Vertical Addition: Addition of 3-digit and 2-digit numbers with some regrouping beyond 1000

To solve this problem, we'll proceed by using vertical addition:

• Step 1: Align the numbers by their place values.
• Step 2: Add the digits in the units place: $3 + 9 = 12$. Write down 2 and carry over 1 to the tens column.
• Step 3: Add the digits in the tens place along with the carried-over value: $7 + 9 + 1 = 17$. Write down 7 and carry over 1 to the hundreds column.
• Step 4: Add the digits in the hundreds place along with the carried-over value: $2 + 8 + 1 = 11$. Write down 1, and since there's no more digit to process, the remaining 1 represents a thousand. Thus, we write down 11 for the thousands and hundreds place.

Therefore, the solution to the addition problem is $1172$.

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

• Step 1: Write the numbers 346 and 965 in a columnar fashion, aligning them by place value.
• Step 2: Add the numbers starting with the ones place.
• Step 3: Move to the tens place and add the digits, including any carry from the ones place.
• Step 4: Continue to the hundreds place, again including any carry from the tens place.

Let's break this down:

Step 1: Write vertically:
$\begin{aligned} &346\\ + &965\\ \end{aligned}$

Step 2: Add the ones place:
$6 + 5 = 11$. Write down 1 and carry over 1 to the tens place.

Step 3: Add the tens place (including carry):
$4 + 6 = 10$, plus the carry 1 makes 11. Write down 1 and carry over 1 to the hundreds place.

Step 4: Add the hundreds place (including carry):
$3 + 9 = 12$, plus the carry 1 makes 13. Write down 13 as there are no more places to carry over.

Thus, the sum of 346 and 965 is $\underline{1311}$.

Therefore, the solution to the problem is $\mathbf{1311}$.

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

• Step 1: Line up the numbers according to their place values.

• Step 2: Add the numbers column by column from right to left.

• Step 3: Carry over any values greater than 9 to the next column.

Now, let's work through each step:

Step 1: Align the numbers vertically by place value:

$\begin{array}{c} \phantom{+}~~~~~653 \\ + \phantom{+}399 \\ \end{array}$

Step 2: Add the numbers in the ones column (rightmost column):

$3 + 9 = 12$

The result is 12. Place the 2 in the ones column and carry over 1 to the tens column.

Step 3: Add the numbers in the tens column, including the carry:

$5 + 9 + 1 = 15$

The result is 15. Place the 5 in the tens column and carry over 1 to the hundreds column.

Step 4: Add the numbers in the hundreds column, including the carry:

$6 + 3 + 1 = 10$

Place the 0 in the hundreds column and the 1 also in the next higher column (thousands place).

Therefore, the sum of $653$ and $399$ is $1052$.

To solve this problem, we'll perform vertical addition:

• Step 1: Add the units digits $6$ and $7$.
• $6 + 7 = 13$
• Place $3$ in the units place and carry over $1$ to the tens place.


• Step 2: Add the tens digits plus any carryover: $1$ (carry) + $1$ (from 716) + $2$ (from 427).
• $1 + 1 + 2 = 4$
• Place $4$ in the tens place.


• Step 3: Add the hundreds digits plus any carryover: $7$ (from 716) + $4$ (from 427).
• $7 + 4 = 11$
• Place $1$ in the hundreds place and carry over another $1$ to the next higher place value (thousands).


• Step 4: Place the carryover in the thousands place.
• This gives a final number, arranged as $\underline{1143}$.

Therefore, the solution to the problem is $1143$.

To solve this problem, we will perform the addition of the numbers 877 and 656 using the vertical column method. Let's break it down step by step:

• Step 1: Write the numbers vertically aligned by their place values: units, tens, and hundreds.
• Step 2: Start by adding the units column (rightmost column): $7 + 6 = 13$. Write down 3 in the units place and carry over 1 to the tens place.
• Step 3: Next, add the tens column: $7 + 5 = 12$. Adding the carryover 1 gives total $13$. Write down 3 in the tens place and carry over 1 to the hundreds place.
• Step 4: Finally, add the hundreds column: $8 + 6 = 14$. Adding the carryover 1 gives total $15$. Since this is the leftmost column, write down the entire result, 15, in the appropriate place.

The sum of the numbers is therefore $1533$.

Hence, the correct answer to the problem is $1533$.

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

• Step 1: Identify the given numbers - 986 and 757.
• Step 2: Apply the vertical addition method.
• Step 3: Perform the calculation column by column, starting from the right. Carry over if necessary.

Now, let's work through each step:

Starting with the units column:
$6 + 7 = 13$. Since 13 is greater than 9, we write down 3 and carry over 1 to the tens column.

Next, in the tens column:
$8 + 5 = 13$, and adding the carry over 1 gives us 14. Again, we write down 4 and carry over 1 to the hundreds column.

Finally, in the hundreds column:
$9 + 7 = 16$, and adding the carry over 1 gives us 17. Here, we write down 17 as there are no other columns to carry over to.

Therefore, the final sum is $1743$.

To verify, let's match this result with the given choices. The correct choice is: $1743$.

To solve this problem, we'll perform vertical addition. Here are the steps:

• Step 1: Write the numbers 999 and 185 vertically, aligning them by the rightmost digit.
• Step 2: Begin adding from the rightmost column.

Let's start with the units column:

• The unit digits are 9 (from 999) and 5 (from 185).
• Add them: $9 + 5 = 14$.
• Write down 4 and carry over 1 to the next column (tens place).

Next, the tens column:

• The tens digits are 9 (from 999) and 8 (from 185), plus the carry-over value 1.
• Add them: $9 + 8 + 1 = 18$.
• Write down 8 and carry over 1 to the next column (hundreds place).

Finally, the hundreds column:

• The hundreds digits are 9 (from 999) and 1 (from 185), plus the carry-over value 1.
• Add them: $9 + 1 + 1 = 11$.
• Write down 1 and carry over the 1 to form a new thousands column.

Since there's nothing else to add in the thousands column, write down the carry-over as 1.

Therefore, the sum of 999 and 185 is $\mathbf{1184}$.