What fraction of his study time remains? Problem is below.?

Question

Mark spent 1/3 of his study time doing math homework and 2/7 preparing for a history exam. What fraction of his study time remains?

Answer 1

The easiest way to solve this is to convert both fractions to a common fraction.

Since the first denomenator that accomplishes that is 21 (3 x 7)
you can convert to
Math
1/3 = 7/21
History
2/7 = 6/21

add them up

7/21 + 6/21 = 13/21

Subtract from the whole (21/21) you get

21/21 - 13/21 = 8/21

You can come up with the number of minutes by multiplying that fraction times the total minutes in his study time. For instance, if he had two hours to study, then the solution for all would be:

Math (7/21 x 120) = 40 minutes (rounded)
History (6/21 x 120) = 34 minutes (rounded)
Left over (8/21 x 120) = 46 minutes (rounded)
Total = 120 minutes

Answer 2

Find the smallest common denominator of the 2 fractions (LCD). For 1/3 and 2/7, the smallest number the 2 denominators have in common is 21.

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

Total amount spent studying: 7/21 + 6/21 = 13/21
Total amount of study time remaining: 21/21 - 13/21 = 8/21

Answer 3

Let the remaining time be x units

1/3 + 2/7 + x = 1

13/21 + x = 1

x = 1 - 13/21

x = 8/21