Question 1: Estimate the product of 4.68 and 3.29 by rounding each to the nearest whole number. Write your estimate.

Answer: 15

Question 2: Calculate the exact product of 4.68 and 3.29. Then, estimate the product by rounding both numbers to one decimal place. Show your working.

Answer: 15.4

Question 3: Estimate the product of 0.97 and 0.56 using compatible numbers. Explain your reasoning.

Answer: Approximately 1×0.5=0.5 because 0.97 is close to 1 and 0.56 is close to 0.5.

Question 4: A recipe calls for 2.75 kg of flour and 1.49 kg of sugar. Estimate the total weight by rounding to the nearest half kilogram. Show your steps.

Answer: Approximate 2.75 as 3 kg and 1.49 as 1.5 kg; total approximately 4.5 kg.

Question 5: Estimate the product of 6.13 and 2.78 by rounding each to the nearest tenth. Show your calculations.

Answer: 17.1

Question 6: A store sells 12.4 packs of paper each containing approximately 8.6 sheets. Estimate the total number of sheets in all packs. Show your reasoning.

Answer: Estimate 12×9=108 packs; total sheets approximately 108×9≈972 sheets.

Question 7: Calculate 3.75 × 4.22 exactly. Then estimate the product by rounding each to the nearest whole number. Show your work.

Answer: Approximately 4×4=16

Question 8: Estimate the product of 0.43 and 0.59 using compatible numbers. Explain your reasoning.

Answer: Approximate as 0.4×0.6=0.24 because these are close to the given numbers.

Question 9: A farmer harvests approximately 18.7 acres of wheat and 23.5 acres of corn. Estimate the total area harvested by rounding to the nearest ten acres and adding.

Answer: Round to 20 and 20; total approximately 40 acres.

Question 10: Estimate the product of 9.32 and 7.48 by rounding each to the nearest whole number. Show your work.

Answer: Approximately 9×7=63

Question 11: Estimate the product of 5.89 and 2.33, then compare your estimate with the exact product. Explain whether your estimate was too high or too low and why.

Answer: Estimate as 6×2.3=13.8; actual product slightly higher, so estimate was slightly low.

Question 12: Identify and correct the mistake in this estimation: Students estimated 7.2×3.8 as 28 by rounding both to 7 and 4, then multiplying 7×4.

Answer: Rounding 7.2 to 7 and 3.8 to 4 gives an overestimate; the correct approach is to round to 7 and 4 or to 7.2 and 3.8 for better accuracy, but multiplying 7×4 gives an estimate of 28 which is close but less precise. The mistake is in assuming the rounded numbers perfectly reflect the original decimals.