Question

Sandra used partial products to find the product of 438 × 17 by multiplying 438 by 1 and 438 by 7 to get 3,066. Find the product of 438 × 17 by using partial products. Is sandra correct? Compare your answer to sandra's and explain why it is or is not the same.

Answer 1

Let us determine the product of 438 and 17 by partial products.

Consider $438 = 400+30+8$

and $17 = 10+7$

So, $438 \times 17 = (400+30+8) \times (10+7)$

$438 \times 17 = (400\times 10)+(30 \times 10)+(8 \times 10) +(400 \times 7)+(30 \times 7)+(8 \times 7)$

= $438 \times 17 = (4000+300+80+2800+210+56)$

= 7446

Therefore, the product of 438 and 17 is 7446.

No, Sandra's answer is not correct.

Because she should have expressed 17 as (10+7), then if she multiplied (438 by 10) and (438 by 7). And, then added the results.Then her answer would be correct.