The problem asks for the total time Carmen spent on two assignments. She spent $\frac{1}{2}$ hours on her history assignment and $\frac{1}{5}$ hours on her English assignment. To find the total time, we need to add these two fractions.

Here’s how you can do it step by step:

1. Find a common denominator: The denominators of the fractions are 2 and 5. The least common denominator (LCD) is 10.

   Convert both fractions to have a denominator of 10:

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

2. Add the fractions: $\frac{5}{10} + \frac{2}{10} = \frac{7}{10}$

So, the total time Carmen spent on the assignments is $\frac{7}{10}$ hours.

Would you like more details on the solution? Let me know if you need further explanations.

Here are some related questions for you:

1. What is the method to add fractions with different denominators?
2. How do you find the least common denominator?
3. Can you subtract fractions in a similar way to addition?
4. What happens when the numerators of two fractions are the same but the denominators are different?
5. How can you simplify fractions to their simplest form?

Tip: When adding or subtract