1. **State the problem:** Multiply the mixed number $12 \frac{2}{3}$ by 20. 2. **Convert the mixed number to an improper fraction:** $$12 \frac{2}{3} = \frac{12 \times 3 + 2}{3} = \frac{36 + 2}{3} = \frac{38}{3}$$ 3. **Set up the multiplication:** $$\frac{38}{3} \times 20$$ 4. **Rewrite 20 as a fraction:** $$\frac{38}{3} \times \frac{20}{1}$$ 5. **Multiply the numerators and denominators:** $$\frac{38 \times 20}{3 \times 1} = \frac{760}{3}$$ 6. **Simplify the fraction if possible:** 760 and 3 have no common factors other than 1, so the fraction is already in simplest form. 7. **Convert the improper fraction back to a mixed number:** Divide 760 by 3: $$760 \div 3 = 253 \text{ remainder } 1$$ So, $$\frac{760}{3} = 253 \frac{1}{3}$$ **Final answer:** $$12 \frac{2}{3} \times 20 = 253 \frac{1}{3}$$