Add 3 5/7 + 7 1/2 . What is the sum?
A : 10 2/3
B : 10 3/14
C : 11 5/7
D : 11 3/14
To add these fractions, we need to convert the mixed numbers into improper fractions.
3 5/7 can be written as (3 * 7 + 5)/7 = 26/7.
Similarly, 7 1/2 can be written as (7 * 2 + 1)/2 = 15/2.
Now, add the two fractions: (26/7) + (15/2).
To add these fractions, we need a common denominator, which is the least common multiple of 7 and 2, which is 14.
So, we can rewrite the fractions with the common denominator: (26/7) + (15/2) = (26 * 2)/(7 * 2) + (15 * 7)/(2 * 7) = 52/14 + 105/14.
Now, add the fractions: (52/14) + (105/14) = (52 + 105)/14 = 157/14.
The sum is 157/14.
To convert the improper fraction back to a mixed number, we divide the numerator (157) by the denominator (14) and write the remainder as a fraction.
157 divided by 14 is 11 with a remainder of 3.
So, the answer is 11 3/14.
Therefore, the correct option is D: 11 3/14.