Question

Use the standard algorithm to find the product of 2,456 and 867. Record the products of each multiplying through by each place value in 867 as well as the final product.(2 points) The product of multiplying by the ones digit is . The product of multiplying by the tens digit is . The product of multiplying by the hundreds digit is . The product is .

Answer 1

2,135,572 is incorrect

Answer 2

To calculate the product of 2,456 and 867 using the standard algorithm, we will multiply 2,456 by each digit of 867 separately, keeping in mind their place values.

### Step 1: Multiply by the ones digit (7)
\[
\begin{array}{c}
\phantom{0} 2456 \\
\times \phantom{0} 7 \\
\hline
\phantom{0} 17192 \\
\end{array}
\]
**Product of multiplying by the ones digit (7):** 17,192

### Step 2: Multiply by the tens digit (6)
Since this digit is in the tens place, we will multiply by 6 and then add a zero to the right.
\[
\begin{array}{c}
\phantom{0} 2456 \\
\times \phantom{0} 6 \\
\hline
\phantom{0} 14736 \\
\end{array}
\]
Now we add a zero:
\[
\begin{array}{c}
\phantom{0} 14736 \\
\phantom{0} 0 \\
\hline
\phantom{0} 147360 \\
\end{array}
\]
**Product of multiplying by the tens digit (6):** 147,360

### Step 3: Multiply by the hundreds digit (8)
Since this digit is in the hundreds place, we will multiply by 8 and then add two zeros to the right.
\[
\begin{array}{c}
\phantom{0} 2456 \\
\times \phantom{0} 8 \\
\hline
\phantom{0} 19648 \\
\end{array}
\]
Now we add two zeros:
\[
\begin{array}{c}
\phantom{0} 19648 \\
\phantom{0} 00 \\
\hline
\phantom{0} 1964800 \\
\end{array}
\]
**Product of multiplying by the hundreds digit (8):** 1,964,800

### Final Step: Add all the products together
Now we sum all of the products:
\[
\begin{array}{r}
\phantom{00} 17192 \\
+ \phantom{0} 147360 \\
+ 1964800 \\
\hline
\phantom{0} 2132572 \\
\end{array}
\]

The final product of multiplying 2,456 by 867 is **2,135,572**.

### Summary
- The product of multiplying by the ones digit is **17,192**.
- The product of multiplying by the tens digit is **147,360**.
- The product of multiplying by the hundreds digit is **1,964,800**.
- The final product is **2,135,572**.