Let's solve each part of the problem, which requires rewriting each expression as a single fraction.

a. $\frac{3}{8} + \frac{1}{8}$

Since the denominators are the same (both are 8), we can simply add the numerators: $\frac{3}{8} + \frac{1}{8} = \frac{3 + 1}{8} = \frac{4}{8} = \frac{1}{2}$

b. $\frac{4}{5} + \frac{3}{4}$

To add these fractions, we need a common denominator. The least common denominator (LCD) of 5 and 4 is 20.

Now, rewrite each fraction with denominator 20: $\frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20}, \quad \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}$

Now, add the fractions: $\frac{16}{20} + \frac{15}{20} = \frac{16 + 15}{20} = \frac{31}{20}$ This is an improper fraction, so it can also be written as a mixed number: $1 \frac{11}{20}$, but leaving it as $\frac{31}{20}$ is perfectly valid.

c. $\frac{6}{7} - \frac{2}{5}$

To subtract these fractions, we again need a common denominator. The least common denominator of 7 and 5 is 35.

Now, rewrite each fraction with denominator 35: $\frac{6}{7} = \frac{6 \times 5}{7 \times 5} = \frac{30}{35}, \quad \frac{2}{5} = \frac{2 \times 7}{5 \times 7} = \frac{14}{35}$

Now, subtract the fractions: $\frac{30}{35} - \frac{14}{35} = \frac{30 - 14}{35} = \frac{16}{35}$

Thus, the solution to each part is:

• a. $\frac{1}{2}$
• b. $\frac{31}{20}$
• c. $\frac{16}{35}$

Do you want further details on any of the steps?

Here are 5 related questions:

1. How do you find the least common denominator (LCD) of two fractions?
2. What is the difference between proper and improper fractions?
3. How can you convert an improper fraction to a mixed number?
4. What happens if you subtract a larger fraction from a smaller one?
5. Can you multiply fractions without finding a common denominator?

Tip: When adding or subtracting fractions, always simplify the final result if possible.