1. **State the problem:** Show that $\frac{1}{5}$ is the same as $\frac{2}{10}$.\n\n2. **Formula and rule:** Two fractions $\frac{a}{b}$ and $\frac{c}{d}$ are equivalent if $a \times d = b \times c$.\n\n3. **Work:** Check if $1 \times 10 = 5 \times 2$.\n$$1 \times 10 = 10$$\n$$5 \times 2 = 10$$\nSince both products are equal, $\frac{1}{5} = \frac{2}{10}$.\n\n4. **Explanation:** Multiplying numerator and denominator of $\frac{1}{5}$ by 2 gives $\frac{2}{10}$, so they represent the same value.\n