Let's simplify the given expression step by step:

$2 \frac{1}{2} - \frac{1}{8} - 1 \frac{1}{2}$

Step 1: Convert Mixed Numbers to Improper Fractions

• $2 \frac{1}{2} = \frac{5}{2}$
• $1 \frac{1}{2} = \frac{3}{2}$

Thus, the expression becomes:

$\frac{5}{2} - \frac{1}{8} - \frac{3}{2}$

Step 2: Find a Common Denominator

The denominators are 2 and 8. The least common denominator is 8.

• Convert $\frac{5}{2}$ to have denominator 8: $\frac{5}{2} = \frac{20}{8}$
• Convert $\frac{3}{2}$ to have denominator 8: $\frac{3}{2} = \frac{12}{8}$

Thus, the expression becomes:

$\frac{20}{8} - \frac{1}{8} - \frac{12}{8}$

Step 3: Perform Subtraction

$\frac{20}{8} - \frac{1}{8} = \frac{19}{8}$ $\frac{19}{8} - \frac{12}{8} = \frac{7}{8}$

Final Answer:

$\frac{7}{8}$

Would you like a more detailed explanation or have any questions?

Related Questions:

1. How do you convert mixed fractions to improper fractions?
2. What is the least common denominator, and how is it found?
3. How do you simplify fractions after performing operations?
4. What is the difference between proper and improper fractions?
5. How do you add or subtract fractions with different denominators?

Tip:

When working with mixed fractions in subtraction or addition, always convert them to improper fractions first to avoid mistakes.