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.
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