Bill says that he can add 23 and 40 without regrouping, Do you think Bill is correct? Explain your answer

Yes, Bill is correct.

Given that the sum of the ones column is lower than 10 he does not need to regroup.

You have to regroup when the additions of the digits of the same place add up more than ten. For example adding 23 and 47.

In the columns of ones you have 3 + 7 = 10, then you write 0 in the ones column and carry the one to the next column (to the left). Now, regrouping, you will have 1 + 2 + 4 in the columns of the tens to obtain 7. And the result is 70.