Let's solve the problems shown in the image.

6) $\frac{3}{8} + \frac{1}{2}$

To add these fractions, we need a common denominator. The least common denominator (LCD) for 8 and 2 is 8.

Convert $\frac{1}{2}$ to have a denominator of 8: $\frac{1}{2} = \frac{4}{8}$

Now add the fractions: $\frac{3}{8} + \frac{4}{8} = \frac{7}{8}$

7) $\frac{2}{3} + \frac{1}{5}$

The LCD for 3 and 5 is 15.

Convert each fraction: $\frac{2}{3} = \frac{10}{15}, \quad \frac{1}{5} = \frac{3}{15}$

Add the fractions: $\frac{10}{15} + \frac{3}{15} = \frac{13}{15}$

8) $\frac{2}{8} + \frac{1}{2}$

The LCD for 8 and 2 is 8.

Convert $\frac{1}{2}$ to have a denominator of 8: $\frac{1}{2} = \frac{4}{8}$

Add the fractions: $\frac{2}{8} + \frac{4}{8} = \frac{6}{8} = \frac{3}{4}$

9) $\frac{3}{8} - \frac{2}{3}$

The LCD for 8 and 3 is 24.

Convert each fraction: $\frac{3}{8} = \frac{9}{24}, \quad \frac{2}{3} = \frac{16}{24}$

Subtract the fractions: $\frac{9}{24} - \frac{16}{24} = -\frac{7}{24}$

10) $\frac{3}{10} - \frac{2}{5}$

The LCD for 10 and 5 is 10.

Convert $\frac{2}{5}$ to have a denominator of 10: $\frac{2}{5} = \frac{4}{10}$

Subtract the fractions: $\frac{3}{10} - \frac{4}{10} = -\frac{1}{10}$

Final Answers:

6. $\frac{7}{8}$
7. $\frac{13}{15}$
8. $\frac{3}{4}$
9. $-\frac{7}{24}$
10. $-\frac{1}{10}$

Would you like any details on these calculations, or do you have any questions?

Related Questions:

1. How do you find the least common denominator of two fractions?
2. What is the difference between adding and subtracting fractions?
3. Can a fraction's numerator be larger than its denominator?
4. How do you convert an improper fraction to a mixed number?
5. What is the process of simplifying fractions?

Tip: Always simplify fractions to their lowest terms unless instructed otherwise.