Multi-digit multiplication (standard algorithm) Transitional Reasoning Download PDF

Questions

1. 1.

   A water conservation district distributes rainwater harvesting kits across 38 residential zones. In each zone, technicians assemble 145 basic collection barrels and 82 high-capacity filtration barrels. A project supervisor calculates the total number of barrels distributed by first finding the total number of barrels per zone and then multiplying by 38 using the standard multiplication algorithm. What is the total number of barrels distributed across all 38 zones?

   • A) 8,626
   • B) 8,246
   • C) 5,510
   • D) 2,497
2. 2.

   A community sports complex is replacing all the seats in its two main grandstands. Grandstand 1 has 34 rows with 126 seats in each row, while Grandstand 2 has 28 rows with 145 seats in each row. The venue manager has a stockpile of 8,500 numbered plaques to label every seat across both grandstands. How many plaques will remain in the stockpile after every seat in both grandstands has been labeled?

   • A) 56
   • B) 244
   • C) 256
   • D) 156
3. 3.

   A logistics supervisor reviews an invoice where the total shipping charge was calculated by multiplying a three-digit base fee by 27 using the standard multiplication algorithm. The digits of the base fee are obscured by an ink smudge, but the first partial product generated from multiplying this base fee by the ones digit is clearly legible as 1,841. What is the complete final product of the multiplication on this invoice?

   • A) 6,831
   • B) 7,101
   • C) 7,371
   • D) 5,260
4. 4.

   A distribution warehouse is preparing emergency relief kits for regional shelters. Each large cargo pallet holds 425 hygiene packs, and a cargo flight is loaded with 36 of these pallets. A logistics coordinator calculates the total number of hygiene packs using the standard multiplication algorithm, where the first partial product represents the packs on 6 pallets and the second partial product represents the packs on the remaining 30 pallets. By how many packs does the quantity accounted for in the second partial product exceed the quantity in the first partial product?

   • A) 1,275 packs
   • B) 8,500 packs
   • C) 10,200 packs
   • D) 15,300 packs
5. 5.

   A regional library orders 275 boxes of books, with each box containing 48 books. An inventory clerk computes the total number of books using the standard multiplication algorithm but accidentally aligns the second partial product directly under the ones column without shifting it one place to the left. How many fewer books does the clerk's final sum show than the actual total number of books?

   • A) 3,300 books
   • B) 7,700 books
   • C) 8,800 books
   • D) 9,900 books