These are simple arithmetic problems. The following steps will make you understand the problems.

Addition;

1/2 + 2/3 = (1x3)/6 + (2x2)/6 ---- taking lcm (6)

3/6 + 4/6 = 7/6

Subtraction;

1/2 - 2/3 = (1x3)/6 - (2x2)/6 ---- taking lcm 6

= 3/6 - 4/6 = -1/6

Multiplication;

1/2 x 2/3 = (1x2)/(2x3)

= 2/6

= 1/3

Division;

(1/2) / (2/3)

1/2 x 3/2

3/4

Addition;

1/2 + 2/3 = (1x3)/6 + (2x2)/6 ---- taking lcm (6)

3/6 + 4/6 = 7/6

Subtraction;

1/2 - 2/3 = (1x3)/6 - (2x2)/6 ---- taking lcm 6

= 3/6 - 4/6 = -1/6

Multiplication;

1/2 x 2/3 = (1x2)/(2x3)

= 2/6

= 1/3

Division;

(1/2) / (2/3)

1/2 x 3/2

3/4