1. **Stating the problem:** Find how much $\frac{3}{2}$ is less than $6 \frac{3}{10}$. 2. **Convert mixed numbers to improper fractions:** $6 \frac{3}{10} = \frac{6 \times 10 + 3}{10} = \frac{63}{10}$ 3. **Find the difference:** $$\frac{63}{10} - \frac{3}{2}$$ 4. **Find common denominator:** The least common denominator of 10 and 2 is 10. 5. **Rewrite fractions with common denominator:** $$\frac{63}{10} - \frac{3 \times 5}{2 \times 5} = \frac{63}{10} - \frac{15}{10}$$ 6. **Subtract numerators:** $$\frac{63 - 15}{10} = \frac{48}{10}$$ 7. **Simplify the fraction:** $$\frac{48}{10} = \frac{\cancel{48}^{24}}{\cancel{10}^{5}} = \frac{24}{5}$$ 8. **Convert to mixed number:** $$\frac{24}{5} = 4 \frac{4}{5}$$ **Final answer:** $4 \frac{4}{5}$ is how much $\frac{3}{2}$ is less than $6 \frac{3}{10}$.