Well, you take the two denominators and find a number that both numbers match. So 3/4 (4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, etc.) and 3/9 (9, 18, 27, 36, 45, 54, etc.). Now take the first number that matches both numbers (36) and ask yourself, 'what do I have to multiply to get that number?' Well, for 4 and 36, you multiply 4 and 9 to get 36, and for 9 and 36, you multiply 9 and 4 to get 36. Then you multiply the top number by the same one you did with the bottom one. So you add up the two numbers, and you have your answer (3/4: 4*9=36 3*9=27 27/36 39: 9*4= 36 3*4=12 12/36 Total=12+27= 39/36=1 3/36=1 1/12). The answer is 1 1/12!
Second moment of area about an axis along any diameter in the plane of the cross section (i.e. x-x, y-y) is each equal to (1/4)pi r^4. The second moment of area about the zz-axis (along the axis of the cylinder) is the sum of the two, namely (1/2)pi r^4.
The derivation is by integration of the following: int int y^2 dA over the area of the cross section, and can be found in any book on mechanics of materials.