Question: Work out $3 \frac{1}{8} - \frac{5}{4}$
Give your answer as an improper fraction in its simplest form.
1. **State the problem:** We need to calculate $3 \frac{1}{8} - \frac{5}{4}$ and express the answer as an improper fraction in simplest form.
2. **Convert mixed number to improper fraction:**
$$3 \frac{1}{8} = \frac{3 \times 8 + 1}{8} = \frac{24 + 1}{8} = \frac{25}{8}$$
3. **Rewrite the subtraction:**
$$\frac{25}{8} - \frac{5}{4}$$
4. **Find a common denominator:**
The denominators are $8$ and $4$. The least common denominator (LCD) is $8$.
5. **Convert $\frac{5}{4}$ to denominator $8$:**
$$\frac{5}{4} = \frac{5 \times 2}{4 \times 2} = \frac{10}{8}$$
6. **Subtract the fractions:**
$$\frac{25}{8} - \frac{10}{8} = \frac{25 - 10}{8} = \frac{15}{8}$$
7. **Simplify the fraction:**
$15$ and $8$ have no common factors other than $1$, so $\frac{15}{8}$ is already in simplest form.
**Final answer:**
$$\boxed{\frac{15}{8}}$$