9 - 3 / 1/3 +1 =?

After doing the math and following order of operations I learned when I was in school I got the answer -1.

I did 3 / 1/3. Since it is a fraction we have to flip the fraction and multiply it by 3. This then gives me 9.

Next I did 9 + 1 and got the answer 10.

For the last step I did 9 - 10 and got my final answer as -1.

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This is the same answer I came up with.

The problem you’ve come across there is to strictly follow BODMAS without treating addition and subtraction (and possibly multiplication and division) with equal precedence - meaning one should not be solved before the other and instead should just be solved left to right.

Another way to think about subtraction is that you’re actually adding a negative number. So 9 - 9 + 1 is really 9 + (-9) + 1.

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Thank you for the feedback! I appreciate it! I Now I understand more and will see a problem like this in a different lens.

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This is where I find it all interesting and look forward to hearing what Ben says.

I see valid arguments for all three answers so far 1, 9 and -1

And at a minimum it proves you have to be careful when writing these things down and be aware of the audience that may be using it, as well, if you are using it in code, how a computer will see it…

Never mind that it doesn’t even include some multiplication in there to add further complexities.

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Are those answers really valid?

Take a look at @Donlod’s answer. The fraction, 1/3, has got priority over / and ÷ respectively.

3 / (1/3) = 9

There was a reason why Ben used / and ÷. He used / to indicate a fraction, and ÷ to indicate a “normal” division. As @garypettie said, maths puzzles are intentionally hard to read so people get confused. With the parentheses, everything would be clear.

When writing code, e.g. for shaders, I often use “unnecessay” parentheses to increase the redability to avoid creating a puzzle for future me.

Nina - I said valid arguments :wink:

Remember Ben says the question is almost invalid with not enough information in it…

You (and I getting to 1) made the assumption the third gets priority and is done first…
Type it into a calculator with no brackets and ints only, so no pre division, you’ll get 9
If you were taught (and even BODMAS does say) addition before subtraction you get to -1.

A computer and a compiler with it’s own rules will get the same answer every time and we can twist the equation to get the answer we expect…
Throw an unclear equation to the real world you may expect different answers from different people…

Oops, you are right. I actually meant arguments.

Type it into a calculator with no brackets and ints only, so no pre division, you’ll get 9

It’s time again for my good old friend CASIO. :slight_smile:

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The Casio strikes again! :wink:

I got out as result one.

I think I have learned that the fraction 1/3 must not be included in the total calculation, but always has priority in the calculation. That’s why it says
9-3/0.333_+1=
Then point calculation before line calculation
9-9+1=
And then the addition and subtraction
0+1=1

I’ll see what’s right.

A slighly suspicious 1 is what i get…

Well I also get 1 if it’s

9 - ( 3 / ( 1/3 ) ) + 1

but if you do it step by step without the priority of operations you’d get

nine, minus three, divided by one third, plus one

so… 19?

It really sucks when you need to complete a “mathematical skill question” to get a prize or something and you can’t trust the guys submitting the problem to you know about priority of operations

And yeah, agree with others in the thread, whenever I’ve had to use it in code I never relied on the built in priority of operations, I just threw superfluous parentheses everywhere. Bonus points if the environment lets me add line breaks without it meaning something

9 - (
  3 / (
    1 / 3
  )
) + 1

This looks silly now but when instead of 9 it’s stuff like get_user_karma_points($current_users[$current_index], 'weekly') it helps

I too came to this answer, I definitely understand there being multiple ways to solve, and like Ben says in the video, its ambiguous for a reason to start discussion. How about we all give our answer in terms of absolute value? Then we’re all correct by saying the value would be one hahahah

Got 1 as well.

9- 3÷ 1/3 +1
= 9- (3/1) ÷(1/3)+1
= 9- (3÷1)/(1÷3)+1
= 9-(3)/(1/3)+1
=9-9+1
=1

My answer is: 1

9 - 3 / ( 1/3 ) + 1
= 9 - 9 + 1
= 1

I also arrived at an answer of 1.

First I put parens around the ‘three divided by one third’ part.
Then I converted one third to 0.333 in my head. (‘because it is’)
Then I knew that three divided by 0.333 would be like multiplying by 3 (oh, memories…)
So then the equation became:

9 - 9 + 1 = ?

Nine minus nine is zero. Added one. Got the answer.

Like a few before me I assumed that I could write the equation down as the following:
9 - 3 / 1 / 1 / 3 + 1 which leads to 9.
The correct notation would be 9 - 3 / 1 / (1 / 3) + 1 which lead to 1.

At school I learned a mnemonic -sentense- to remember the precedence of all maths equations.

  • " M eneer V an D alen W acht O p A ntwoord"

first Powers(M), then Multiply(V), then Divide(D), then Square Root(W), then Addition(O) and finally Subtract(A).

But that’s many years ago, now it’s more about writing math more precisely, using ‘()’.

With this I got 9 as answer.

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That’s cool. I never really thought about the other mnemonics used in other languages. Did Mr Van Dalen ever get his answer, or is he still waiting?! :smiley:

No!, The answer lies in the correct calculation. :wink:
But I see the introduction of BODMAS. But that a difficult thing to remember. Which resembles to me as a assembly instruction …

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