Addition: Solve using a closed formula

To find the sum of the numbers $26$ and $19$, we perform the following step-by-step arithmetic calculation:

• Step 1: Arrange the numbers in a vertical column for addition:
  $\phantom{+1}26$
  $+\phantom{1}19$

• Step 2: Start adding from the unit column (right to left). Add the digits in the ones column:

  • 6 (from 26) + 9 (from 19) = 15. Write down 5 and carry over 1 to the tens column.

• Step 3: Move to the tens column and add:

  • 2 (from 26) + 1 (from 19) + 1 (carry) = 4, write down 4.

Thus, the sum of $26$ and $19$ is $45$.

Therefore, the correct answer is $45$.

To solve this problem, we'll use the information that $40 + 40 = 80$. We'll employ the following steps:

• Step 1: Realize that $39$ is 1 less than $40$. Therefore, $39 + 39$ can be rewritten using the relationship $40 + 40$ as $(40 - 1) + (40 - 1)$.
• Step 2: Simplify the expression to calculate the total: $(40 + 40) - (1 + 1) = 80 - 2$.
• Step 3: Subtract 2 from 80 to obtain the result.

Now, let's perform the calculation:

$40 + 40 = 80$ implies that $39 + 39 = 80 - 2 = 78$.

Therefore, the solution to the problem is $78$.

To solve $41 + 41$, notice that it can be related to $40 + 40 = 80$ by adding one to each of the constituent numbers $40$. This can be expressed as:

$41 + 41 = (40 + 1) + (40 + 1)$.

Breaking it down, we have:

• $40 + 40 = 80$
• Add $1 + 1$ to this result, which is $2$.

Thus, the total becomes:

$80 + 2 = 82$.

Therefore, the sum of $41 + 41$ is $\textbf{82}$.

To solve the problem of adding 39 and 24, follow these steps:

• Step 1: Write the numbers in a column format, aligning the digits by their place value (ones under ones, tens under tens):
    39
  +  24
  ------

• Step 2: Add the digits in the 'ones' column: 9 + 4 = 13. Write the 3 in the 'ones' place and carry over 1 to the 'tens' place.

• Step 3: Add the digits in the 'tens' column along with the carry: 3 + 2 + 1 (carry) = 6. Write the 6 in the 'tens' place.

• Final Calculation:
      63

Therefore, the sum of 39 and 24 is $63$.