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:
- Add the first two products: \[ 1530 + 15300 = 16830 \]
- 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.