Use the standard algorithm to find the product of 765 and 222. Record the products of each multiplying through by each place value in 222 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 .
First, we multiply 765 by the ones digit of 222, which is 2:
765 × 2 = 1530
Next, we multiply 765 by the tens digit of 222, which is 2:
765 × 20 = 15300
Finally, we multiply 765 by the hundreds digit of 222, which is 2:
765 × 200 = 153000
Now we add up all the products:
1530 + 15300 + 153000 = 169830
So, the product of 765 and 222 is 169830.
To find the product of 765 and 222 using the standard algorithm, we can use long multiplication.
First, let's multiply 765 by the ones digit of 222 (which is 2):
\[
\begin{align*}
&\phantom{\times}765\\
\times &\phantom{0}2\\
\hline
&\phantom{=}1530\\
\end{align*}
\]
Next, we multiply 765 by the tens digit of 222 (which is 2, but we'll introduce a placeholder 0 as it represents the tens place):
\[
\begin{align*}
&\phantom{\times}765\\
\times &\phantom{0}20\\
\hline
&\phantom{0}15300\\
\end{align*}
\]
Finally, we multiply 765 by the hundreds digit of 222 (which is 2, but we'll introduce two placeholder 0's as it represents the hundreds place):
\[
\begin{align*}
&\phantom{\times}765\\
\times &200\\
\hline
&153000\\
\end{align*}
\]
Now, let's add up the three products we calculated:
\[
\begin{align*}
&\phantom{\times}765\\
\times &\phantom{0}222\\
\hline
&\phantom{\times} 1530\\
&\phantom{\times} 15300\\
&\phantom{\times} 153000\\
\hline
& 169530\\
\end{align*}
\]
Therefore, the product of 765 and 222 is 169530.
To find the product of 765 and 222 using the standard algorithm, we'll multiply each digit in the second number (222) by each digit in the first number (765), and then add the results.
Step 1: Multiply the ones digit (2) of the second number by each digit in the first number:
765 * 2 = 1530
Step 2: Multiply the tens digit (2) of the second number by each digit in the first number, but shifted one place to the left:
765 * 20 = 15300
Step 3: Multiply the hundreds digit (2) of the second number by each digit in the first number, shifted two places to the left:
765 * 200 = 153000
Step 4: Add up the results from steps 1, 2, and 3 to get the final product:
1530 + 15300 + 153000 = 169830
Therefore, the product of 765 and 222 is 169830.
To summarize:
- The product of multiplying 765 by the ones digit (2) of 222 is 1530.
- The product of multiplying 765 by the tens digit (20) of 222 is15300.
- The product of multiplying 765 by the hundreds digit (200) of 222 is 153000.
- The final product of multiplying 765 by 222 is 169830.