Vertical Addition: Addition of 3-digit and 2-digit numbers with the regrouping of thousands

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

• Step 1: Align the Numbers

We will align the numbers by their place values:

$\begin{aligned} &957 \\ +& \\ &~~43 \\ \end{aligned}$

• Step 2: Perform Addition from Right to Left
• Units Place (rightmost column):

Add the digits in the ones place: $7 + 3 = 10$.
Since 10 is greater than 9, write down 0 in the ones place and carry over 1 to the tens place.

• Tens Place (middle column):

Add the digits in the tens place, including the carry-over: $5 + 4 + 1 = 10$.
Again, write down 0 in the tens place and carry over 1 to the hundreds place.

• Hundreds Place (leftmost column):

Add the digits in the hundreds place, including the carry-over: $9 + 1 = 10$.
Write down the entire 10 since there is no further place to carry over.

• Step 3: Write Down the Final Answer

The result of the addition is 1000.

Therefore, the solution to the problem is $1000$.

To solve this problem, we'll perform a vertical addition of two numbers:

• Step 1: Arrange the numbers vertically by their place value:

$\begin{aligned} & 987 \\ + & 13 \\ \hline \end{aligned}$

• Step 2: Add the digits in the ones place.

Add 7 (ones place of 987) to 3 (ones place of 13) to get 10. Since this sum is 10, we write down 0 in the ones place and carry over 1 to the tens place.

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

Add 8 (tens place of 987) to 1 (tens place of carry-over) + 1 (tens place of 13). This is 8 + 1 + 1 = 10. We write 0 in the tens place and carry over 1 to the hundreds place.

• Step 4: Add the digits in the hundreds place.

Add 9 (hundreds place of 987) to 1 (carry-over). This sum is 9 + 1 = 10. We write 0 in the hundreds place and carry over 1 to the next higher place, the thousands place.

• Step 5: Combine the result.

Since the only carried-over is 1 to the thousands place, we write it as is. So the result of the addition is 1000.

Therefore, the solution to this problem is $1000$.

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

• Step 1: Align the numbers vertically by place value.
• Step 2: Add digits in each column starting from the right (units) to the left (hundreds), carrying over if necessary.
• Step 3: Write the final sum at the bottom.

Let's work through the solution:

Step 1: We have the numbers aligned as:

$\begin{aligned} &921 \\ +& \\ &~~79 \\ \end{aligned}$

Step 2: Start adding from the units column:

• Units: $1 + 9 = 10$. Write 0 and carry over 1 to the tens column.
• Tens: $2 + 7 + 1 \text{ (carry over)} = 10$. Write 0 and carry over 1 to the hundreds column.
• Hundreds: $9 + 1 \text{ (carry over)} = 10$. Write 0 and carry over 1 to a new thousands column.
• Thousands: No additional digits to add, so just write 1.

Step 3: Combine the results to obtain the final sum:

The sum is $1000$.

Therefore, the solution to the problem is $1000$.

To solve this problem, we need to add 945 and 45 using vertical addition. We'll do this step by step:

Step 1: Write both numbers vertically, aligning them by place value:

$\begin{array}{c} 945 \\ +45 \\ \underline{\phantom{000}} \end{array}$

Step 2: Start adding from the rightmost column (the units):

• Add the units place: $5 + 5 = 10$. Write 0 in the units place and carry over 1 to the next tens place.

$\begin{array}{c} &1 \\ 945 \\ +45 \\ \underline{\phantom{00}0} \end{array}$

Step 3: Move to the tens place and add, including the carryover:

• Add tens place: $4 + 4 + 1 = 9$. Write 9 in the tens place.

$\begin{array}{c} 945 \\ +45 \\ \underline{\phantom{0}90} \end{array}$

Step 4: Finally, add the hundreds place:

• Add hundreds place: Since there is no carryover, $9 + 0 = 9$.

$\begin{array}{c} 945 \\ +45 \\ \underline{990} \end{array}$

Therefore, the sum of 945 and 45 is $990$.

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

• Step 1: Align the numbers for vertical addition:
  $\ \ \ 977$
  $+ 23$
• Step 2: Start by adding the units digits.
  The units digit of $977$ is $7$ and the units digit of $23$ is $3$.
  $7 + 3 = 10$. Write $0$ in the units place and carry over $1$ to the tens place.
• Step 3: Add the tens digits including the carryover.
  The tens digit of $977$ is $7$ and the tens digit of $23$ is $2$.
  Including the carryover $1$:
  $7 + 2 + 1 = 10$. Write $0$ in the tens place and carry over $1$ to the hundreds place.
• Step 4: Add the hundreds digits including the carryover.
  The hundreds digit of $977$ is $9$. There are no hundreds in $23$, so only the carryover $1$ is added:
  $9 + 1 = 10$. Write $0$ in the hundreds place and carry over $1$ to the thousands place.
• Step 5: Since $23$ does not have a thousands place digit, just write the $1$ from the previous carryover in the thousands place.

After completing all these steps, the final sum is $1000$.