1. **Problem:** Simplify the expression $12 + 14\frac{1}{2} + \frac{1}{4}21 + 41$. 2. **Step 1:** Convert mixed numbers and fractions to improper fractions or decimals for easier addition. $14\frac{1}{2} = 14 + \frac{1}{2} = 14.5$ $\frac{1}{4}21$ means $\frac{1}{4} \times 21 = 5.25$ 3. **Step 2:** Add the numbers step-by-step: $12 + 14.5 = 26.5$ $26.5 + 5.25 = 31.75$ $31.75 + 41 = 72.75$ 4. **Step 3:** Convert the decimal back to a mixed number if desired: $72.75 = 72 + \frac{3}{4} = 72\frac{3}{4}$ **Final answer:** $72\frac{3}{4}$