understanding. You continue to point out the difference between the 9 and the 29. That is not in question.

5*5-5/5+5
25-5/5+5 <== That 25 is an intermediate value.
25-1+5 <== That 1 is an intermediate value because we did division before subtraction, according to a standard convention.
24+5 <== That 24 is an intermediate value.
29

5*5-5/5+5
25-5/5+5 <== Again with the 25.
20/5+5 <== This time, we have a 20. Didn't see that, before. We did subtraction before division. This violates a standard convention.
4+5 <== And a 4. That's new.
9

That is ALL the intermediate values. This is how we see EXACTLY what is going on. The final result is just not sufficient to discern the matter.

The first version requires the calculator to store some intermediate values and to suspend temporarily some operations.
The second version doesn't store anything and just ploughs through as it encounters values or operations.

Which one is right? Well, if you go with the most standard convention, 29. If you're doing something else, there is no reason 9 can't be correct. Like I said earlier, my primary programming language would produce 22.5. Is that wrong? No. One must be sure one knows what one is doing. If you know your simple calculator doesn't follow the most standard convention, then you will know that it will produce 9. So? That may or may not be the desired result. One last time, there is no substitute for knowing what you are doing. Calculators do not provide mandates. They require some human to understand what it is they are providing. It has always been this way.

#### Subhotosh Khan

##### Super Moderator
Staff member
It does not matter. I told you Casio (or a bunch of others) anyway - what's your point? I don't know what you mean with your other point.....Obviously I'm pressing the same keys every time in the same order, just different answers.
If you execute following "button" Pushing - you will get:

5 * 5 ENTER (or =) -> display 25

- 5 ENTER (or =) -> display 20

/ 5 ENTER (or =) -> display 4

+ 5 ENTER (or =) -> display 9

#### giorgiopin

##### New member
If you execute following "button" Pushing - you will get:

5 * 5 ENTER (or =) -> display 25

- 5 ENTER (or =) -> display 20

/ 5 ENTER (or =) -> display 4

+ 5 ENTER (or =) -> display 9

I get 9 by only pressing ENTER or = once, at the end. Not multiple times as you have done.

#### topsquark

##### Full Member
If you are looking on how to do this on a calculator then yes, the order of the keystrokes matter. But 29 is the actual answer and you need to learn how to do that, not decide on which calculator is better. The best way to do this kind of problem is to sit down and work it out using PEDMAS or one of its kin.

-Dan

#### giorgiopin

##### New member
You are not understanding. You continue to point out the difference between the 9 and the 29. That is not in question.

5*5-5/5+5
25-5/5+5 <== That 25 is an intermediate value.
25-1+5 <== That 1 is an intermediate value because we did division before subtraction, according to a standard convention.
24+5 <== That 24 is an intermediate value.
29

5*5-5/5+5
25-5/5+5 <== Again with the 25.
20/5+5 <== This time, we have a 20. Didn't see that, before. We did subtraction before division. This violates a standard convention.
4+5 <== And a 4. That's new.
9

That is ALL the intermediate values. This is how we see EXACTLY what is going on. The final result is just not sufficient to discern the matter.

The first version requires the calculator to store some intermediate values and to suspend temporarily some operations.
The second version doesn't store anything and just ploughs through as it encounters values or operations.

Which one is right? Well, if you go with the most standard convention, 29. If you're doing something else, there is no reason 9 can't be correct. Like I said earlier, my primary programming language would produce 22.5. Is that wrong? No. One must be sure one knows what one is doing. If you know your simple calculator doesn't follow the most standard convention, then you will know that it will produce 9. So? That may or may not be the desired result. One last time, there is no substitute for knowing what you are doing. Calculators do not provide mandates. They require some human to understand what it is they are providing. It has always been this way.
5x5-5÷5+5=? How two sets of people can come up with different answers to this simple sum is, in fact, in question for me. Yes, I am aware that people are making calculations using different protocols. Maybe I have come to the wrong forum. My point, from the opening post, was that there is more than one way to solving the sum, ending with conflicting results. I want to know how this has come about etc. There is a multitude of us who hold the answer to be 9. It is nothing to do with us forgetting, or being mistaken etc. It is the way we were taught. We weren't taught about PEDMAS or such (I only heard of it this weekend when coming across this issue). The way we were taught: if you had an answer of 29, the sum would have been written (5x5)-(5÷5)+5=29. I have friends and family all over the world. I have not asked everyone but all the people I have asked say 9, no exception.

I go back to the beginning.....How can this be? I find this very worrying. Can someone please explain how this can be and how long ago the second method came about and which method came first and who, on earth, is right etc etc.

I get what you mean about intermediate values. Also, from what I have found out myself, this PEDMAS has been around for a very long time.

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#### giorgiopin

##### New member
If you are looking on how to do this on a calculator then yes, the order of the keystrokes matter. But 29 is the actual answer and you need to learn how to do that, not decide on which calculator is better. The best way to do this kind of problem is to sit down and work it out using PEDMAS or one of its kin.

-Dan
The calculator is not the issue. Please see previous posts..