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

It's not a dumb question at all! In fact, it's a great opportunity to discuss fractions and why the sum in this case is greater than 1 whole.

To understand why the sum is greater than 1 whole, let's break it down.

The fraction 5/7 represents the proportion of students who have a sister. This means that out of a total of 7 students, 5 have a sister.

The fraction 1/2 represents the proportion of students who have a brother. This means that out of a total of 2 students, 1 has a brother.

The fraction 3/14 represents the proportion of students who do not have siblings. This means that out of a total of 14 students, 3 do not have siblings.

Now let's add these fractions together:

5/7 + 1/2 + 3/14

To add fractions, we need to have a common denominator. In this case, the common denominator is 14, because it is the least common multiple of 7 and 2.

Converting each fraction to have a denominator of 14, we get:

(10/14) + (7/14) + (6/14)

Adding the numerators, we get:

23/14

Now, let's simplify this fraction. 23/14 is an improper fraction, which means the numerator is greater than the denominator. To convert it to a mixed number, we divide the numerator (23) by the denominator (14). The quotient is 1 with a remainder of 9. So, the fraction can be written as:

1 9/14

Therefore, the sum of the fractions is 1 9/14 or 1 and 9/14.

Now, to answer the question why it makes sense for the sum to be greater than 1 whole, it's because fractions are part of a whole. In this case, when we combine the proportions of students with sisters, brothers, and no siblings, we find that the total exceeds the number of students surveyed (which is 1 whole). This is because some students have both sisters and brothers or no siblings at all. So, the sum of the fractions represents the combined portion of students with siblings and without siblings, which is greater than the total number of students in the survey.