Final answer:
Dinah spends 13/15 of her homework time on math and writing.
Step-by-step explanation:
To find the fraction of Dinah's homework time spent on math and writing, we need to add the fractions 1/5 and 2/3.
To add fractions, we need to have a common denominator. In this case, the common denominator is 15. So, we rewrite 1/5 as 3/15 and 2/3 as 10/15.
Now, we can add 3/15 and 10/15 to get a total of 13/15. Therefore, Dinah spends 13/15 of her homework time on math and writing.