Solve Vertical Addition: Finding the Sum of 45 + 77

$\begin{aligned} &45 \\ +& \\ &77 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

To solve this problem, we'll follow these steps:

• Step 1: Add the digits in the units column.
• Step 2: Add the digits in the tens column, considering any carried value.
• Step 3: Write down the resulting number as the answer.

Now, let's work through each step:
Step 1: Add the units digits. The units digit of 45 is 5, and the units digit of 77 is 7. Adding these gives: $5 + 7 = 12$. Since 12 is greater than 9, we write down 2 in the units column and carry over 1 to the tens column.
Step 2: Add the tens digits. The tens digit of 45 is 4, and the tens digit of 77 is 7. Including the carry-over 1 gives: $4 + 7 + 1 = 12$. Since 12 is a two-digit number, we write down 2 in the tens column and carry over 1 again, which is written in the hundreds column.
Step 3: Since there is nothing to add to the carried 1 in the hundreds column, we simply write it down as is.

Therefore, the solution to the problem is $122$.