1. **State the problem:** Divide $1 \frac{3}{4}$ by 7 and express the answer in cm. 2. **Convert mixed number to improper fraction:** $$1 \frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac{7}{4}$$ 3. **Set up the division:** $$\frac{7}{4} \div 7$$ 4. **Rewrite division as multiplication by reciprocal:** $$\frac{7}{4} \times \frac{1}{7}$$ 5. **Multiply numerators and denominators:** $$\frac{7 \times 1}{4 \times 7} = \frac{7}{28}$$ 6. **Simplify the fraction by canceling common factors:** $$\frac{\cancel{7}}{4 \times \cancel{7}} = \frac{1}{4}$$ 7. **Final answer:** $$\frac{1}{4} \text{ cm}$$ So, dividing $1 \frac{3}{4}$ by 7 gives $\frac{1}{4}$ cm.