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
.

3 answers

To find the product of 765 and 222 using the standard algorithm, we will break down the multiplication by each digit in 222.

Step 1: Multiply by the ones digit

The ones digit of 222 is 2. \[ 765 \times 2 = 1530 \] The product of multiplying by the ones digit is 1530.

Step 2: Multiply by the tens digit

The tens digit of 222 is 2, but since it is in the tens place, we multiply by 20. \[ 765 \times 20 = 15300 \] The product of multiplying by the tens digit is 15300.

Step 3: Multiply by the hundreds digit

The hundreds digit of 222 is 2, so we multiply by 200. \[ 765 \times 200 = 153000 \] The product of multiplying by the hundreds digit is 153000.

Step 4: Add all the products together

Now, we will sum all the products calculated in the previous steps: \[ 1530 + 15300 + 153000 \] Calculating this step by step:

  1. Add the first two products: \[ 1530 + 15300 = 16830 \]
  2. Then, add the third product: \[ 16830 + 153000 = 169830 \]

Final Product

The product is 169830.

To summarize:

  • The product of multiplying by the ones digit is 1530.
  • The product of multiplying by the tens digit is 15300.
  • The product of multiplying by the hundreds digit is 153000.
  • The product is 169830.
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