I had to use google translate for this one, because I didn't suspect the translation to my language to be so literal.
My take is that this sentence is badly worded. How do these fractions specifically use those prime factors?
Apparently the idea is that a fraction 1/N, where N is a prime factor of the base, is rational in that base.
So for base 10, at least 1/2 and 1/5 have to be rational.
And given that a product of rational numbers is rational, no matter what combination of those two you multiply, you'll get a number rational in base 10, so 1/2 * 1/2 = 1/4 is rational, (1/2)^3 = 1/8 is rational etc.
Same thing goes for the sum of course.
So apparently those fractions use those prime factors by being a product of their reciprocals, which isn't mentioned here but should have been.
My take is that this sentence is badly worded. How do these fractions specifically use those prime factors?
Apparently the idea is that a fraction 1/N, where N is a prime factor of the base, is rational in that base.
So for base 10, at least 1/2 and 1/5 have to be rational.
And given that a product of rational numbers is rational, no matter what combination of those two you multiply, you'll get a number rational in base 10, so 1/2 * 1/2 = 1/4 is rational, (1/2)^3 = 1/8 is rational etc.
Same thing goes for the sum of course.
So apparently those fractions use those prime factors by being a product of their reciprocals, which isn't mentioned here but should have been.