arrays and an expanded algorithm of 29x47=
To find the product of 29 and 47 using an expanded algorithm, we can use the concept of arrays and multiplication.
Step 1: Create two rows of arrays representing the two numbers, 29 and 47.
```
2 9
x 4 7
```
Step 2: Multiply each digit of the second number (47) with each digit of the first number (29). Start with the rightmost digit (7) and multiply it by each digit in the first number.
```
2 9
x 4 7
-----------
2 9 <-- Multiply 7 by 9
+ 1 4 5 <-- Multiply 7 by 2 and shift one place to the left
-----------
```
Step 3: Multiply the second digit (4) of the second number with each digit of the first number, shifting the result one place to the left compared to the previous multiplication.
```
2 9
x 4 7
-----------
1 1 6 <-- Multiply 4 by 6 and shift two places to the left
+ 5 8 <-- Multiply 4 by 2 and shift one place to the left
-----------
```
Step 4: Add up the products obtained in the previous steps.
```
2 9
x 4 7
-----------
1 1 6
+ 5 8
-----------
```
Step 5: The final result is 116 + 58 = 174.
Therefore, 29 multiplied by 47 equals 174.