To solve the multiplication of [tex]\( 924 \times 327 \)[/tex] using the standard algorithm, let's break the problem down step by step. We will perform the multiplication by considering each digit of the second number (327) starting from the units place, then the tens place, and finally the hundreds place.
1. Multiply [tex]\( 924 \)[/tex] by the units place of [tex]\( 327 \)[/tex] (which is 7):
[tex]\[
924 \times 7 = 6468
\][/tex]
2. Multiply [tex]\( 924 \)[/tex] by the tens place of [tex]\( 327 \)[/tex] (which is 2, but since it's in the tens place it represents 20):
[tex]\[
924 \times 2 = 1848
\][/tex]
Since this represents 20, we must multiply this result by 10:
[tex]\[
1848 \times 10 = 18480
\][/tex]
3. Multiply [tex]\( 924 \)[/tex] by the hundreds place of [tex]\( 327 \)[/tex] (which is 3, but since it's in the hundreds place it represents 300):
[tex]\[
924 \times 3 = 2772
\][/tex]
Since this represents 300, we must multiply this result by 100:
[tex]\[
2772 \times 100 = 277200
\][/tex]
4. Add up all the intermediate results from the above steps:
[tex]\[
6468 \quad \text{(from units place multiplication)}
\][/tex]
[tex]\[
+ 18480 \quad \text{(from tens place multiplication)}
\][/tex]
[tex]\[
+ 277200 \quad \text{(from hundreds place multiplication)}
\][/tex]
[tex]\[
\text{----------------------}
\][/tex]
Now, summing these, we get:
[tex]\[
6468 + 18480 + 277200 = 302148
\][/tex]
Thus, the complete standard multiplication for [tex]\( 924 \times 327 \)[/tex] is [tex]\( 302148 \)[/tex].
