2. A student performs the following estimations: 24 + 190 = 210, 151 + 319 = 470, 974 + 1022 = 1990. Based on these estimations, what is the student's estimate of 452 + 5017?
Answer: B
The student's estimate of 452 + 5017 is 5470.
The student likely rounds the numbers in the addition problem to arrive at their estimation. For 452, rounding to the nearest hundred gives 500, and for 5017, rounding to the nearest hundred gives 5000. Thus, the estimate would be 500 + 5000 = 5470.
A) 5430
This option is incorrect because estimating 452 as 430 and 5017 as 5000 would yield a total of 4430, which is not close to the result of 5470. This underestimation fails to reflect the rounding approach demonstrated in the student's previous estimations.
B) 5470
This is the correct answer as it accurately reflects the estimation process used by the student. By rounding 452 to 500 and 5017 to 5000, the sum calculated is 500 + 5000, resulting in an estimate of 5470.
C) 5500
This option is incorrect as it overestimates the sum. Rounding 452 to 500 is appropriate, but rounding 5017 to 5000 is more accurate than rounding it to 5000 plus an additional 500, which would lead to an estimate of 5500.
D) 5400
This option is also incorrect. If the student had estimated 452 as 400 and 5017 as 5000, it would yield a sum of 5400. However, this method does not align with the rounding strategy the student has applied in their earlier estimations.
Conclusion
The estimation of 5470 is definitively correct as it follows the rounding technique used in the previous calculations. Other options either underestimate or overestimate the addition based on incorrect rounding, making them invalid in the context of the student's demonstrated approach to estimation.