Wednesday, April 16, 2008

POTW #24

Consider, if A and B are any integers, then A@B = A – B + 1.

For example 9@3 = 9 – 3 + 1 = 7.


(a) Find 3@(2@4).

(b) Does 3@(2@4) = (3@2)@4?

27 comments:

Ethan said...

I think the @ sign means subtract

Daniel Gordon said...

A)3@(2@4) You go by order of operations. (Parentheses, Exponents, Multiply, Divide, Add, Subtract)Parenthesis is first, so you do (2@4). Acording to the example it would look like this:
2-4+1 which equals -1. Now the problem looks like this: 3@(-1)
So you use the example and make it be 3+1+1 (it could also look like this: 3-(-1)+1 )The final answer is 5.
B) 3@(2@4)= 5. (3@2)@4: Parenthesis firts. 3-2+1=2. Now the problem looks like this: (2)@4.
So you do 2-4+1= -1. So, 3@(2@4) & (3@2)@4 are NOT the same!

gavriella said...

i agree with daniel you have to use order of operations and i also agree with his answers. he did the math right

Anonymous said...

u do have to use the order of operations or it wont work

Ben S. said...

Ethan- the @ sign is defined in the problem

Also, why wouldn't you need order of operations to make the problem work?

All other problems need it. What is the point of explicitly saying it?

Also, I agree with what Daniel said.

Danielle said...

gosh daniel! you took my answer too! yeah i got 5 for the first one and -1 for the second one. So, they do not equal each other.

Jake B said...

you have to do the order of operation to get the answers for both of them because if you didn't you would get it wrong

Jake B said...

and i got the same answer as every1 else

Andrew The Great said...

the first one is definitely five and the way the equation works the second one is common sense that they does not equal each other. So basically what every1 else said :-)

Mrs. Cooper said...

Nice comments.
So does that mean that there IS or IS NOT an associative property of @ ????

Iris said...

I agree with what Daniel said: A=5 because you do the parentheses first. The parentheses part(2@4) =-1. Then 3@-1=5 because 3--1+1=5. If you did 3@2 first, the answer would be -1. I think that 3@(2@4) is not equal to (3@2)@4. So, there is Not an associative property of @.

Leslie said...

Along with everyone else i got the same thing...5 and -1.

Rebecca S. said...

@ does not stand for minus or plus, it means that when you see A@B, it means A-B+1. So what you would do, is follow the order of operations and do 2-4+1 first. then 3--1+1 or 3+1+1=5. So the answer to (a) would be 5.

Mitch said...

I agree with what Daniel Gordon said at the beginning because you must use PEMDAS (Parenthesis, Exponents, etc.....) So (a) is equal to 5 if you use the (Please Excuse my dear aunt sally) technique.

Mitch said...

For (b) i got -1 which isn't the same as (a) therefore (a) is equal to 5 and (b) is no or -1

Unknown said...

Well the @ sighn must mean that you do minus and then +1 at the end so its liek first perenthethis (PEMDAS) so 2-4+1 which is -1 then u do 3-(-1)+1 which is 5 the a) is 5 ( btw if i said any of the same things as any1 else sorry but i don't like to read them becuase i get the answer)

Anonymous said...

You have to do order of operations so you do (2-4+1)and that is -1. Then 3@5= 3-(-1)+1 is 5. Then (3@2)is 2. 2@4 is -1. So no they are not the same

Yacova said...

just clarifying...are we supposed to know what the @ sign means?

Yacova said...

i also agree with daniel, use order of operations so do parenthesis first so 2@4 would be the same as 2-4+1 which is equal to -1 and then you do 3@-1 which is the same as 3+1+4 which is 5

Yardi said...

for a) you can do 2@4 which would, like cobi said, be 2-4+1 which would actually be -1... then its like the same thing as A@B and add them together and subtract the 1 and you would get 5!!! i just read cobi's sorry if i copied anyone else!!! hehe

Yardi said...

ohhhh theres a second one! THEY ARE LIKE NOT EQUAL AT ALL! the first ones 5 the second is like -1 or something

Theman12345543211 said...

@ means you subtract the number in front and add 1 but the problems aren't equal because the left side equals 5 and the right -1

Anonymous said...
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Anonymous said...

i think the first answer is 5 and the second answer is no and yes order of operations is important

Anonymous said...

i think the first answer is 5 and the second answer is no and yes order of operations is important

R.J. said...

i dont understand is it asking for what the @ symbolizes?

Mrs. Cooper said...

The problem tells you that @ means subtract a and b and then add 1.