I am trying to work out pace by doing time / distance. So for example if I run for for 39 minutes and cover 5 miles it gives me
39 / 5 = 7.8
This is correct but I want to result to be in minutes and seconds rather than a decimal. So what I actually want back is 7.48. I could also take the 0.8 and do
(60 / 100) * 80
But surely there is a way to do it in one calculation?
Take the fractional part of your calculation of $7. 8$ minutes/mile, and multiply by $60$ to calculate the number of seconds this fraction of a minutes amounts to:
$$7 \;\mathrm{ minutes} + (0.8 \times 60 = 48\;\mathrm{seconds}.)$$
Hence, $7.8$ minutes/mile is equal to a $7$-minute, $48$-second mile.
This can also be done as a standard fraction: $$\dfrac{39\;\mathrm{minutes}}{5 \;\mathrm{miles}} = 7 + \frac 45 \;\text{minutes per mile} = 7 + \frac 45\times 60 = 7 \;\text{minutes}, 48\;\text{seconds per mile}$$
If you want to express with one single formula, you can write: $$ \left \lfloor \frac{x}{y} \right \rfloor + \left ( \frac{x}{y}-\left \lfloor \frac{x}{y} \right \rfloor \right)\cdot 60 = $$
With your example, plugging in the numbers:
$$ \left \lfloor \frac{39}{5} \right \rfloor + \left ( \frac{39}{5}-\left \lfloor \frac{39}{5} \right \rfloor \right)\cdot 60 = $$
$$ 7 + (7.8 - 7)\cdot60=$$
$$7 + 0.8 \cdot 60 = 7.48 $$
where $\lfloor x \rfloor$ is the floor function. Then, you have to remember that this result does not mean 7.48 minutes but 7 minutes and 48 seconds.
If you are programming it then there is the concept of integer division $$7/3=2$$ and remainder calculation (called Modulo) where $$7 modulo 3 = 1$$. You can use these functions to display in one "sentence" minutes and seconds.
