Add, answer as a mixed number in simplest form.

Question

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:

   • $27÷10=2$ remainder $7$,
   • So, $\frac{27}{10}=2\frac{7}{10}$.

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