Question

Add 3 wholes and 5 seveths + 7 wholes and 1 half
. What is the sum?(1 point)
Responses

10314
10 and 3 over 14

11314
11 and 3 over 14

1023
10 and 2 thirds

1157

Answer 1

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.

1. **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: \(7 + \frac{1}{2} = \frac{7 \times 2 + 1}{2} = \frac{14 + 1}{2} = \frac{15}{2}\)

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:
\[
\frac{15}{2} \times \frac{7}{7} = \frac{105}{14}
\]

3. **Add the two fractions:**
\[
\frac{52}{14} + \frac{105}{14} = \frac{52 + 105}{14} = \frac{157}{14}
\]

4. **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).