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. The product of multiplying by the ones digit is 1276. The product of multiplying by the tens digit is 25520. The product of multiplying by the hundreds digit is 95700. The product is .

Answer 1

To find the product of 319 and 384 using the standard algorithm, we will multiply 319 by each digit of 384, starting from the ones place, and then we will sum these products.

Here are the steps using the standard algorithm:

1. Multiply by the ones digit (4): \[ 319 \times 4 = 1276 \]

2. Multiply by the tens digit (8): \[ 319 \times 8 = 2552 \quad (Remember to add a zero because we are in the tens place, so it becomes 25520) \]

3. Multiply by the hundreds digit (3): \[ 319 \times 3 = 957 \quad (Add two zeros because we are in the hundreds place, so it becomes 95700) \]

Now we can add these three partial products together:

\[ 1276

• 25520
• 95700 \] Let's align the numbers for addition:

     1276
   25520
+ 95700
--------

Now, performing the addition:

1. Start from the rightmost column:
   • \(6 + 0 + 0 = 6\)
2. Next column:
   • \(7 + 2 + 0 = 9\)
3. Next column:
   • \(2 + 5 + 7 = 14\) (write down 4 and carry over 1)
4. Next column:
   • \(1 + 5 + 5 + 1 = 12\) (write down 2 and carry over 1)
5. Finally, from the leftmost column (including carry):
   • \(9 + 1 = 10\) (write down 10)

Putting this together, we get:

     1276
   25520
+ 95700
--------
  122256

Thus, the final product of \(319 \times 384\) is: \[ \text{The product is } 122256. \]