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

To solve this problem, let's use vertical addition as follows:

• Step 1: Align the numbers by their place values:
              $569$
           + $431$

• Step 2: Start with the units column:
        Add $9 + 1 = 10$. Write 0 in the units place and carry over 1 to the tens column.

• Step 3: Move to the tens column:
        Add $6 + 3 = 9$, then include the carried 1, making it $9 + 1 = 10$. Write 0 in the tens place and carry over 1 to the hundreds column.

• Step 4: Finally, the hundreds column:
        Add $5 + 4 = 9$, then add the carried 1, making it $9 + 1 = 10$. Write 0 in the hundreds place and put 1 in the next column (thousands, a new place in this context).

The sum of the numbers is, thereby:
                      $1000$

Therefore, the total is $1000$.

To solve this vertical addition problem, let's break down each step:

• Step 1: Align the numbers for vertical addition:
      742
  +  258
     

• Step 2: Add the units column (rightmost digits):
      2 + 8 = 10, write down $0$ and carry over $1$ to the tens column.

• Step 3: Add the tens column, including the carry:
      4 + 5 + 1 (carry) = 10, write down $0$ and carry over $1$ to the hundreds column.

• Step 4: Add the hundreds column, including the carry:
      7 + 2 + 1 (carry) = 10, write down $0$ and carry over $1$ to the thousands position.

• Since there is a carry in the thousands position, write down $1$ as the leading digit.

Therefore, the sum of $742$ and $258$ is $1000$.

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

• Step 1: Add the units column
• Step 2: Add the tens column, including any carry from the units
• Step 3: Add the hundreds column, including any carry from the tens

Now, let's work through each step:

Step 1: Add the units column.

The units are $5$ (from $685$) and $5$ (from $315$).
$5 + 5 = 10$. Write $0$ in the units place and carry over $1$ to the tens place.

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

The tens are $8$ (from $685$) and $1$ (from $315$), plus the $1$ carried over.
$8 + 1 + 1 = 10$. Write $0$ in the tens place and carry over $1$ to the hundreds place.

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

The hundreds are $6$ (from $685$) and $3$ (from $315$), plus the $1$ carried over.
$6 + 3 + 1 = 10$. Write $0$ in the hundreds place and $1$ in the thousands place.

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

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

• Add the digits in the units place (rightmost).
• Add the digits in the tens place, including any carry from the units place.
• Add the digits in the hundreds place, including any carry from the tens place.

Let's work through the addition step-by-step:

Step 1: Add the Units Place
The units digits are 3 and 7. Adding these gives $3 + 7 = 10$.
Write 0 in the units place of the answer and carry over the 1 to the tens column.

Step 2: Add the Tens Place
The tens digits are 4 and 5, plus the carryover 1. Adding these gives $4 + 5 + 1 = 10$.
Write 0 in the tens place of the answer and carry over the 1 to the hundreds column.

Step 3: Add the Hundreds Place
The hundreds digits are 5 and 4, plus the carryover 1. Adding these gives $5 + 4 + 1 = 10$.
This gives us 10 in the hundreds and thousands places.

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

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

• Step 1: Align the numbers vertically by their place values.
  The numbers are given as:

$\begin{aligned} &822 \\ + &178 \\ \end{aligned}$

• Step 2: Add the digits from right to left, starting with the units place.

Units place addition:
$2 + 8 = 10$

We place $0$ in the units place and carry over $1$ to the tens place.

• Step 3: Add the digits in the tens place, including the carry-over.

$2 + 7 = 9$, plus the carried over $1$:
$9 + 1 = 10$

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

• Step 4: Add the digits in the hundreds place, including the carry-over.

$8 + 1 = 9$, plus the carried over $1$:
$9 + 1 = 10$

Place $0$ in the hundreds place and carry over $1$ to the next place, creating a new thousands place digit.

Resulting sum:

$\begin{aligned} &1000 \end{aligned}$

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