Vertical Addition: Addition of 3-digit numbers with the regrouping of numbers in excess of ten

To solve this problem, we'll use a step-by-step vertical addition approach:

Step 1: Add the units place digits.

The units digit of $772$ is $2$, and that of $135$ is $5$. Adding these gives:

$2 + 5 = 7$

Step 2: Add the tens place digits, including any carry from the units place.

The tens digit of $772$ is $7$, and that of $135$ is $3$. Since there is no carry from the units place, we simply add the two digits:

$7 + 3 = 10$

We write down $0$ in the tens place and carry over $1$ to the hundreds place.

Step 3: Add the hundreds place digits, including any carry from the tens place.

The hundreds digit of $772$ is $7$, and that of $135$ is $1$. Including the carry of $1$, we perform the addition:

$7 + 1 + 1 = 9$

Therefore, there is no additional carry to move forward.

Bringing all parts together, we form the resulting number. Hence, the sum is:

$907$

To solve this problem, we will perform vertical addition, a common technique for summing numbers.

Let's add the numbers 383 and 308 step-by-step:

• Step 1: Add the units (rightmost) column:
  The units digits are 3 and 8.
  $3 + 8 = 11$.
  Since this sum is greater than 9, we write down 1 in the units place and carry over 1 to the next column (tens place).
• Step 2: Add the tens column, including the carry:
  The tens digits are 8 and 0, plus the 1 carried over.
  $8 + 0 + 1 = 9$.
  Write 9 in the tens place.
• Step 3: Add the hundreds column:
  The hundreds digits are 3 and 3.
  $3 + 3 = 6$.
  Write 6 in the hundreds place.

Putting it all together, the sum of 383 and 308 is $691$.

Therefore, the correct answer to the problem is $691$.

To solve this problem using vertical addition, we follow these steps:

• Step 1: Add the digits in the ones column:
  The ones digits are $4 + 7 = 11$. We write down the 1 and carry over the other 1 to the tens column.
• Step 2: Add the digits in the tens column, including the carry:
  The tens digits are $6 + 2 = 8$, plus the carry of $1$ makes $9$. We write down the 9.
• Step 3: Add the digits in the hundreds column:
  The hundreds digits are $6 + 2 = 8$. No carry from the previous column this time. We write down the 8.

Therefore, combining these, the final result of adding 664 and 227 is $891$.

The correct choice from the multiple-choice options is $891$.

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

• Step 1: Properly align the two numbers 791 and 145 vertically by their place values.

• Step 2: Add the digits column by column, starting from the rightmost column (units position).

• Step 3: Apply carrying over when the sum of any column exceeds 9.

Now, let's work through each step:

Step 1: Arrange the numbers:

$\begin{array}{c} & 7 & 9 & 1 \\ + & 1 & 4 & 5 \\ \hline \end{array}$

Notice the digits are aligned correctly according to their place value.

Step 2: Start adding from the rightmost column:

• Units column: $1 + 5 = 6$. Write 6 in the units place.

• Tens column: $9 + 4 = 13$. Write 3 in the tens place and carry over 1 to the hundreds place.

• Hundreds column: $7 + 1 = 8$, plus the carry over 1 gives $8 + 1 = 9$. Write 9 in the hundreds place.

Step 3: The final result is:

$\begin{array}{c} & & 9 & 3 & 6 \\ \end{array}$

Therefore, the sum of 791 and 145 is $\textbf{936}$.

To solve this problem, we'll follow the process of vertical addition:

• Step 1: Add the Ones Place: Add the digits in the ones place (4 + 3).
  Result: 7; no carrying is required.
• Step 2: Add the Tens Place: Add the digits in the tens place (9 + 7).
  Result: 16; write down 6 and carry over the 1.
• Step 3: Add the Hundreds Place: Add the digits in the hundreds place along with the carry (4 + 2 + 1).
  Result: 7; no additional carrying is required.

Combining these results, the final sum is $767$.

The correct multiple-choice answer is Choice 2: 767.

To solve this problem, we'll use vertical addition, a method of adding numbers by aligning them by their rightmost digits (unit place) and dealing with carrying as necessary:

• Step 1: Align the numbers by place value:
      $\phantom{+}855 \\$ + $\phantom{+}117$
• Step 2: Add the digits in the unit's place:
  The digits in the unit's place are $5$ and $7$. Adding them gives $12$. Write down $2$ in the unit column and carry over $1$ to the tens column.
• Step 3: Add the digits in the ten's place:
  The digits in the ten's place are $5$ and $1$, plus the carried over $1$, giving us $7$. Write $7$ in the tens column.
• Step 4: Add the digits in the hundred's place:
  The digits in the hundred's place are $8$ and $1$. Adding them gives $9$.

Summing these gives us the total:
    $\phantom{+}855 \\$ + $\phantom{+}117 \\$   \underline{\phantom{.}972} \)

Thus, the answer is $972$.