6÷2(1+2)= ?

Status
Not open for further replies.
Islander said:
These are equivalent ;)

6 ÷ 2(1 + 2)

6 ÷ 2 x (1 + 2)
Click to expand...

DemiLion said:
Nope, they are completely different calculations.
Click to expand...

D'ya know something? I think I was wrong. It's been a while since I did maths at school and I'd forgotten the difference between the two formulae above.

So Mark is correct, the two ARE different as, without the "x" between 2 & the bracket, 2(1+2) does indeed become a separate calculation and therefore the answer is 1.
 
If you did this by algebra the equation looks like this:

a ÷ b(c+d) = e

this would also be written as:

a ÷ bc + bd = e

inserting the numbers back in would be:

6 ÷ 2 + 4 = e

Using BODMAS the answer would be 7

However, it is apparent from the structure and logic of the equation that the sequence of divide and then add is not the intended outcome. Therefore it should be:

a ÷ (bc+bd) = e which becomes 6 ÷ (4+2) = 1 (applying BODMAS)

This assumption is shown better by transposing the algebra:

a ÷ b(c+d) = e is transposed to become e * b(c+d) = a

Assuming the answer is 1 putting the numbers into the transposition gives:

1 * 2(2+1) = 6 which is correct
 
Ploddles said:
Definitely 1.
Multiply Divide Add Subtract.
None of this multiply and divide have equal status nonsense.
Click to expand...

Exactly! i never thought this rule existed.
 
Could you use this calculation to work out take off velocity of an airoplane on a conveyor belt ?
 
Islander said:
'fraid not.

a(b+c) is the same as a x (b+c)
Click to expand...

Written as a separated element, as above, the result is the same, but written in a complex calculation they are different.

The Plus, Minus, Multiply and Divide symbols in mathematics are the equivalent of commas in grammar and separate the different subcalculations within. Thus by writing the assumed multiplication sign you change the rhythm of the calculation.
 
I skipped through reading the thread so I got no clues, but the answer is 1.

you work out the brackets first, 2(1+2)=2(3)=2x3=6, then divide the 6 by 6=1
 
The symbols are simply operators. You don't need to use the operator when the multiplier is outside of a parenthesis pair and the multiplicand the result of an operation within simply because it's implied whereas between two numbers it's needed to avoid confusion. In algebraic statements where symbols are used rather than numbers, placing two symbols next to each other, i.e. ab gives the same implied multiplication operator and in this case, using the operator would add confusion so it's either not used or replaced with a dot (a.b). Again it's just an operator.

The two statements are mathematically equivalent. :p
 
Islander said:
The symbols are simply operators. You don't need to use the operator when the multiplier is outside of a parenthesis pair and the multiplicand the result of an operation within simply because it's implied whereas between two numbers it's needed to avoid confusion. In algebraic statements where symbols are used rather than numbers, placing two symbols next to each other, i.e. ab gives the same implied multiplication operator and in this case, using the operator would add confusion so it's either not used or replaced with a dot (a.b). Again it's just an operator.

The two statements are mathematically equivalent. :p
Click to expand...

Yes, but you are only looking at the 2nd part of the original formula. It's how it works with the "6/" beforehand that is the issue here. The missing "x" says that the 2(1+2) is a standalone calculation and that the 2 is not initially connected to the "6/". Therefore, you look at the 2(1+2) as a calculation first which = 6. You then divide the 6 at the beginning by it and get an answer of 1.
 
if you believe in "multiplication by juxtaposition" (google it) you will get 1.

if not, you will get 9.
 
Is this still going on :(

It's 9. Or binary 1001 as I mentioned earlier.

I wasn't taught BODMAS or BIDMAS or anything like that at school. At least I don't remember it being called that. I was just taught how to do it properly without fancy words.

ALWAYS deal with the CONTENTS of the brackets first. Dealing with innermost brackets first when nested.

ALWAYS infer multiplication of anything in brackets.

Always work left to right once you have dealt with the brackets.


6÷2(1+2) = 6÷2(3) = 6÷2*3 = 3*3 = 9


Anything else is a massive fail.
 
Last edited:
fabs said:
Yes, but you are only looking at the 2nd part of the original formula. It's how it works with the "6/" beforehand that is the issue here. The missing "x" says that the 2(1+2) is a standalone calculation and that the 2 is not initially connected to the "6/". Therefore, you look at the 2(1+2) as a calculation first which = 6. You then divide the 6 at the beginning by it and get an answer of 1.
Click to expand...

but the original question is 6÷2(1+2) , not 6/2(1+2) (that implies a fraction which would indeed =1)
 
fabs said:
Yes, but you are only looking at the 2nd part of the original formula. It's how it works with the "6/" beforehand that is the issue here. The missing "x" says that the 2(1+2) is a standalone calculation and that the 2 is not initially connected to the "6/". Therefore, you look at the 2(1+2) as a calculation first which = 6. You then divide the 6 at the beginning by it and get an answer of 1.
Click to expand...

