You can write it just as given:
... (time spent in video games)/(time spent in television) = (10 minutes)/(1 hour)
However, the intent is to end with a pure number (no units), so we need to convert hours to minutes or vice versa. Most folks know that 1 hour is 60 minutes, so that is probably the easier conversion.
... = (10 minutes)/(60 minutes)
... = 10/60 . . . . . . . . . the units in numerator and denominator are the same, so cancel
... = 1/6 . . . . . . . . . . . .the fraction is reduced in the usual way
The ratio in simplest form is 1/6.
Both values need to be in the same usable form. So, I would convert the two values into minutes. That leaves you 10 minutes of video games and 60 minutes of television. This ratio would be 10/60 or 10:60. Simplified would be 1/6 or 1:6.
It would be equal to 20/180 minutes = 1/9 minutes
so, your answer is 1/9