1. Stating the problem: We are given a set of fractions and asked to solve the first distinct problem, which is to simplify and compare fractions such as $\frac{12}{5}$ and $\frac{36}{15}$.\n\n2. Formula and rules: To compare or simplify fractions, we use the rule that two fractions $\frac{a}{b}$ and $\frac{c}{d}$ are equivalent if $ad = bc$. To simplify a fraction, divide numerator and denominator by their greatest common divisor (GCD).\n\n3. Simplify $\frac{36}{15}$: Find GCD of 36 and 15.\nGCD(36,15) = 3.\nDivide numerator and denominator by 3:\n$$\frac{36}{15} = \frac{36 \div 3}{15 \div 3} = \frac{12}{5}$$\n\n4. Compare $\frac{12}{5}$ and $\frac{36}{15}$: After simplification, both are $\frac{12}{5}$, so they are equivalent.\n\n5. Explanation: Simplifying fractions helps us see if two fractions represent the same value. Here, $\frac{36}{15}$ simplifies to $\frac{12}{5}$, confirming equivalence.\n\nFinal answer: $\frac{12}{5} = \frac{36}{15}$