Question

Dan must do homework for 1/2 an hour and clean his room for 1/3 of an hour before he can play. What fraction of an hour must Dan do homework and clean before he can play?

Answer 1

Answer:
`(5)/(6)\ of\ an\ hour`

Explanation:

You need to analize the information provided in the exercise.

According to the data given, Dan must do homework for
`(1)/(2)` of an hour.

He also must clean his room for
`(1)/(3)` of an hour.

Then, in order to find the fraction of an hour in which Dan must do the actividies mentioned above before he can play, you need to add the fractions given.

Since they have different denominators, you need to find the Least Common Denominator. This is:

`LCD=2*3\\\\LCD=6`

Divide each original denominator by the LCD and multiply the corresponding numerator by the quotient obtained.

Then:

`(1)/(2)+(1)/(3)=((1)(3)+(1)(2))/(6)=(5)/(6)\ of\ an\ hour`