Question: Divide. Simplify your answer.
$5\ 1/4 \div 3$
1. **State the problem:** We need to divide $5\ 1/4$ by $3$ and simplify the answer.
2. **Convert the mixed number to an improper fraction:**
$$5\ 1/4 = \frac{5 \times 4 + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4}$$
3. **Write the division as multiplication by the reciprocal:**
$$\frac{21}{4} \div 3 = \frac{21}{4} \times \frac{1}{3}$$
4. **Multiply the numerators and denominators:**
$$\frac{21 \times 1}{4 \times 3} = \frac{21}{12}$$
5. **Simplify the fraction:**
Find the greatest common divisor (GCD) of $21$ and $12$, which is $3$.
$$\frac{\cancel{3} \times 7}{\cancel{3} \times 4} = \frac{7}{4}$$
6. **Convert the improper fraction back to a mixed number:**
$$\frac{7}{4} = 1\ \frac{3}{4}$$
**Final answer:** $1\ \frac{3}{4}$