Final answer:
The maximum number of 5 × 1 cell stripes that can be cut out from a rectangle of 7 × 9 cells is 9. This is achieved by placing the stripes vertically to fit 1 stripe per column across 9 columns.
Step-by-step explanation:
To determine the maximum number of 5 × 1 cell stripes that can be cut out from a rectangle of 7 × 9 cells, we must calculate how many such stripes fit into the area of the rectangle. Since we have stripes of 5 cells in length and 1 cell in width, we need to consider how they can be arranged within the rectangle. For the optimal use of space, the stripes can be placed either horizontally or vertically. In a 7 × 9 rectangle, more stripes can be fit in horizontally since 9 is greater than 7.
Laying the stripes horizontally, each stripe uses up 5 cells of width. Therefore, the number of stripes that can be placed in one row (horizontally) is 9 / 5, which needs to be rounded down since you can't have a partial stripe. So, you can fit 1 stripe in each horizontal row. Since there are 7 horizontal rows, you can have 7 stripes in total.
If we instead placed the 5 × 1 cell stripes vertically, each stripe would use up 5 cells of height. Thus, in the height direction, you can fit 7 / 5 = 1 stripe (rounded down). Along the width, you would have 9 stripes total (1 vertical stripe for each column of cells).
Comparing these two arrangements, fitting the stripes horizontally yields a total of 7 stripes, while fitting them vertically yields a total of 9 stripes. Therefore, the maximum number of 5 × 1 cell stripes that can be cut out is 9, which is the greater of the two possible arrangements.