   SEARCH HOME Math Central Quandaries & Queries  Question from patrick, a student: Associative test: Can you explain the following to me? Is the following operation associative?: x*y=x+y+1 1) x*(y*z)=x*(y+z+1)=x+(y+z+1)+1=x+y+z+2 2) (x*y)*z=(x+y+1)*z=(x+y+1)+z+1=x+y+z+2 The answer is yes as 1) = 2) My specific questions are: 1) How x*(y*z)=x*(y+z+1)=x+(y+z+1)+1 ? 2) How (x+y+1)*z=(x+y+1)+z+1? Thank you!! Hi Patrick,

I don't know what $x, y$ and $z$ are but I am going to assume they are numbers. You have a new operation, asterisk, that works as follows. To "asterisk" two numbers you add the two numbers and then add 1.

Look at 1) $x*(y*z).$ You do what is inside the parentheses first, $y*z,$ which, according to the "asterisk" rule is $y + z + 1.$ So now you have $x*(y + z + 1).$ According to the "asterisk" rule you are to add $x$ to $(y + z + 1)$ and then add $1.$ Thus $x*(y + z + 1) = x+(y + z + 1) + 1.$

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.