Final answer:
Amir's original array of cupcakes was 8 by 6, totaling 48 cupcakes. He can split it into two smaller arrays in various ways, such as two 4 by 6 arrays, or a 2 by 6 array and a 6 by 6 array, and add the products of these arrays to find the total.
Step-by-step explanation:
Amir made an 8 by 6 array of cupcakes which means a total of 8 multiplied by 6 cupcakes, or 48 cupcakes. When he breaks it into two smaller arrays, the products of the dimensions of these arrays should still total 48. There are multiple combinations that he can choose, assuming he breaks the array into two rectangular arrays.
For example, he might break the 8 by 6 array into a 4 by 6 array and a 4 by 6 array, which he would then calculate as 4 times 6 plus 4 times 6 to find the total number of cupcakes. Another possibility is breaking it into a 2 by 6 array and a 6 by 6 array, then the calculation would be 2 times 6 plus 6 times 6. The key concept is that the sum of the two products must equal the product of the original array dimensions.