Vertical Addition: Addition of 2-digit and 1-digit numbers with the regrouping of tens

To approach this problem, we'll use vertical addition of the numbers 12 and 8:

• Step 1: Write the numbers vertically, aligning their place values.
  $\begin{aligned} &12 \\ +& \\ &~~8 \\ \hline &~~? \\ \end{aligned}$
• Step 2: Start adding from the rightmost column (units position).
  Add the units: $2 + 8 = 10$.
  Write down the 0 in the units column and carry over the 1 to the tens column.
• Step 3: Move to the next column on the left (tens position).
  Add the tens: $1 + 1 = 2$ (including the carryover 1).
  Write down the result in the tens column.
• Step 4: Combine these results to find the final sum:
  $\begin{aligned} &12 \\ +& \\ &~~8 \\ \hline &20 \\ \end{aligned}$

Therefore, the solution to the problem is $20$.

To solve this problem, we will perform vertical addition as follows:

• Step 1: Write the numbers in a column, aligning them by the right:

• $\begin{array}{c} 23 \\ + 7 \\ \hline \end{array}$

• Step 2: Add the digits in the rightmost column (ones place):

• The digits are 3 and 7. So, $3 + 7 = 10$. Write 0 in the ones place and carry over 1 to the tens place.

  $\begin{array}{c} 23 \\ + 7 \\ \hline ~~~ 0 \end{array}$

• Step 3: Add the digits in the tens place:

• The digits are 2 and, due to the carry, 1. So, $2 + 1 = 3$. Write 3 in the tens place.

  $\begin{array}{c} 1~~ \\ 23 \\ + 7~ \\ \hline 30 \end{array}$

Therefore, the sum of 23 and 7 is $30$.

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

• Step 1: Add the ones place digits.
• Step 2: If needed, adjust by carrying over any excess to the tens place.
• Step 3: Add the tens place digits.

Now, let's work through each step:
Step 1: We start by adding the digits in the ones place: $5 + 5 = 10$. Since $10$ is greater than $9$, we write down $0$ in the ones place and carry over $1$ to the tens place.
Step 2: Then, add the tens place digits. The tens digit of 45 is 4, and we add the carried over 1: $4 + 1 = 5$.
Step 3: Therefore, after adding, the complete sum is $50$.

Thus, the solution to the problem is $50$, which corresponds to choice 4.

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

• Step 1: Align the numbers vertically according to their place values:
  $\begin{aligned} &67 \\ +& \\ &~~3 \\ &\underline{\phantom{776}} \end{aligned}$
• Step 2: Begin adding from the rightmost column (units).
• Step 3: Add the digits in the units place: $7 + 3 = 10$.
• Step 4: Since the result is 10, write down the 0 under the units column and carry over the 1 to the tens column.
• Step 5: Next, add the digits in the tens column: $6 + 1 = 7$.
• Step 6: Combine the results from the tens and units columns to form the final sum.

Therefore, the solution to the problem is $70$.

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

• Step 1: Align the numbers $74$ and $6$ vertically.
• Step 2: Begin by adding the digits in the ones place.
• Step 3: Move to the tens place and include any carryover.

Let's work through each step:

Step 1: Write the numbers vertically, aligning by place value:
$\begin{aligned} &74 \\ +& \\ &~6 \\ \hline \\ &~~ \\ \end{aligned}$

Step 2: Add the ones place. The digit in the ones place of 74 is 4, and for 6 is 6. Add them together:
$4 + 6 = 10$.

Since the result is 10, write down 0 in the ones place and carry over 1 to the tens place.

Step 3: Now, move to the tens place. Add the tens digit from 74, which is 7, and add the 1 carried over from the previous step:
$7 + 1 = 8$.

This results in:
$\begin{aligned} &74 \\ +& \\ &~6 \\ \hline \\ &80 \\ \end{aligned}$

Therefore, the solution to the problem is $80$.

The problem is to perform vertical addition for the numbers $81$ and $9$. Here’s the step-by-step approach:

• Step 1: Align the numbers vertically by their rightmost digits. The digit $1$ from $81$ is aligned with $9$.
• Step 2: Add the digits in the units place: $1 + 9 = 10$. Here, $10$ is a two-digit result, where $0$ remains in the units place and $1$ is carried to the tens place.
• Step 3: Add the digits in the tens place, including the carried digit: $8 + 1 = 9$. This accounts for the $1$ we carried over from the units place addition.

Since no further carrying is necessary, the result of adding $81$ and $9$ is $90$.

Therefore, the solution to the problem is $90$, which corresponds to choice 2.