What is 23×17 in array and an expanded algorithm
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!
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.
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.