Question

Simplify answer if necessary. 8 3/8 + 7 1/4 + 12 1/2

Answer 1

To add the mixed numbers \(8 \frac{3}{8}\), \(7 \frac{1}{4}\), and \(12 \frac{1}{2}\), we first convert each mixed number into an improper fraction.

1. **Convert \(8 \frac{3}{8}\)**:
\[
8 \frac{3}{8} = \frac{8 \times 8 + 3}{8} = \frac{64 + 3}{8} = \frac{67}{8}
\]

2. **Convert \(7 \frac{1}{4}\)**:
\[
7 \frac{1}{4} = \frac{7 \times 4 + 1}{4} = \frac{28 + 1}{4} = \frac{29}{4}
\]

3. **Convert \(12 \frac{1}{2}\)**:
\[
12 \frac{1}{2} = \frac{12 \times 2 + 1}{2} = \frac{24 + 1}{2} = \frac{25}{2}
\]

Now we need to find a common denominator for \(\frac{67}{8}\), \(\frac{29}{4}\), and \(\frac{25}{2}\). The least common multiple of the denominators 8, 4, and 2 is 8.

4. **Convert \(\frac{29}{4}\) to a denominator of 8**:
\[
\frac{29}{4} = \frac{29 \times 2}{4 \times 2} = \frac{58}{8}
\]

5. **Convert \(\frac{25}{2}\) to a denominator of 8**:
\[
\frac{25}{2} = \frac{25 \times 4}{2 \times 4} = \frac{100}{8}
\]

Now we can add all the fractions together:
\[
\frac{67}{8} + \frac{58}{8} + \frac{100}{8} = \frac{67 + 58 + 100}{8} = \frac{225}{8}
\]

Next, we will convert \(\frac{225}{8}\) back into a mixed number:
\[
225 \div 8 = 28 \quad \text{remainder } 1
\]
So,
\[
\frac{225}{8} = 28 \frac{1}{8}
\]

Thus, the simplified sum is:
\[
\boxed{28 \frac{1}{8}}
\]