You have a mixture of units of measurement so lets change them so that they may be compared directly. Using the 24 hour clock
#color(blue)("Consider 2:12 am")#.
#color(brown)("Note that:")#
#color(brown)("If you remove "7 1/2" hours from this you end up in the previous")# #color(brown)("evening so lets do a sort of cheat.")#
#color(green)("Building the time reference point for "2:12" am")#
A full day on the 24 hour clock is 24. Then to get to 2:12 am you have an additional 2 hours 12 minutes giving a total time of
#color(red)(24)+ 2" hours" + 12" minutes"# from 2 midnights ago
#color(red)("Shifting 1 of the hours")color(green)(" into the minutes")# gives:
Write this as #color(red)(23)+2" hours" color(green)(+ 60)+12" minutes"#
This gives us: #color(magenta)(25" hours "+ 72" minutes")#
;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider the subtraction")#
Subtract from this the #7 1/2# hours written as 7 hours + 30 minutes
#color(magenta)( 25" hours" + 72" minutes")#
#ul(color(white)(2)7" hours" + 30" minutes") larr" Subtract"#
#18" hours"+42" minutes"#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#1800# hours is #18-12-> 6" pm "color(green)( larr" converting back to 12 hour clock")#
So the time is #6" pm" +42" minutes"#
Writing this in the same format as the in the question we have:
#6:42" pm"#
