Question

Use the standard algorithm to find the product of 246 and 188. Record the products of each multiplying through by each place value in 188 as well as the final product.(2 points)

Answer 1

To find the product of 246 and 188 using the standard algorithm, we will multiply 246 by each digit in 188, starting from the rightmost digit and moving to the left, while keeping track of place values.

### Step 1: Multiply 246 by the units digit of 188 (which is 8)

\[
\begin{align*}
& \quad \ 246 \\
\times & \quad 8 \\
\hline
& \quad 1968 \quad \text{ (This is 246 multiplied by 8)}
\end{align*}
\]

### Step 2: Multiply 246 by the tens digit of 188 (which is 8 in the tens place, representing 80)

\[
\begin{align*}
& \quad \ 246 \\
\times & \quad 80 \\
\hline
& \quad 19680 \quad \text{ (This is 246 multiplied by 8 and shifted one position to the left)}
\end{align*}
\]

### Step 3: Multiply 246 by the hundreds digit of 188 (which is 1, representing 100)

\[
\begin{align*}
& \quad \ 246 \\
\times & \quad 100 \\
\hline
& \quad 24600 \quad \text{ (This is 246 multiplied by 1 and shifted two positions to the left)}
\end{align*}
\]

### Step 4: Add all the products from the steps above

Now, we add the three partial products together:

\[
\begin{align*}
& \quad 1968 \\
+ & \quad 19680 \\
+ & \quad 24600 \\
\hline
& \quad 46208 \\
\end{align*}
\]

### Final Product
Thus, the final product of \( 246 \times 188 \) is:

\[
\boxed{46208}
\]