Question

Nick tried to evaluate 42 x 36 using partial products. His work is:42 X 36Step 1: 1.200 = 30 x 4 tensStep 2: 600 = 30 x 2 tensStep 3: 240 = 6 x 4 tensStep 4: 12 = 6 x 2 onesStep 5 2,052Find Nick's mistake.

Answer 1

In order to calculate a partial product, we need to separate each digit from each number, then we multiply them similar to the distributive property:

$\begin{gathered} 42=40+2 \\ 36=30+6 \\ 42\cdot36=(40+2)\cdot(30+6)=40\cdot30+40\cdot6+2\cdot30+2\cdot6 \end{gathered}$

The mistake in Nick's steps was made in Step 2, where he multiplied 30 by 2 tens, that is, 30 by 20, resulting in 600. The correct product in this step should be 30 by 2 ones, that is, 30 by 2, resulting in 60.