Let's solve each subtraction problem step by step and show how to work them out.

1. $\frac{1}{2} - \frac{1}{4}$

1. Find the least common denominator (LCD) of 2 and 4: $\text{LCD} = 4$.
2. Rewrite fractions with the denominator 4:
   • $\frac{1}{2} = \frac{2}{4}$
   • $\frac{1}{4} = \frac{1}{4}$
3. Subtract the numerators:
   $\frac{2}{4} - \frac{1}{4} = \frac{2 - 1}{4} = \frac{1}{4}$ Answer: $\frac{1}{4}$

2. $\frac{1}{3} - \frac{1}{6}$

1. Find the LCD of 3 and 6: $\text{LCD} = 6$.
2. Rewrite fractions with the denominator 6:
   • $\frac{1}{3} = \frac{2}{6}$
   • $\frac{1}{6} = \frac{1}{6}$
3. Subtract the numerators:
   $\frac{2}{6} - \frac{1}{6} = \frac{2 - 1}{6} = \frac{1}{6}$ Answer: $\frac{1}{6}$

3. $\frac{2}{3} - \frac{1}{6}$

1. Find the LCD of 3 and 6: $\text{LCD} = 6$.
2. Rewrite fractions with the denominator 6:
   • $\frac{2}{3} = \frac{4}{6}$
   • $\frac{1}{6} = \frac{1}{6}$
3. Subtract the numerators:
   $\frac{4}{6} - \frac{1}{6} = \frac{4 - 1}{6} = \frac{3}{6}$
4. Simplify $\frac{3}{6}$:
   $\frac{3}{6} = \frac{1}{2}$ Answer: $\frac{1}{2}$

4. $\frac{3}{4} - \frac{1}{2}$

1. Find the LCD of 4 and 2: $\text{LCD} = 4$.
2. Rewrite fractions with the denominator 4:
   • $\frac{3}{4} = \frac{3}{4}$
   • $\frac{1}{2} = \frac{2}{4}$
3. Subtract the numerators:
   $\frac{3}{4} - \frac{2}{4} = \frac{3 - 2}{4} = \frac{1}{4}$ Answer: $\frac{1}{4}$

5. $\frac{5}{6} - \frac{1}{3}$

1. Find the LCD of 6 and 3: $\text{LCD} = 6$.
2. Rewrite fractions with the denominator 6:
   • $\frac{5}{6} = \frac{5}{6}$
   • $\frac{1}{3} = \frac{2}{6}$
3. Subtract the numerators:
   $\frac{5}{6} - \frac{2}{6} = \frac{5 - 2}{6} = \frac{3}{6}$
4. Simplify $\frac{3}{6}$:
   $\frac{3}{6} = \frac{1}{2}$ Answer: $\frac{1}{2}$

6. $\frac{5}{6} - \frac{2}{3}$

1. Find the LCD of 6 and 3: $\text{LCD} = 6$.
2. Rewrite fractions with the denominator 6:
   • $\frac{5}{6} = \frac{5}{6}$
   • $\frac{2}{3} = \frac{4}{6}$
3. Subtract the numerators:
   $\frac{5}{6} - \frac{4}{6} = \frac{5 - 4}{6} = \frac{1}{6}$ Answer: $\frac{1}{6}$

7. $\frac{1}{4} - \frac{1}{8}$

1. Find the LCD of 4 and 8: $\text{LCD} = 8$.
2. Rewrite fractions with the denominator 8:
   • $\frac{1}{4} = \frac{2}{8}$
   • $\frac{1}{8} = \frac{1}{8}$
3. Subtract the numerators:
   $\frac{2}{8} - \frac{1}{8} = \frac{2 - 1}{8} = \frac{1}{8}$ Answer: $\frac{1}{8}$

Summary of Answers:

1. $\frac{1}{4}$
2. $\frac{1}{6}$
3. $\frac{1}{2}$
4. $\frac{1}{4}$
5. $\frac{1}{2}$
6. $\frac{1}{6}$
7. $\frac{1}{8}$

Would you like further explanations or practice questions?

Here are 5 related problems to expand your understanding:

1. $\frac{7}{12} - \frac{5}{12}$
2. $\frac{2}{5} - \frac{1}{10}$
3. $\frac{4}{7} - \frac{2}{14}$
4. $\frac{3}{8} - \frac{1}{4}$
5. $\frac{9}{10} - \frac{3}{5}$

Tip: Always simplify your answer if possible to reduce fractions to their lowest terms!