The problem requires us to add two fractions, $\frac{3}{5}$ and $\frac{1}{2}$, and then express the result as an improper fraction and a mixed number.

1. Problem Description

The problem requires us to add two fractions, $\frac{3}{5}$ and $\frac{1}{2}$, and then express the result as an improper fraction and a mixed number.

2. Solution Steps

To add the fractions $\frac{3}{5}$ and $\frac{1}{2}$, we need to find a common denominator. The least common multiple of 5 and 2 is

1

0. So, we convert both fractions to equivalent fractions with a denominator of

1

0.

$\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}$

$\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}$

Now, we can add the equivalent fractions:

$\frac{6}{10} + \frac{5}{10} = \frac{6+5}{10} = \frac{11}{10}$

The total is $\frac{11}{10}$.

Now we convert this improper fraction to a mixed number. We divide 11 by 10:

$11 \div 10 = 1$ with a remainder of $1$.

So, $\frac{11}{10} = 1\frac{1}{10}$.

3. Final Answer

$\frac{3}{5} + \frac{1}{2} = \frac{6}{10} + \frac{5}{10} = \frac{11}{10} = 1\frac{1}{10}$

The fractions are:

$\frac{6}{10} + \frac{5}{10} = \frac{11}{10} = 1\frac{1}{10}$