during a week a student spends 1/5 of her time in bed,1/8 of her time doing home work and 2/5 of her time in lessons.What fraction of her time is left for doing other things?
Change the fractions to decimals. Add them. Subtract the sum from 1.
To find the fraction of time that is left for doing other things, we need to subtract the time spent in bed, doing homework, and in lessons from the total time available in a week.
Let's assign variables to represent the time spent in each activity:
- Time spent in bed: 1/5 of the week
- Time spent doing homework: 1/8 of the week
- Time spent in lessons: 2/5 of the week
To find the fraction of time left for doing other things, we need to subtract these from 1 (since we want the fraction of time remaining):
1 - (1/5 + 1/8 + 2/5)
To simplify the expression, we need to find a common denominator for the fractions:
1 - (8/40 + 5/40 + 16/40)
Combining the fractions with the common denominator:
1 - (29/40)
Now subtract the fractions:
1 - 29/40 = (40/40) - (29/40) = 11/40
Therefore, the fraction of time left for doing other things is 11/40.