What is 23×17 in array and an expanded algorithm

Question

What is 23×17 in array and an expanded algorithm

Answer 1

23 × 17? Oh, let me put on my clown hat and entertain you with a little math circus!

Well, to calculating this, we can break it down into an array representation. Imagine a little grid where each cell represents a product of two numbers. We'll go for it, shall we?

Let's start with the rows and columns:
| 1 | 7
--|-----|-----
2 | 2 | 14
3 | 3 | 21

Wait, did you expect something more complex? I’m afraid I just spilled a bucket of simplicity on this one. Anyway, if you want an expanded algorithm to reach the same answer, let me clown around a bit more!

First, you multiply 7 by 3 (which gives you 21), and then you multiply 7 by 20 (which gives you 140). Next, you multiply 1 by 3 (which gives you 3), and finally, you multiply 1 by 20 (which gives you 20). Add them all up, and voila! You'll end up with 391.

I hope I brought some laughter to your mathematical quest. Remember, even numbers need a good chuckle every now and then!

Answer 2

To find the product of 23 and 17 using an array and an expanded algorithm, follow these steps:

1. Create an array with two rows and two columns.
```
[ ][ ]
[ ][ ]
```

2. Write the numbers 23 and 17 along the top and left side of the array.
```
23 17
[ ][ ]
[ ][ ]
```

3. Starting from the top left corner of the array, multiply the corresponding numbers together.
```
23 17
[ 391 ][ ]
[ ][ ]
```

4. Multiply the number in the top left corner by the number to its right, and fill in the result in the next column.
```
23 17
[ 391 ][391 ]
[ ][ ]
```

5. Multiply the number in the top left corner by the number below it, and fill in the result in the next row.
```
23 17
[ 391 ][391 ]
[391 ][ ]
```

6. Multiply the number in the top right corner by the number below it, and fill in the result in the next row.
```
23 17
[ 391 ][391 ]
[391 ][391 ]
```

7. Add all the numbers in the array together to get the final product.
```
23 17
[ 391 ][391 ]
[391 ][391 ]
_________
391 + 391 + 391 + 391 = 1,586
```

So, 23 multiplied by 17 equals 1,586.

Answer 3

To find the product of 23 and 17, we can use an array method.

First, let's create a grid with two rows and two columns:

2 3
× 1 7

Now, we need to multiply the digits in each position of the grid:

2 3
× 1 7
__________
6
+ 1 4
__________

Now, let's add the results vertically:

391

So, 23 multiplied by 17 equals 391.

Now, let's discuss an expanded algorithm to find the product of 23 and 17:

Step 1: Multiply 3 (the units digit of 23) by 17:
3 * 17 = 51

Step 2: Multiply 20 (the tens digit of 23) by 17:
20 * 17 = 340

Step 3: Add the results from Step 1 and Step 2:
51 + 340 = 391

Therefore, using the expanded algorithm, we find that 23 multiplied by 17 equals 391.