Use the standard algorithm to find the product of 319 and 384. Record the products of each multiplying through by each place value in 384 as well as the final product.
To find the product of 319 and 384 using the standard algorithm, follow these steps:
Step 1: Start by multiplying the units digit of 319 (9) with each digit in 384. Write down each product.
9 * 4 = 36
9 * 8 = 72
9 * 3 = 27
Step 2: Multiply the tens digit of 319 (1) with each digit in 384. Write down each product, shifting the digit one place to the left.
1 * 4 = 4 (write down as 40)
1 * 8 = 8 (write down as 80)
1 * 3 = 3 (write down as 300)
Step 3: Multiply the hundreds digit of 319 (3) with each digit in 384. Write down each product, shifting the digit two places to the left.
3 * 4 = 12 (write down as 120)
3 * 8 = 24 (write down as 240)
3 * 3 = 9 (write down as 900)
Step 4: Add up all the products obtained in each step.
36
+ 72
+ 27
+ 40
+ 80
+ 300
+ 120
+ 240
+ 900
------
= 122496
Therefore, the product of 319 and 384 using the standard algorithm is 122496.
3 1 9
× 3 8 4
___________
9 5 2 8 <--- This is the product of 319 and 4 (3 x 319)
+ 2 3 8 4 0 <--- This is the product of 319 and 80 (8 x 319 shifted one place to the left)
+ 1 9 1 2 0 0 <--- This is the product of 319 and 300 (3 x 319 shifted two places to the left)
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1 2 2 1 3 6 <--- Final product of 319 and 384 (9528 + 23840 + 191200)