Whether it's implied or explicit, the order of operations remains the same :)
 
antihero said:
but the original question is 6÷2(1+2) , not 6/2(1+2) (that implies a fraction which would indeed =1)
Click to expand...

I haven't got a divided sign on my keyboard so that's why I used a "/". In this case it means the same thing as, when you type a formula into Excel, "/" means divided by.

So, in the case of the original question:

2(1+2) is a calculation on it's own, the lack of a "x" between the 2 and "(" indicates that they are tied together. The result of this calculation is 6, therefore 6 divided by 6 is 1.

So, whilst 2(1+2) and 2x(1+2) do indeed give the same answer, the former binds them together as a standalone calculation.
 
2blue4u said:
Is this still going on :(

It's 9. Or binary 1001 as I mentioned earlier.

I wasn't taught BODMAS or BIDMAS or anything like that at school. At least I don't remember it being called that. I was just taught how to do it properly without fancy words.

ALWAYS deal with the CONTENTS of the brackets first. Dealing with innermost brackets first when nested.

ALWAYS infer multiplication of anything in brackets.

Always work left to right once you have dealt with the brackets.


6÷2(1+2) = 6÷2(3) = 6÷2*3 = 3*3 = 9


Anything else is a massive fail.
Click to expand...

Yep, the priority only applies to the calculation inside the parentheses. The order of operations outside the parentheses remains the same whether the operators are explicitly stated or implied :)
 
fabs said:
2(1+2) is a calculation on it's own, the lack of a "x" between the 2 and "(" indicates that they are tied together. The result of this calculation is 6, therefore 6 divided by 6 is 1.
Click to expand...

By what reasoning or mathematical rule did you come by this?


This

6÷2(1+2)

implies

(6÷2)(1+2)

Not

6÷(2(1+2) as you suggest.
 
fabs said:
Yes, it does for the 2nd part of the formula, as I've already said. But the fact that the"x" is omitted affects the way it is calculated with the 6 at the beginning.
Click to expand...

Sorry, but the order of operations outside of the parentheses remains the same regardless of whether they're implied or explicit.

Left to right after the parentheses have been resolved. :)
 
fabs said:
But the fact that the"x" is omitted affects the way it is calculated with the 6 at the beginning.
Click to expand...
Nope. Sorry, it doesn't. It matters not whether the 'x' is there, omitted, inferred or arrives in a box of corn flakes. The operators are handled in the same way. The inclusion, or omission, of an actual 'x' as opposed to an inferred 'x' matters not.
 
fabs said:
I haven't got a divided sign on my keyboard so that's why I used a "/". In this case it means the same thing as, when you type a formula into Excel, "/" means divided by.

So, in the case of the original question:

2(1+2) is a calculation on it's own, the lack of a "x" between the 2 and "(" indicates that they are tied together. The result of this calculation is 6, therefore 6 divided by 6 is 1.

So, whilst 2(1+2) and 2x(1+2) do indeed give the same answer, the former binds them together as a standalone calculation.
Click to expand...

Thats exactly why there is no definitive answer to the question...thats what I was getting at. To me, using "/" does indeed mean divide by, but to others it means "over". That, including a complete divide in how to use brackets correctly ("multiplication by juxtapostion") means that this thread will forever be like groundhog day. No one will win.
 
Islander said:
Sorry, but the order of operations outside of the parentheses remains the same regardless of whether they're implied or explicit.

Left to right after the parentheses have been resolved. :)
Click to expand...

2blue4u said:
Nope. Sorry, it doesn't. It matters not whether the 'x' is there, omitted, inferred or arrives in a box of corn flakes. The operators are handled in the same way. The inclusion, or omission, of an actual 'x' as opposed to an inferred 'x' matters not.
Click to expand...


No, as I've already said, the lack of "x" has a very important meaning here. It does actually mean that the first 2 is linked to the contents of the brackets and forms a single calculation. I don't see how you can possibly think that it doesn't matter whether the "x" is there or not, mathematical formulae must be accurate by their very nature so every change, including the showing or not showing of symbols will change the result. In this case it is definitely significant and changes the meaning of the formula in the way I have described
 
antihero said:
Thats exactly why there is no definitive answer to the question...thats what I was getting at. To me, using "/" does indeed mean divide by, but to others it means "over". That, including a complete divide in how to use brackets correctly ("multiplication by juxtapostion") means that this thread will forever be like groundhog day. No one will win.
Click to expand...

