how to solve this math problem?

in a 24 hour day, there are :

24 * 60 = 1440 minutes. So that is our "whole".

Now we need to figure out how many of those minutes contain a "1" in it that would be displayed correctly.

hour 1 - 0 minutes will be correct due to the hour.
hour 2 - 01, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, and 51. 15 min are bad, so 45 min will display correctly.
hour 3 - same as hour 2, 45 min.
hour 4 - 9, same as hour 2, 45 min per hour
hour 10 - 0 min
hour 11 - 0 min
hour 12 - 0 min

Then multiply that by 2 for the PM side of the clock, which will be identical to the AM side of the clock.

So count up the minutes that will be a correctly displayed time:

45 min per hour over 8 hours: 45 * 8 = 360. Double that for PM: 360 * 2 = 720

So 720 minutes out of the 1440 will display correctly. Find our fraction and reduce:

720 / 1440
1/2

The clock will function properly 1/2 of the time.