Explanation: Addition is associative: (a+b)+c = a+(b+c). Multiplication: (a*b)*c = a*(b*c). Subtraction not: (a-b)-c a-(b-c), e.g., (5-3)-1=1, 5-(3-1)=3. Division not: (a/b)/c a/(b/c), e.g., (8/4)/2=1, 8/(4/2)=4. Exponentiation not: (a^b)^c a^(b^c), e.g., (2^3)^2=64, 2^(3^2)=512. Associativity requires grouping irrelevance, which holds for add and mult over reals, but counterexamples disprove for others. Common confusion might arise from commutativity, but associativity is distinct, and testing with numbers confirms only addition and multiplication satisfy universally in these contexts.

Explanation: Isabella’s estimate is closest. The exact product is 1.592×8=12.736. Interpreting the student estimates as reasonable rounded approximations of 1.592 and 8, Isabella used 1.590×8=12.72, Michael used 1.600×8=12.80, and Jayden and Sarah appear to have rounded the multiplier to 10, producing much larger values (≈15.90 and 16.00). Compute absolute errors: |12.736−12.72| = 0.016 for Isabella; |12.736−12.80| = 0.064 for Michael; Jayden and Sarah differ by over 3.1. Because Isabella’s error (0.016) is the smallest, her estimate is the closest to the actual value. Thus Isabella is the student with the best estimate.

Explanation: Unit price = $2.67 ÷ 3 = $0.89 per can. Multiply by 8: $0.89 × 8 = $7.12, so 8 cans cost $7.12. Cross-checking with different methods confirms accuracy. This builds foundational skills for ratios in algebra and real-life budgeting.

Explanation: Identify the maximum and minimum temperatures from the data: the highest recorded temperature is 34°F (at 1 PM) and the lowest is −54°F (at 6 AM). The difference between the greatest and least values equals the greatest minus the least. Since subtracting a negative is equivalent to adding its absolute value, compute 34 − (−54) = 34 + 54. Adding these gives 88. Therefore, the range of recorded temperatures—the difference between the greatest and least recorded readings—is 88°F. This calculation shows how to handle negative values correctly when finding a spread: always subtract the minimum from the maximum, and remember that subtracting a negative increases the result by the absolute value of that negative number.

Explanation: In 12,679, the places are 1 (ten thousands), 2 (thousands), 6 (hundreds), 7 (tens), 9 (ones), satisfying both conditions. Similarly, 12,769 has 1 (ten thousands), 2 (thousands), 7 (hundreds), 6 (tens), 9 (ones), also matching. 12,796 has 1 (ten thousands) but 6 (ones), not 9. 21,679 has 2 (ten thousands), 1 (thousands), so 1 is not in ten thousands, though 9 is ones. 21,769: 2 (ten thousands), 1 (thousands), 9 (ones), but 1 wrong place. 21,796: 2 (ten thousands), 1 (thousands), 6 (ones), neither condition fully met. The key is verifying each digit's place value precisely, as shifting digits changes places, leading to mismatches in the other options.