1. The problem is to calculate $3490 \div 42$ using a fast method. 2. One fast method is to simplify the division by factoring or approximating. 3. First, write the division as a fraction: $$\frac{3490}{42}$$ 4. Simplify by dividing numerator and denominator by 2 (since 42 is even): $$\frac{3490}{42} = \frac{\cancel{3490}}{\cancel{42}} = \frac{1745}{21}$$ 5. Now divide 1745 by 21 using long division or approximation: - $21 \times 80 = 1680$ - $1745 - 1680 = 65$ 6. So, $$1745 \div 21 = 80 + \frac{65}{21} = 80 + 3 + \frac{2}{21} = 83 + \frac{2}{21}$$ 7. The fraction $\frac{2}{21}$ is approximately $0.095$. 8. Therefore, the final answer is approximately $$83.095$$ 9. In summary, $$3490 \div 42 \approx 83.095$$