Question

Use the standard algorithm to multiply 475×96475×96 . Record the product of multiplying by the ones digit, the product of multiplying by the tens digit, and the final product.(2 points)

Answer 1

To multiply \( 475 \times 96475 \) using the standard algorithm, we will break down the multiplication into steps based on the digits of the second number (96475).

### Step 1: Multiply by the ones digit (5)
Multiply \( 475 \) by \( 5 \).

\[
\begin{array}{c}
475 \\
\times 5 \\
\hline
2375
\end{array}
\]

### Step 2: Multiply by the tens digit (7)
Next, we multiply \( 475 \) by \( 7 \), but since this is in the tens place, we will add a zero to the right.

\[
\begin{array}{c}
475 \\
\times 7 \\
\hline
3325 \\
\end{array}
\]
So, write down \( 3325 \) as \( 33250 \).

### Step 3: Multiply by the hundreds digit (4)
Multiply \( 475 \) by \( 4 \), adding two zeros to the right (since this digit is in the hundreds place).

\[
\begin{array}{c}
475 \\
\times 4 \\
\hline
1900 \\
\end{array}
\]
So, write down \( 1900 \) as \( 190000 \).

### Step 4: Multiply by the thousands digit (6)
Now, multiply \( 475 \) by \( 6 \), adding three zeros to the right (as this digit is in the thousands place).

\[
\begin{array}{c}
475 \\
\times 6 \\
\hline
2850 \\
\end{array}
\]
So, write down \( 2850 \) as \( 2850000 \).

### Step 5: Multiply by the ten-thousands digit (9)
Finally, multiply \( 475 \) by \( 9 \), adding four zeros to the right (as this digit is in the ten-thousands place).

\[
\begin{array}{c}
475 \\
\times 9 \\
\hline
4275 \\
\end{array}
\]
So, write down \( 4275 \) as \( 42750000 \).

### Step 6: Add all the products
Now, we add up the products from each step:

\[
\begin{align*}
\quad \quad \quad 2375 \\
+ \quad \quad \quad 33250 \\
+ \quad \quad \quad 190000 \\
+ \quad \quad 2850000 \\
+ 42750000 \\
\hline
\quad 45768525 \\
\end{align*}
\]

### Final Product
Thus, the final product of \( 475 \times 96475 \) is \( 45768525 \).

### Summary of Products
- Product of multiplying by the ones digit (5): **2375**
- Product of multiplying by the tens digit (7): **33250**
- Final Product: **45768525**