when you set up 3 * (1/3), you're both multiplying and dividing by a 3. these two cancel out, and you're left with one. 3 *(1/3) is simply 1.
12 * (1/3), when you set it up, doesn't cancel out the same. multiply straight across the top (12 * 1), then divide by the bottom (3). 12/3 = 4, so 12*(1/3) is 4.
9 * (1/9) gives you the same result as the first one. the multiplied 9 and the divided 9 cancel out, and you're left with 1.