Its not about speed and mental maths. Thats not the point. Obviously you need to show that you are comfortable with numbers.Take some extra seconds to do your calculations. Thats a better outcome than trying to do things quickly and getting the calcs wrong.

5% error margin is okay.

So, for calculations involving large numbers you can apply the following approaches:

• Increase the number of steps by expanding the numbers e.g 43*78= (40+3)*78= 40*78 + 3*78 = 40*70+ 40*8+ 3*78. Hope you get the point
• Round up or down and add % error, so in example above you can use 40*80 

So, for a large number divided by 365, its okay to use 350 or 400 but make sure to compensate for the error % or you could expand the numerator in multiples of 365. E.g. 4568/365 = (365*12 + 188)/365 

(edited)

It's a deviation of ~4%, so that is fine. You might quickly check in with the interviewer if it's OK to give an approximate number or if they want you to calculate precisely. 

Another trick that might be even easier is to divide by 400 and then add 10%.