Solve the Fraction Addition: 1/5 + 3/10 + 2/5 Step-by-Step

Solve the following exercise:

$\frac{1}{5}+\frac{3}{10}+\frac{2}{5}=\text{?}$

To solve this problem, we need to add the fractions $\frac{1}{5}$, $\frac{3}{10}$, and $\frac{2}{5}$.

First, we need to find a common denominator for all the fractions. The denominators we have are 5, 10, and 5. The least common multiple (LCM) of these numbers is 10.

Let's convert each fraction to have a denominator of 10:

• $\frac{1}{5}$ can be converted to: $\frac{1 \times 2}{5 \times 2} = \frac{2}{10}$
• $\frac{3}{10}$ is already with a denominator of 10, so it remains: $\frac{3}{10}$
• $\frac{2}{5}$ can be converted to: $\frac{2 \times 2}{5 \times 2} = \frac{4}{10}$

Now we can add the fractions:

$\frac{2}{10} + \frac{3}{10} + \frac{4}{10} = \frac{2 + 3 + 4}{10} = \frac{9}{10}$

Therefore, the sum of the fractions is $\frac{9}{10}$.

So, the solution to the problem is $\frac{9}{10}$.