16/9 is the fully reduced fraction, meaning that 16 and 9 have no common divisors.
(32:18 e.g. would be the same ratio, but the fraction isn’t fully reduced because both 32 and 18 are divisble by 2)
Ratios are generally given in their fully reduced fraction because it’s more convenient and just sorta sounds “neater” if you’re dealing with exclusively whole numbers, as opposed to having decimals. Though this is just a rule of thumb. There’s no fixed rule for this. E.g. 16:10 “should” be written as 8:5, but it’s written as 16:10 instead to make it similar to 16:9.
So in the end the “rule” is that we just sorta settle on something that sounds good.
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