[olau]

I was taught something of the same.

But I think it was misguided. I'll note that 1/3 is not a number, it's a calculation. So more complicated.

And fractions are generally much more complicated than the decimal system. Beyond some simple fractions that you're bound to experience in your everyday life, I don't think it makes sense to drill fractions. In the end, when you actually need to know the answer to a computation as a number, you're more likely to make a mistake because you spend your time juggling fractions instead of handling numerical instability.

Decimal notation used to be impractical because calculating with multiple digits was slow and error-prone. But that's no longer the case.

[volemo]

> I'll note that 1/3 is not a number, it's a calculation. So more complicated.

1/3 is a calculation the same way 42 is a calculation (4*10^1 + 2*10^0). Nothing is real except sets containing sets! /j

[DemocracyFTW2]

Yes, true. *BUT* 1/3 is a fraction with denominator 3. 1/5 is a fraction with another denominator, and 1/7 has yet another. So how much is 1/3 + 1/5 + 1/7? You can't just add up, you first have to multiply to get to common ground. The decimal expansions of these use the same base and are readily comparable.

[tsimionescu]

This is ultimately a matter of definitions, and neither defining the fractions nor the decimals as the "true" representation of rationals is ultimately more or less correct.

But, operations on fractions are definitely easier than operations on decimals. And fractions have the nice property that they have finite representations for all rational numbers, whereas decimal representations always have infinite representations even for very simple numbers, such as 1/3.

Also, if you are going to do arithmetic with infinite decimal representations, the you have to be aware that the rules are more complex then simply doing digit-by-digit operations. That is, 0.77... + 0.44... ≠ 1.11... even though 7+4 = 11. And it gets even more complex for more complicated repeating patterns, such as 0.123123123... + 0.454545... (that is, 123/999 + 45/99). I doubt there is any reason whatsoever to attempt to learn the rules for these things, given that the arithmetic of fractions is much simpler and follows from the rules for division. The fact that a handful of simple cases work in simple ways doesn't make it a good idea to try.

[anthk]

Rationals are numbers, not calculations. They can evaluate to themselves as members from a set.