Question

Use a standard algorithm to find the product of 765 and 222 record the product of each multiplying through by each place value in 222 as well as the final product

Answer 1

To find the product of 765 and 222 using the standard algorithm, we will multiply 765 by each digit of 222, taking into account the place value of each digit. Here are the steps:

1. **Set up the multiplication:**

```
765
x 222
______
```

2. **Multiply 765 by the ones place (2):**

```
765
x 222
______
1530 (765 x 2)
```

3. **Multiply 765 by the tens place (2, but this is actually 20):**
You will place this row one position to the left (shift it left by one digit).

```
765
x 222
______
1530 (765 x 2)
1530 (765 x 2, shifted left)
```

4. **Multiply 765 by the hundreds place (2, but this is actually 200):**
You will place this row two positions to the left (shift it left by two digits).

```
765
x 222
______
1530 (765 x 2)
1530 (765 x 2, shifted left)
1530 (765 x 2, shifted left twice)
```

5. **Add up the results:**
Align the numbers by their place values:

```
765
x 222
______
1530 ---> 765 x 2 (ones)
1530 ---> 765 x 2 (tens, shifted left)
+ 1530 ---> 765 x 2 (hundreds, shifted left twice)
________
169230
```

6. **Final sum:**
Adding all rows together:

```
765
x 222
______
1530
1530 0
+ 1530 00
________
169230
```

The final product of 765 and 222 is **169,230**.