Which multiplication problem is modeled by the array?

A rectangle with dimensions 24 by 18 units is partitioned into a 10 by 20 unit rectangle, a 10 by 8 unit rectangle, a 10 by 4 unit rectangle, and an 8 by 4 unit rectangle.

(1 point)
Responses

24×18=400+80+160+32=672

24 × 18 = 400 + 80 + 160 + 32 = 672

24×18=400+80+80+32=592

24 × 18 = 400 + 80 + 80 + 32 = 592

24×18=200+40+160+32=432

24 × 18 = 200 + 40 + 160 + 32 = 432

24×18=100+40+160+32=332

24 × 18 = 100 + 40 + 160 + 32 = 332
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1 answer

To determine which multiplication problem is modeled by the array, we first need to sum the areas of the smaller rectangles within the larger 24 by 18 rectangle.

The smaller rectangles are:

  1. 10 by 20 = 200
  2. 10 by 8 = 80
  3. 10 by 4 = 40
  4. 8 by 4 = 32

Now, let's calculate the total area of the smaller rectangles:

  • Area of 10 by 20 = 200
  • Area of 10 by 8 = 80
  • Area of 10 by 4 = 40
  • Area of 8 by 4 = 32

Adding these areas together: 200 + 80 + 40 + 32 = 352

Now, comparing it with the selection of responses given:

  1. 24×18=400+80+160+32=672
  2. 24 × 18 = 400 + 80 + 160 + 32 = 672
  3. 24×18=400+80+80+32=592
  4. 24 × 18 = 400 + 80 + 80 + 32 = 592
  5. 24×18=200+40+160+32=432
  6. 24 × 18 = 200 + 40 + 160 + 32 = 432
  7. 24×18=100+40+160+32=332
  8. 24 × 18 = 100 + 40 + 160 + 32 = 332

It seems that none of the options add up to the area of 352. However, the closest multiplication expression is:

24 × 18 = 432 (from options 5 and 6).

During the analysis of areas and expressed problems with layers or addition that are not precisely reached in the partition theory here in the options.

If you're strictly looking for the multiplication related to the partitioned parts accurately derived could be best represented by alternative values associated accordingly through total values from the rectilinear areas.

The 24 × 18 = 432 suggests an underlying structure valid but presents a nondisputed correct alignment of distinct portions.

Thus, best deemed to select: 24 × 18 = 200 + 40 + 160 + 32 = 432. (Option 6 for its calculated construct aligns)