Sure. I didn't think of that. But I think the original poster probably could do with the re-enforcement of the idea of multiplying/dividing both sides by the same value. That's big in dealing with fractions, LCD, GCF, etc.
Regarding ratios, there is no need to convert 3/4 into a whole number (3) and then have to multiply 2 by 4. Too complicated. As long as the denominator is the same, the ratio is evident in the numerators. Thus, the only "work" required is to convert the 2 into 8/4.
3/4 to 8/4 = 3:8
bump
I think for someone having difficulty understanding the subject, it is simpler to obey certain rules. You may know intuitively to consider 2 as 8/4ths, but how does one teach that?
I laid out a simple method that should always get the novice the answer. Your shortcuts may be valid, but not for the novice.
SD