Question

Which partial products are incorrect? What is the correct final product?

Twenty-six is multiplied by twelve. Partial products of twelve, forty, six hundred, and two thousand are added resulting in final product of two thousand six hundred fifty-two.

Answer 1

Explanation:

26×12 = 312

partial products are "strange". but ok, since your teacher wants it that way :

multiply the tens with the tens : 20×10 = 200

multiply the tens with the ones : 20×2 = 40

multiply the ones with the tens : 6×10 = 60

multiply the ones with the ones : 6×2 = 12

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312

so, 12 and 40 are correct from the original list, 600 and 2000 are wrong.

how do you do it conceptually ?

26×12 start with the left digit (1),

multiply the left number right to left

6×1 (no carry) 6

2×1 2

26

next digit to the right (2),

also move the result one position

6×2 (carry 1) 2

2×2 (plus carry) 5

52

now we add position related

26

52

---------

2

1 (and carry 1)

3 (2 plus carry)

312