Question

Add, answer as a mixed number in simplest form.
1 1/2 + 1 1/5
[__] [__]/[__]

Answer 1

To add the mixed numbers \(1 \frac{1}{2}\) and \(1 \frac{1}{5}\), we follow these steps:

1. Convert each mixed number to an improper fraction.
- For \(1 \frac{1}{2}\):
\[
1 \frac{1}{2} = \frac{2 \cdot 1 + 1}{2} = \frac{3}{2}
\]

- For \(1 \frac{1}{5}\):
\[
1 \frac{1}{5} = \frac{5 \cdot 1 + 1}{5} = \frac{6}{5}
\]

2. Now, we add the two improper fractions:
\[
\frac{3}{2} + \frac{6}{5}
\]

3. To add these fractions, we need a common denominator. The least common multiple of \(2\) and \(5\) is \(10\).

Convert each fraction:
- For \(\frac{3}{2}\):
\[
\frac{3}{2} = \frac{3 \cdot 5}{2 \cdot 5} = \frac{15}{10}
\]

- For \(\frac{6}{5}\):
\[
\frac{6}{5} = \frac{6 \cdot 2}{5 \cdot 2} = \frac{12}{10}
\]

4. Now add the two fractions:
\[
\frac{15}{10} + \frac{12}{10} = \frac{27}{10}
\]

5. Convert the improper fraction \(\frac{27}{10}\) back to a mixed number:
- \(27 \div 10 = 2\) remainder \(7\),
- So, \(\frac{27}{10} = 2 \frac{7}{10}\).

Thus, the answer in simplest form is:
\[
\boxed{2 \frac{7}{10}}
\]