Question

An online book store has 182 boxes of books in its warehouse. Each box has 32 books. Part A Which equation represents the best estimate of the total number of books in the warehouse? (1 point) Responses 180 × 30 = 5,400 180 × 30 = 5 , 400 180 × 40 = 7,200 180 × 40 = 7 , 200 190 × 40 = 7,600 190 × 40 = 7 , 600 200 × 40 = 8,000

Answer 1

To find the best estimate of the total number of books in the warehouse, we can round the numbers to make the multiplication simpler.

The warehouse has 182 boxes, which we can round to 180. Each box has 32 books, which we can round to 30 for estimation purposes.

So, the best estimated equation would be:

180 × 30 = 5,400

Therefore, the correct response is: 180 × 30 = 5,400.

Answer 2

Part B Use the drop-down box to explain the estimate in Part A. (1 point) The best estimate is an over estimate or overestimate

Answer 3

The best estimate is an overestimate.

This is because rounding down the number of boxes from 182 to 180 and rounding down the number of books in each box from 32 to 30 leads to a total that may be less than the actual total when further refined. Thus, the estimate using these rounded numbers (180 × 30) gives a lower total than the actual values (182 × 32).

Therefore, the estimate is conservative and does not exceed the actual total.

Answer 4

Part C Use the drop-down boxes to explain your answer in Part B. (1 point) 180 ___ 182 and 30 ____ 32, so 180 × 30 ___ 182 × 32 . in the blanks use greater than less than and equal signs

Answer 5

The sentence can be completed as follows:

180 < 182 and 30 < 32, so 180 × 30 < 182 × 32.

This means that 180 is less than 182, and 30 is less than 32, leading to the conclusion that the product of 180 and 30 is less than the product of 182 and 32.