Question

Why are there three partial products in 481x352 and only two partial products in 481x302?

Answer 1

352 can be separated by 300, 50, and 2. These numbers can produce 3 partial products.

302 can only produce 2 partial products because the only numbers to consider are 300 and 2. 0 is not considered because any number multiplied by 0 is equal to 0.
            481   ( 400 + 80 + 1)
          x352    (300 + 50 + 2)
                2       (2 x 1)
            160       (2 x 80)
            800       (2 x 400)   Partial product 1 = 962
              50     (50 x 1)
          4000     (50 x 80)
        20000      (50 x 400)   Partial product 2 = 24,050
            300      (300 x 1)
        24000      (300 x 80)
      120000      (300 x 400) Partial product 3 = 144,300
      169,312