I have this question to answer and I don't know where to start. 1*9=0, 9*8=72 and 2*8=9, then 9*9 =? Thank you.

Greg Potts

Hi Greg,

This operation "*" is a distorted multiplication of two integers, I am going to call it star-multiplication. The way you star-multiply two numbers is to subtract 1 from the first number, add one to the second number, and then multiply. If you write ordinary multiplication as "x" then

1*9 = (1-1)x(9+1) = 0x10 = 0
9*8 = (9-1)x(8+1) = 8x9 = 72
2*8 = (2-1)x(8+1) = 1x9 = 9

In many ways star-multiplication doesn't behave like multiplication. In particular

9*8 is not equal to 8*9
1*9 = 0 (You can star-multiply two non-zero numbers and get zero.)
5*0 = 4 (Star-multiplying by zero doesn't necessarily give zero.)

Can you solve these equations?

3*a = 12
3*a = 9
Cheers,
Penny
Go to Math Central