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
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