\begin{tabular}{|l|l|l|l|} $\newline$ \hline & $?$ & $?$ & $5$ \\ $\newline$ \hline $40$ & $?$ & $?$ & $200$ \\ $\newline$ \hline $?$ & $2400$ & $?$ & $?$ \\ $\newline$ \hline & $?$ & $960$ & \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ What are the missing factors? $\newline$ What are the missing partial products? $\newline$ Total Product $=15,600$

Full solution

Q. \begin{tabular}{|l|l|l|l|}

\newline

\hline &

?

?

5

\newline

\hline

40

?

?

200

\newline

\hline

?

2400

?

?

\newline

\hline &

?

960

& \\

\newline

\hline

\newline

\end{tabular}

\newline

What are the missing factors?

\newline

What are the missing partial products?

\newline

Total Product

=15,600

Pattern of Multiplication: First, let's look at the pattern of multiplication. We're multiplying something by $5$ , $40$ , $200$ , $2400$ , and so on. It looks like we're multiplying by powers of $10$ each time.
Find First Missing Factor: Let's start with the first missing factor. We know that something times $5$ equals $40$ . So, the missing factor is $40$ divided by $5$ , which is $8$ .
Find Second Missing Factor: Now, let's find the second missing factor. We have $8$ times something equals $200$ . To find the missing factor, we divide $200$ by $8$ , which gives us $25$ .
Find Third Missing Factor: Next, we need to find the third missing factor. We have $25 \times \text{something} = 2400$ . Dividing $2400$ by $25$ gives us $96$ .
Find Fourth Missing Factor: Finally, we need to find the fourth missing factor. We have $96 \times \text{something} = 960$ . Dividing $960$ by $96$ gives us $10$ .
Check Total Product: Now, let's check if our factors multiply to give the total product of $15,600$ . We multiply all the factors: $8 \times 25 \times 96 \times 10$ . This equals $192,000$ , which is not $15,600$ . Oops, looks like we made a mistake somewhere.