To find the sum of 3 wholes and 5 sevenths + 7 wholes and 1 half, we first convert everything to improper fractions or mixed numbers.
-
Convert the mixed numbers to improper fractions:
- 3 wholes and 5 sevenths: \(3 + \frac{5}{7} = \frac{3 \times 7 + 5}{7} = \frac{21 + 5}{7} = \frac{26}{7}\)
- 7 wholes and 1 half: \(7 + \frac{1}{2} = \frac{7 \times 2 + 1}{2} = \frac{14 + 1}{2} = \frac{15}{2}\)
-
Find a common denominator for \(\frac{26}{7}\) and \(\frac{15}{2}\):
- The common denominator of 7 and 2 is 14.
- Convert \(\frac{26}{7}\) to have a denominator of 14: \[ \frac{26}{7} \times \frac{2}{2} = \frac{52}{14} \]
- Convert \(\frac{15}{2}\) to have a denominator of 14: \[ \frac{15}{2} \times \frac{7}{7} = \frac{105}{14} \]
-
Add the two fractions: \[ \frac{52}{14} + \frac{105}{14} = \frac{52 + 105}{14} = \frac{157}{14} \]
-
Convert \(\frac{157}{14}\) back to a mixed number:
- Divide 157 by 14, which gives 11 remainder 3.
- So, \(\frac{157}{14} = 11\) whole parts and \(\frac{3}{14}\) as the remainder.
Thus, the sum of 3 wholes and 5 sevenths + 7 wholes and 1 half is:
11 and 3 over 14 (which corresponds to the response choice 11 3/14).