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

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 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'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 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 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 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 $\mathbf{1184}$.

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 $1052$.