Let's solve the expression:

$\frac{3}{7} \times 0.5 + \frac{4}{7} \times 0.5$

First, multiply each fraction by 0.5:

$\frac{3}{7} \times 0.5 = \frac{3 \times 0.5}{7} = \frac{1.5}{7}$

$\frac{4}{7} \times 0.5 = \frac{4 \times 0.5}{7} = \frac{2}{7}$

Now, add the two fractions:

$\frac{1.5}{7} + \frac{2}{7} = \frac{1.5 + 2}{7} = \frac{3.5}{7}$

Finally, simplify:

$\frac{3.5}{7} = 0.5$

So, the value of the expression is $0.5$.

Would you like more details on any step? Here are some related questions to explore:

1. What is the general process for adding fractions?
2. How do you multiply a fraction by a decimal?
3. How do you simplify fractions like $\frac{3.5}{7}$?
4. What are other ways to solve expressions involving fractions and decimals?
5. How does the distributive property apply to this problem?

Tip: When multiplying fractions by decimals, it's often helpful to convert the decimal into a fraction first!