But over and divide by are the same. :thinking:
 
fabs said:
No, as I've already said, the lack of "x" has a very important meaning here. It does actually mean that the first 2 is linked to the contents of the brackets and forms a single calculation. I don't see how you can possibly think that it doesn't matter whether the "x" is there or not, mathematical formulae must be accurate by their very nature so every change, including the showing or not showing of symbols will change the result. In this case it is definitely significant and changes the meaning of the formula in the way I have described
Click to expand...

Then we'll have to agree to disagree.

All the following have the same outcome in my book. 9!

6/2(1+2)

(6/2)(1+2)

6/2*(1+2)

(6/2)*(1+2)
 
fabs said:
No, as I've already said, the lack of "x" has a very important meaning here. It does actually mean that the first 2 is linked to the contents of the brackets and forms a single calculation. I don't see how you can possibly think that it doesn't matter whether the "x" is there or not, mathematical formulae must be accurate by their very nature so every change, including the showing or not showing of symbols will change the result. In this case it is definitely significant and changes the meaning of the formula in the way I have described
Click to expand...

That's just wrong. The 'x' doesn't have to be there because it's implied. If it were there it wouldn't change a thing. It's an operator and it's subject to the rules of order of operations.

Resolve the parentheses and then perform the operations in order of priority moving left to right when they have the same level of priority.
 
"Just because something is implied rather than written does not give it any special rank in the order of operations.

The problem in it's simplest form, with nothing implied would look like this:

(1+1+1+1+1+1 (over) 1) ÷ (1+1 (over) 1) * ((1(over) 1) + (1+1 (over) 1))

From here, nothing is implied, This again, works out to 9. "
 
2blue4u said:
Then we'll have to agree to disagree.

All the following have the same outcome in my book. 9!

6/2(1+2)

(6/2)(1+2)

6/2*(1+2)

(6/2)*(1+2)
Click to expand...

I'll tell it as it was explained to me by a (very good)maths teacher.

a(b+c) is actually a shorthand of (a*(b+c)). The lack of the multiplication symbol is what indicates this. This is why it is written as 2(1+2) as that is the calculation that must be done before the 6 even comes into play. As I keep saying, the lack of the multiplication symbol is for a reason otherwise we would never use it at all.
 
We use the implied operation for much the same reason as we use & or @. It's shorthand - it has no other significance.

ETA

If we used the implied form all the time then it would be very confusing. 4 x 3 would be 43.
 
Last edited:
Islander said:
That's just wrong. The 'x' doesn't have to be there because it's implied. If it were there it wouldn't change a thing. It's an operator and it's subject to the rules of order of operations.

Resolve the parentheses and then perform the operations in order of priority moving left to right when they have the same level of priority.
Click to expand...

Oh for the love of.....

2(1+2) and 2*(1+2) give the same answer but the lack of "x" in the first example is implied for a reason. The fact that the symbol is missing is what indicates that the calculation must be done as a whole before the 6 comes into play. This is why the "x" is implied rather than shown.
 
fabs said:
I'll tell it as it was explained to me by a (very good)maths teacher.

a(b+c) is actually a shorthand of (a*(b+c)). The lack of the multiplication symbol is what indicates this. This is why it is written as 2(1+2) as that is the calculation that must be done before the 6 even comes into play. As I keep saying, the lack of the multiplication symbol is for a reason otherwise we would never use it at all.
Click to expand...

I was taught it the same way. The phrase used was 'take the multiplier inside the brackets'.
 
It's just shorthand. It doesn't have any effect whatsoever on the order of operations!
 
2blue4u said:
By what reasoning or mathematical rule did you come by this?

This

6÷2(1+2)

implies

(6÷2)(1+2)

Not

6÷(2(1+2) as you suggest.
Click to expand...

No it doesn't, why do you introduce brackets when they are not in the equation.

I'm certainly sure there are some people here with great mathematical skills but to my knowledge of doing 3 years of advanced mathematics for graphics I've seen equations more complex than this and always the brackets have to resolve first and that means inside the bracket and anything immediately attached in this case the 2, there is no "x" in there so the there is no reason to talk about multiplication. Simply first solve the bracket:
2(1+2) = 6

Then solve the whole equation:

6 / 6 = 1

This is how it goes. And what I've been doing for calculating light intensity in computer graphics and always got the correct results on the screen, so I believe in what I see :-)

End
 
Status
Not open for further replies.
Back
Top