Consider the following quotients: 1. $368.39$ divided by $17$ 2. $170.50$ divided by $62$ 3. $875.65$ divided by $83$ Their correct sequence in decreasing order is:

Concept & Logic When asked to order complex decimal divisions, do not calculate the exact quotients. Instead, use rough mental estimation to determine the magnitude of each quotient. Step-by-Step Solution * Analyze Quotient 1: $$\frac{368.39}{17}$$ Estimate: $17 \times 20 = 340$. Since $368$ is greater than $340$, this quotient is strictly greater than $20$ (approx. $21.6$). * Analyze Quotient 2: $$\frac{170.50}{62}$$ Estimate: $60 \times 3 = 180$. Since $170$ is less than $180$, this quotient is strictly less than $3$ (approx. $2.75$). * Analyze Quotient 3: $$\frac{875.65}{83}$$ Estimate: $83 \times 10 = 830$. Since $875$ is slightly more than $830$, this quotient is slightly more than $10$ (approx. $10.5$). * Compare the estimated magnitudes: Quotient 1 ($>20$) > Quotient 3 ($\approx 10$) > Quotient 2 ($<3$). The decreasing order is 1, 3, 2. Exam Strategy & Shortcut Look at the leading digits and ignore the decimals entirely. $360 / 18 = 20$. $180 / 60 = 3$. $880 / 80 = 11$. The order is obviously $20 > 11 > 3$. This maps directly to sequence 1, 3, 2. This mental math takes less than 10 seconds. Common Pitfall The biggest mistake is attempting to perform actual long division for all three decimals. This is a massive time sink on an exam and is completely unnecessary for ordering questions where the magnitudes are far apart. Final Answer **Therefore, the correct answer is 1, 3, 2.**