Instance of Fractional Int required for definition - haskell

Question

time :: Int -> (Int,Int,Int)
time x = ((x/3600),(x`mod`3600)/60,((x`mod`3600)`mod`60))
Instance of Fractional Int required for definition of time
expample =
time x = (hours, minutes, seconds)
time 3600 = (1,0,0)
given a time in seconds, must show it like this (hours, minutes, seconds) in the example 3600 is 1h 0m 0s

Answer 1

I believe you are getting that error because you are using the / operator with Int arguments. You can use div to get rid of the error, like so:
time :: Int -> (Int,Int,Int)
time x = ((x `div` 3600),(x `mod` 3600) `div` 60,((x `mod` 3600) `mod` 60))
As others have pointed out, (/) requires arguments to be Fractional whereas div is happy with Integral values.

Answer 2

You can't use the normal division operator on integers. This is true in mathematics and in Haskell, because division only works when the mathematical structure is a Field. The integers do not have division defined, but you can perform something similar called integer division (yes, a misleading name) or truncated division. This is achieved in Haskell using the div function, and you can use it as:
time :: Int -> (Int, Int, Int)
time x = (x `div` 3600, (x `mod` 3600) `div` 60, (x `mod` 3600) `mod` 60)
Here I've simply replaced each instance of / with div in its infix form, with no change to your algorithm otherwise.
So what does it mean for a type to implement the / operator? If we load up GHCi:
> :info (/)
class Num a => Fractional a where
(/) :: a -> a -> a
...
-- Defined in 'GHC.Real'
infixl 7 /
This tells us that / is a member of the Fractional typeclass, and anything that implements it must also implement the Num typeclass. Put simply, things that can be divided have to be fractional numbers. What else is in the Fractional typeclass?
> :info Fractional
class Num a => Fractional a where
(/) :: a -> a -> a
recip :: a -> a
fromRational :: Rational -> a
instance Fractional Float
instance Fractional Double
So Fractional numbers have division, a reciprocal operation, and a conversion from a Rational number. Ideally, a * recip a == a / a == 1, since this is true of our familiar fractional sets (rationals, reals, complex numbers).

Answer 3

The reason it's showing you the error is because (/) has the following type:
λ> :t (/)
(/) :: Fractional a => a -> a -> a
So, it accepts and returns only fractional numbers such as Float and Double. One way of solving this problem would be by using div function which has a type of div :: Integral a => a -> a -> a.
time x = ((x `div` 3600),(x`mod`3600) `div` 60,((x`mod`3600)`mod`60))
Another way to solve this problem would be to use the fromIntegral function on the number which will be applied to the / function and do the proper type conversion while returning:
time :: Int -> (Int, Int, Int)
time x = (a,b,c)
where a = ci $ fi x / fi 3600
b = ci $ fi (x `mod` 3600) / fi 60
c = (x `mod` 3600) `mod` 60
fi = fromIntegral
ci = ceiling