We are told that Sam spent 5/6 of an hour at the dentist office. He spent 1/10 of that time in the waiting room. Adn we are asked to find the time he actually spent in the office apart from the waiting time.
So we first try to understand in minutes what is the total time he spent at the dentist:
5/6 of an hour is in fact 5/6 of 60 minutes .And this becomes the product of 5/6 times 60: 50 minutes.
So 50 minutes was the total time at the dentist's office.
Now 1/10 of these 50 minutes was his waiting time. We calculate 1/10 of 50 minutes again via the product of 1/10 times 50. This is : 5 minutes .
So now we can figure out what was the time at the dentist discounting the waiting time:
50 minutes - 5 minutes = 45 minutes.
If they want you to answer in hours, we can convert back the 45 minutes into hours: 3/4 of an hour.
If your teacher wants all calculations in fraction of an hour (may be to practice fractions) you do:
1/10 of 5/6 = 1/10 * 5/6 = 5/60
now subtract this from 5/6:
5/6 - 5/60 = 50/60 - 5/60 = 45/60 = 3/4
Another fraction problem:
Three members of a relay team run a total of 3/8 of a mile. each runner run the same distance. find how far each runner went.
So we understand that the first runner run a distance "x" (unknown), then it met the second runner, how started and run another equal distance "x", and the third one did the same. So at the end, the addition of the three equal distances : x + x + x equals 3/8 of a mile
So we have the equation:
3 x = 3/8 of a mile.
to solve for x we divide both sides of the equal sign by 3 (to isolate the x on the left):
x = 3/8 divided by 3 = 1/8 of a mile.
Each runner run 1/8 of a mile.