Question

Add, answer as a mixed number in simplest form.
2 2/5 + 2 7/10
[__] [__]/[__]

Answer 1

To add the mixed numbers \(2 \frac{2}{5}\) and \(2 \frac{7}{10}\), follow these steps:

1. **Convert the mixed numbers to improper fractions**:
- \(2 \frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{10 + 2}{5} = \frac{12}{5}\)
- \(2 \frac{7}{10} = \frac{2 \times 10 + 7}{10} = \frac{20 + 7}{10} = \frac{27}{10}\)

2. **Find a common denominator**:
The denominators are 5 and 10. The least common multiple of 5 and 10 is 10.
- Convert \(\frac{12}{5}\) to have a denominator of 10:
\[
\frac{12}{5} = \frac{12 \times 2}{5 \times 2} = \frac{24}{10}
\]

3. **Add the fractions**:
Now, add \(\frac{24}{10}\) and \(\frac{27}{10}\):
\[
\frac{24}{10} + \frac{27}{10} = \frac{24 + 27}{10} = \frac{51}{10}
\]

4. **Convert back to a mixed number**:
To convert \(\frac{51}{10}\) back to a mixed number, divide the numerator by the denominator:
\[
51 \div 10 = 5 \text{ remainder } 1
\]
Thus, \(\frac{51}{10} = 5 \frac{1}{10}\).

5. **Final answer**:
The final answer in simplest form is:
\[
5 \frac{1}{10}
\]
In the requested format, that would be:

\[ 5 \quad 1 \quad 10 \]