Gail spent 3/10 of her day at school, and 3/9 of her day sleeping. About how much of her day is left?
A:about 7/10 B:about 1/3
C:about 1/5 D:about 4/10
My answer: I am stuck choosing between 4/10 or 1/3.
3/10+3/9=27/20+30/90=57/90
so 33/90 is left, which is about 1/3
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How is 33/90 left?
How do you get 33/90?
(90/90) - (57/90) = 33/90
To find out how much of her day is left, we need to subtract the time Gail spent at school and sleeping from the total time in a day.
First, let's calculate the sum of the fractions spent at school and sleeping:
3/10 + 3/9
To add these fractions, we need to find a common denominator. The least common multiple of 10 and 9 is 90.
Multiplying the first fraction by 9/9:
(3/10) * (9/9) = 27/90
Multiplying the second fraction by 10/10:
(3/9) * (10/10) = 30/90
Now we can add the fractions:
27/90 + 30/90 = 57/90
So, Gail spent 57/90 of her day at school and sleeping.
To find out how much of her day is left, we need to subtract this sum from 1 (since 1 represents a whole day):
1 - 57/90
To subtract fractions, we need a common denominator. The denominator 90 is already common, so we can simply subtract the numerators:
90/90 - 57/90 = 33/90
Simplifying this fraction, we divide both the numerator and denominator by their greatest common divisor, which is 3:
(33/3) / (90/3) = 11/30
Therefore, Gail has about 11/30 of her day left.
Comparing this with the answer choices, the closest option is D: about 4/10. While it is not an exact match, it is the best approximation from the given options.