Arrays (intro to multiplication) Transitional Reasoning Practice

Questions

1. 1.

   Kendra is designing a mini-quilt using square fabric patches arranged in a rectangular array of 6 rows with 8 patches in each row. She uses dark patches for the entire outer border, which includes the first row, the last row, and the first and last patch of every middle row. The remaining interior space is filled completely with light patches to form a smaller inner rectangular array. What are the dimensions of this inner array, and how many light patches are used?

   • A) 5 rows with 7 patches in each row, giving 35 light patches
   • B) 4 rows with 8 patches in each row, giving 32 light patches
   • C) 6 rows with 6 patches in each row, giving 36 light patches
   • D) 4 rows with 6 patches in each row, giving 24 light patches
2. 2.

   During a robotics club activity, a team arranges sensor pads on a practice floor in a rectangular array of 7 rows with 6 pads in each row. To adjust the field layout, they remove 2 pads from every row. The team then uses all of these removed pads, plus some extra pads from a storage box, to build a new rectangular array consisting of 5 rows with 4 pads in each row. How many extra pads did the team need from the storage box to complete the new array?

   • A) 4
   • B) 8
   • C) 14
   • D) 6
3. 3.

   Liam is setting up chairs in a hall for a music performance. He initially arranges the chairs in 5 rows with 8 chairs in each row. Before the show begins, he adds 2 more identical rows of 8 chairs to the back of the seating section. How many total chairs are in the expanded seating area, and which multiplication equation represents this new array?

   • A) 56 chairs, represented by $7 \times 8 = 56$
   • B) 48 chairs, represented by $6 \times 8 = 48$
   • C) 42 chairs, represented by $7 \times 6 = 42$
   • D) 80 chairs, represented by $10 \times 8 = 80$
4. 4.

   A community art club is making a mosaic tile display on a wall. Sofia initially places ceramic tiles in a rectangular array with 4 rows and 6 tiles in each row. To fit a different picture frame, she decides to rearrange all of the same tiles into a new array that has only 3 rows. How many tiles must Sofia place in each row, and which multiplication equation represents the new array?

   • A) 8 tiles in each row; $3 \times 8 = 24$
   • B) 7 tiles in each row; $3 \times 7 = 21$
   • C) 5 tiles in each row; $3 \times 5 = 15$
   • D) 9 tiles in each row; $3 \times 9 = 27$

Answers and step-by-step solutions appear after you finish the test.