Final answer:
The best estimate of 11 1/5 ÷ 2 2/3 is 4.2, although initially we estimated 3 using round numbers. A more precise estimate is found by converting the mixed numbers to improper fractions and then performing the division.
Step-by-step explanation:
The student has asked for the best estimate of 11 1/5 ÷ 2 2/3. To estimate this division, we can round the numbers to whole numbers or simpler fractions that are easier to divide. In this case, we could round 11 1/5 to 11 and 2 2/3 to 3. 11 divided by 3 gives us an estimate of about 3 ⅗ 1, or simply 3.
To provide an accurate estimation, however, we should convert the mixed numbers to improper fractions. 11 1/5 becomes 56/5, and 2 2/3 becomes 8/3. Dividing these gives (56/5) ÷ (8/3) = (56 × 3)/(5 × 8) = 168/40 which simplifies to 4.2. Thus, a better estimate of 11 1/5 ÷ 2 2/3 would be approximately 4.2 which aligns with our initial rough estimate of 3 when rounded to the nearest whole number.