Yep, they can be negative too :)
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Yes, it applies to even multiplication of fractions and rational and irrational numbers.
Fractions help with numbers that are not whole numbers.
You can have algebraic fractions but, even there, the letters do represent numbers; except that their values are indeterminate.
All fractions are rational numbers.
There is no end to the numbers of maths and there are many classifications of numbers, like primes, fractions, even, odd, positive, negative and others.