posted by Sara .
5th grade math parent. This will sound dumb but.... 5/7 1/2 and 3/14. The sum is 1 3/7 correct? The question reads MArshall surveyed his classmates and found 5/7 have a sister, 1/2 have a brother, and 3/14 do not have siblings. The question is: Why does it make sense for the sum to be greater than 1 whole?
Because those students who have a sister probably have a brother also or vice versa. So it's like they are counted twice. So naturally the count would be greater than the actual number of students.
I'll give you an example. For instance, Marshall has 14 classmates.
5/7 of 14 = 10 students have a sister
1/2 of 14 = 7 students have a brother
3/14 of 14 = 3 students have no siblings
The total is 20 (greater than 14). But what if 6 out of 7 students with a brother have also a sister? Thus, in those 10 students with a sister, 6 of them have also a brother, and so 10 - 6 = 4, and only this 4 students have a sister alone.
To summarize again:
4 have a sister alone
6 have a sister & brother
1 has a brother alone (this is from 7 - 6)
3 have no siblings.
Adding them: 4 + 6 + 1 + 3 = 14 (which is equal to the actual)
Don't worry, it's not really a dumb question. Actually it's pretty tricky. :)
Hope this helps~ :3