Math problem that creates some confusion

[Kilroy]

6/2(1+2)=?


I see one answer. Some people see another, some debate that the equation is fundamentally flawed and it can't be difinatively resoved.


Anyone have a thought on this one?

[nice_lag]

Dan,

I believe that the confusion is arising from how the equation is actually written; it's difficult to use a word processor sometimes to reflect what you're trying to portray. But the way it is written, we get 6/2*3 = 9. It'd be different if it was written like 6/(2(1+2)) where you would have 6/(2*3) = 1. My 2 cents.

[Chambokl]

Yes Dan the answer is 9..... The problem arise that some science department says to their students to do the 2 * brackets first... they define it like this but it doesn't follow the maths logic... BEDMAS...

[jvincent]

nice_lag has it. The way the equation is writtenis ambiguous because the / can be interpreted differently. It's either a "divide" sign or it could be delimiting the numerator from the denominator.

6÷2(1+2) would have only one interpretation.

[Kilroy]

LOL Yah the correct answer is definately 9. What is amazing that the debate goes on for 22 pages (so far) on another forum I frequent. You folks are just too smart for this kind of thing

[leftylucas]

9 is the answer and on a slightly different plane can anyone explain why all the number answers in the 9s times table add up to nine until you get to 11 and 12 ??? Coincidence?

9*1= 9
9*2= 18 (1 + 8 = 9)
9*3= 27 (2 + 7 = 9)

[sharkshooter]

9 is the answer and on a slightly different plane can anyone explain why all the number answers in the 9s times table add up to nine until you get to 11 and 12 ??? Coincidence?

9*1= 9
9*2= 18 (1 + 8 = 9)
9*3= 27 (2 + 7 = 9)

It doesn't really stop where you think it does...


9*11=99; 9+9=18; 1+8=9
9*12=108; 1+0+8=9
9*13=117; 1+1+7=9
9*14=126; 1+2+6=9
...

[leftylucas]

That is weird for sure, I noticed it years ago when I was testing my boys on their times tables. I sure would like to know how that is.

[leftylucas]

The answer is always 9 unless you are a sandbagger and it somehow becomes a 7

[sharkshooter]

... I sure would like to know how that is.

Your wish is my command. Knock yourself out...

Rule for Divisibility by 9 A number is divisible by 9 if the sum of its digits is divisible by 9. For large numbers this rule can be applied again to the result. In addition, the final iteration will result in a 9. Examples A.) 2,880: 2 + 8 + 8 + 0 = 18, 1 + 8 = 9, so 9| 2,880. B.) 3,564,213: 3+5+6+4+2+1+3=24, 2+4=6, so 9 does NOT divide 3,564,213. Proof The proof for the divisibility rule for 9 is essentially the same as the proof for the divisibility rule for 3. For any integer x written as an· · · a3a2a1a0we will prove that if 9|(a0 + a1+ a2+ a3... + an), then 9|x and vice versa. First, we can state that x = a0 + a1×10 + a2×102 + a3×103... + an×10n Next if we let s be the sum of its digits then s = a0 + a1 + a2 + a3 + ... + an . So x - s = (a0 - a0) + (a1 × 10 - a1) + (a2×102 - a2) + ... + (an×10n - an) = a1(10 - 1) + a2(102 - 1) + ... + an(10n - 1). If we let bk = 10k - 1, then bk = 9...9 (9 occurs k times) and bk ­=9(1…1) and we can rewrite the previous equation as x - s = a1(b1)+ a2(b2)+ ... + an (bn) It follows that all numbers bk are divisible by 9, so the numbers ak×bk are also divisible by 9. Therefore, the sum of all the numbers ak×bk (which is x-s) is also divisible by 9. Since x-s is divisible by 9, if x is divisible by 9, then so is s and vice versa. ================= Of course, you need to know the following to understand the above... Congruences Let m be a natural number including 0, and let a and b be integers. Then a≡ b (mod m) if and only if m|(a-b) and “a is congruent to b modulo m”.

[nice_lag]

OMG... flashbacks from university finals are running through my mind.... Arghhh. please golf season come fast!!

[leftylucas]

Good one Sharkshooter but I still think it was the Mayans who made this possible.

[sharkshooter]

Good one Sharkshooter but I still think it was the Mayans who made this possible.

