1. **Stating the problem:** We want to simplify fractions, which means reducing a fraction to its simplest form where the numerator and denominator have no common factors other than 1. 2. **Formula and rules:** To simplify a fraction $\frac{a}{b}$, find the greatest common divisor (GCD) of $a$ and $b$. Then divide both numerator and denominator by the GCD. 3. **Step-by-step process:** - Find $\text{GCD}(a,b)$. - Compute $\frac{a}{\text{GCD}(a,b)}$ and $\frac{b}{\text{GCD}(a,b)}$. - The simplified fraction is $\frac{a/\text{GCD}(a,b)}{b/\text{GCD}(a,b)}$. 4. **Example:** Simplify $\frac{12}{18}$. - Find $\text{GCD}(12,18) = 6$. - Divide numerator and denominator by 6: $\frac{12/6}{18/6} = \frac{2}{3}$. - So, $\frac{12}{18}$ simplifies to $\frac{2}{3}$. 5. **Explanation:** Simplifying fractions makes them easier to work with and compare. Always divide numerator and denominator by their GCD to ensure the fraction is in simplest form.