Question 24030
Is this your entire list of homework problems for today?  I will do one of them, which, I hope, will enable you to do the others.


Let me mention two tricks that will help you with these.  First, a ratio a:b is equivalent to the fraction a/b.  The other thing to remember is that both quantities must be in the same unit.  For example, you convert hours to minutes by multiplying the hours by 60 minutes/hour. So:


{{{45 min : 8 hr = 45 min / (8 hr * (60 min/hr)) = 45 min / 480 min = 45/480}}}


To check whether you have converted correctly, make sure that your final answer is in the units you expect. In this case, we expect the final answer to be a ratio without any units. In the denominator we multiply hr by min/hr to get min, and when we divide min (in the numerator) by min (in the denominator) we are left with a unitless value.


Oh, I almost forgot: To reduce these fractions to their simplest form, you can factor each number into all its primes, and eliminate corresponding factors from the numerator and denominator:


{{{45 = 3 * 3 * 5}}}

{{{480 = 2^5 * 3 * 5}}}

{{{ 45/480 = (3 * (3*5)) / (32 * (3*5)) = 3/32}}}