Perhaps, because,

If you assign numerical values to the letters in the word Mayan, such that a=1, b=2,... , z=26, you get:

m=13, a=1, y=25, a=1, n=14; therefore Mayan = 13+1+25+1+14 = 54

and we all know that 5+4 = 9

[leftylucas]

Exactory, there is no de9ying it, sorry

[Chambokl]

That is why maths is so much fun and so interesting...

[dbleber]

The debate is because it is not always clear if the 6 is the numerator and if the 2(1+2) is the denominator. If so the answer is 1. Otherwise the answer is 9.

You can use this basic scientific Calculator;

http://web2.0calc.com/

[sharkshooter]

The debate is because it is not always clear...

We have rules in mathematics, therefore it is always clear and there can be no debate. In math, there is always one right answer**. That is, of course, the basic difference between mathematics and, say, economics.

In order for the 6 to be the numerator and 2(1+2) to be the denominator (which is required for the answer to be 1), there must be another set of brackets (which has been said above). Without them, the answer must be 9.

Step-by-step, using the rule of order of operations (as has been referred to above), you must have:

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

** unless there are more than one right answer.

For example, what are the square roots of 4? One is 2, that is 2*2=4. What other(s) is(are) there?

To keep it simple, let's stick to real numbers.

[Kilroy]

To keep it simple, let's stick to real numbers.

So statistics cannot be used?

[Chambokl]

Dan... there is only 1 answer and it is 9. It is like golfer who hits out of bound (rehit from the same spot) and drops it at the point of entry and continue.... they are golfing by their own rules... are they wrong or right?

[jvincent]

We have rules in mathematics, therefore it is always clear and there can be no debate. In math, there is always one right answer**. That is, of course, the basic difference between mathematics and, say, economics.

In order for the 6 to be the numerator and 2(1+2) to be the denominator (which is required for the answer to be 1), there must be another set of brackets (which has been said above). Without them, the answer must be 9.

Step-by-step, using the rule of order of operations (as has been referred to above), you must have:

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

** unless there are more than one right answer.

For example, what are the square roots of 4? One is 2, that is 2*2=4. What other(s) is(are) there?

To keep it simple, let's stick to real numbers.

I'll disagree and say that the original equation as typed was ambiguous since the / can either be a divide sign or the separator from numerator to denominator.

To answer your square root question, -2 is the other answer since you are sticking to real numbers.

[dbleber]

I'll disagree and say that the original equation as typed was ambiguous since the / can either be a divide sign or the separator from numerator to denominator.

To answer your square root question, -2 is the other answer since you are sticking to real numbers.

+1 Exactly

[Chambokl]

Not exactly.... the square root if 4 is only 2. It is common mathematical convention that there is only one solution and this solution is positive.

Technically the square root of a number is equal to the absolute value... so the answer is always positive.

[jvincent]

I was going to give the absolute value as the answer but the way the question was worded, again we are on interpretation here, -2 is a valid since |-2| = 2.

[mpare]

I haven't visited the site for a few days (too busy playing golf every day in Alabama). I see that the level of discussion is at a much higher level than another site that I have visited. Congratulations.

[leftygolfguy]

I don't see how ambiguity makes a wrong answer right- and I am an economist.

Ambiguity can imply the question is wrong, or that it may be interpreted incorrectly, either of which would lead to a wrong answer.

I also don't see this as an issue of ambiguity. If there was no open bracket but 2 closed brackets that would be ambiguous. This is written in a way, so as to mean 1 thing.

Nonetheless, there is only 1 answer to the original question (as written) that is correct, 9.

If one mistyped the question and intended there to be 2 sets of brackets, then the answer is still 9, because the question is mistyped.

Only if one ACTUALLY typed a second set of brackets is the correct answer 1.

It's like a four way stop... there is one right order in which to proceed... and its not open to interpretation... unless you live in Ottawa.

[sharkshooter]

It is common mathematical convention that there is only one solution and this solution is positive.

Technically the square root of a number is equal to the absolute value... so the answer is always positive.

Sorry, but you are wrong on that one. It is a simplification to say that the square root of 9 is 3, but it is precise to say either "a square root of 9 is 3" or "the square roots of 9 are +3 and -3".

A square root is that number which, when multiplied by itself, gives the target number. So, it is either the positive or the negative.

[sharkshooter]

Want to try another one?

What comes next:

0,1,1,2,3,5,8,13, ...

[jeffc]

21

[jmwhite]

34, 55, 89...

[mpare]

Yes, indeed.

34, 55, 89...