1. **State the problem:** Add the numbers $1 + \frac{1}{4} + \frac{3}{4} + \frac{6}{4}$.\n\n2. **Recall the property of addition:** Addition is associative and commutative, so we can add fractions and whole numbers in any order.\n\n3. **Convert all to improper fractions or combine stepwise:**\n- $1$ can be written as $\frac{4}{4}$.\n- So the sum becomes $\frac{4}{4} + \frac{1}{4} + \frac{3}{4} + \frac{6}{4}$.\n\n4. **Add the fractions by summing numerators since denominators are the same:**\n$$\frac{4}{4} + \frac{1}{4} + \frac{3}{4} + \frac{6}{4} = \frac{4+1+3+6}{4} = \frac{14}{4}.$$\n\n5. **Simplify the fraction:**\n$$\frac{14}{4} = \frac{\cancel{14}}{\cancel{4}} \times \frac{7}{2}.$$\n\n6. **Convert to mixed number:**\n$$\frac{7}{2} = 3 \frac{1}{2}.$$\n\n**Final answer:** $3 \frac{1}{2}$.