1/2 means

x times 2 = 1

In Z_7 what can you multiply by 2 to equal 1? Or in other words what number less than 7 can you multiply by 2 and get a remainder of 1 when you mod 7?

In Z_7

0x2 = 0

1x2 = 2

2x2= 4

3x2 = 6

4x2 = 1

5x2 = 3

6x2 = 5

So 1/2 would be 4 in Z_7

You can go about the other problems in a similar manor.

-2/3

well what is -2? it is the OPPOSITE of 2, meaning -2 + 2 = 0. So what number in Z_7 is does x + 2 = 0? well thats 5, and then what number times 3 equals 5? From the chart above, thats 6!

See if you can do the rest.