Question: Work out $4 \frac{2}{7} - 2 \frac{3}{7}$. Give your answer as a mixed number in its simplest form.
1. **State the problem:** We need to subtract the mixed numbers $4 \frac{2}{7}$ and $2 \frac{3}{7}$ and express the answer as a mixed number in simplest form.
2. **Convert mixed numbers to improper fractions:**
$$4 \frac{2}{7} = \frac{4 \times 7 + 2}{7} = \frac{28 + 2}{7} = \frac{30}{7}$$
$$2 \frac{3}{7} = \frac{2 \times 7 + 3}{7} = \frac{14 + 3}{7} = \frac{17}{7}$$
3. **Subtract the improper fractions:**
$$\frac{30}{7} - \frac{17}{7} = \frac{30 - 17}{7} = \frac{13}{7}$$
4. **Convert the result back to a mixed number:**
Divide $13$ by $7$:
$$13 \div 7 = 1 \text{ remainder } 6$$
So,
$$\frac{13}{7} = 1 \frac{6}{7}$$
5. **Simplify the fraction if possible:**
The fraction $\frac{6}{7}$ is already in simplest form because $6$ and $7$ have no common factors other than $1$.
**Final answer:**
$$1 \frac{6}{7}$$