janet spent 1/3 of study time on one subject and 2/7 on another subject. what fraction of her study time remains?

We first need to find the common denominator.

1/3 = 7/21
2/7 = 6/21

7/21 + 6/21 = 13/21

21/21 - 13/21 = 8/21 remaining time

To find the fraction of Janet's study time that remains, you need to subtract the fractions she spent on each subject from 1 (the whole).

First, let's find the common denominator for 1/3 and 2/7. The smallest number that both 3 and 7 divide into evenly is 21.

Next, let's convert the fractions to have the same denominator of 21:

1/3 = 7/21
2/7 = 6/21

Now, we can subtract the fractions from 1:

1 - (7/21 + 6/21)

To add the fractions, we add the numerators and keep the denominator the same:

1 - (13/21)

Now, we subtract the fractions:

(21/21) - (13/21)

To subtract the fractions, we subtract the numerators and keep the denominator the same:

8/21

Therefore, the fraction of Janet's study time that remains is 8/21.