1. **State the problem:** We need to subtract the fraction $2/3$ from the mixed number $1\ 3/4$ and express the answer as a mixed number in simplest form. 2. **Convert the mixed number to an improper fraction:** $$1\ \frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac{7}{4}$$ 3. **Find a common denominator:** The denominators are 4 and 3. The least common denominator (LCD) is 12. 4. **Convert both fractions to have denominator 12:** $$\frac{7}{4} = \frac{7 \times 3}{4 \times 3} = \frac{21}{12}$$ $$\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$$ 5. **Subtract the fractions:** $$\frac{21}{12} - \frac{8}{12} = \frac{21 - 8}{12} = \frac{13}{12}$$ 6. **Convert the improper fraction back to a mixed number:** $$\frac{13}{12} = 1\ \frac{1}{12}$$ 7. **Simplify the fraction if possible:** $\frac{1}{12}$ is already in simplest form. **Final answer:** $$1\ \frac{1}{12}$$