how do you do arrays and an expanded algorithm? 23x17?
23x17=391
31x19
589
23×17 usind arrays
To perform mathematical operations like multiplication and store values efficiently, we can use arrays and an expanded algorithm. Let me explain the steps involved in multiplying two numbers using an array and an expanded algorithm, specifically for calculating 23 multiplied by 17.
Step 1: Create two arrays to represent the multiplicand (23) and the multiplier (17). Each array would contain individual digits of the number, represented from right to left. For our example, the arrays would look like this:
Multiplicand (23) array: [3, 2]
Multiplier (17) array: [7, 1]
Step 2: Calculate the product of each digit in the multiplicand array with each digit in the multiplier array.
Product of 3 (from multiplicand) and 7 (from multiplier): 3 x 7 = 21
Product of 3 (from multiplicand) and 1 (from multiplier): 3 x 1 = 3
Product of 2 (from multiplicand) and 7 (from multiplier): 2 x 7 = 14
Product of 2 (from multiplicand) and 1 (from multiplier): 2 x 1 = 2
Step 3: Position the products relative to each other in the answer array.
Answer array: [1, 3, 2, 2]
Step 4: Handle any carry-overs. If a product is greater than 9, then carry over the tens digit to the next position.
Carry-over from 21: 2 (written above 3)
Carry-over from 14: 1 (written above 3)
Step 5: Sum up the values in the answer array.
Sum: 112 + 210 = 322
Therefore, the result of multiplying 23 by 17 is 322.
Keep in mind that when working with larger numbers, this method can become more complex and time-consuming. There are more efficient algorithms available, like the Karatsuba algorithm or the Toom–Cook multiplication algorithm, which are used for multiplying large numbers efficiently.