Question

7 wholes and 1 half plus 4 wholes and 3 fourths

Answer 1

To add the two fractions, we first convert the mixed numbers to improper fractions.

1. **Convert 7 wholes and 1 half to an improper fraction**:
\[
7 \frac{1}{2} = 7 \times 2 + 1 = 14 + 1 = \frac{15}{2}
\]

2. **Convert 4 wholes and 3 fourths to an improper fraction**:
\[
4 \frac{3}{4} = 4 \times 4 + 3 = 16 + 3 = \frac{19}{4}
\]

Now we can add the two improper fractions \(\frac{15}{2}\) and \(\frac{19}{4}\). To do this, we need a common denominator. The least common denominator (LCD) for 2 and 4 is 4.

3. **Convert \(\frac{15}{2}\) to have a denominator of 4**:
\[
\frac{15}{2} \times \frac{2}{2} = \frac{30}{4}
\]

Now, we have:
\[
\frac{30}{4} + \frac{19}{4} = \frac{30 + 19}{4} = \frac{49}{4}
\]

4. **Convert \(\frac{49}{4}\) back to a mixed number**:
- \(49 \div 4 = 12\) (whole part) with a remainder of 1.
- So, \(\frac{49}{4} = 12 \frac{1}{4}\).

Thus, the final answer is:
\[
12 \frac{1}{4}
\]