Vertical Addition: 4 digits

To solve this problem, we will perform the vertical addition of 1054 and 353 as follows:

• Step 1: Align the numbers:
  $\begin{array}{c} ~~ 1054 \\ + \ 353 \\ \underline{\phantom{77600}}\\ \end{array}$

• Step 2: Add the digits in the units place: $4 + 3 = 7$ (no carry is needed).

• Step 3: Add the digits in the tens place: $5 + 5 = 10$. Write down 0 and carry over 1 to the hundreds place.

• Step 4: Add the digits in the hundreds place, including the carry: $0 + 3 + 1 = 4$ (from the carry operation).

• Step 5: Add the digits in the thousands place: $1 + 0 = 1$.

Thus, the solution is $1407$.

Given the choices, the correct answer is choice 4:

1407

Let's solve the problem by completing an addition of the numbers vertically.

• Write the numbers vertically, aligning them by their place values:
  \begin{array}{c@{}c@{}c@{}c@{}c} & 1 & 5 & 4 & 7 \\ + & & 7 & 6 & 5 & 6 \\ \end{array}

• Add the digits starting from the rightmost (units place):

• Units Place: $7 + 6 = 13$. Write 3 and carry over 1 to the tens place.

• Tens Place: $4 + 5 = 9$, plus 1 from the carry-over equals 10. Write 0 and carry over 1 to the hundreds place.

• Hundreds Place: $5 + 6 = 11$, plus 1 from the carry-over equals 12. Write 2 and carry over 1 to the thousands place.

• Thousands Place: $1 + 7 = 8$, plus 1 from the carry-over equals 9. Write 9.

• The final addition gives us:
  $\begin{array}{c} 9 \quad 2 \quad 0 \quad 3 \\ \end{array}$

Thus, the sum of 1547 and 7656 is $\boxed{9203}$.

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

• Step 1: Set up the numbers for addition in a vertical format, aligning the rightmost digits.
• Step 2: Add each column starting from the right, keeping track of the carryover.
• Step 3: Continue the addition for all columns, incorporating any carryover into the next left column.

Now, let's work through the addition process:

Add the units column: $1 + 7 = 8$. No carryover occurs here.

Next, add the tens column: $8 + 1 = 9$. Still, no carryover is involved.

Then, add the hundreds column: $7 + 4 = 11$. Because this is more than 9, we write down 1 and carry over 1 to the next column.

Finally, add the thousands column: $2 + 8 = 10$, plus the 1 carried over gives 11. Thus, we write down 11.

Therefore, the sum of the numbers is $\boxed{11198}$.

To solve the addition of $2789 + 456$, we'll proceed with vertical addition:

• Step 1: Align the numbers by their digits:
  $\begin{array}{c} \phantom{0}2789 \\ +\phantom{0}456 \\ \underline{\phantom{0000}} \\ \end{array}$
• Step 2: Start adding from the rightmost column (ones place):
  $9 + 6 = 15$. Write down $5$ and carry over $1$ to the tens place.
• Step 3: Add the tens place:
  $8 + 5 = 13$, and add the carry over $1$, getting $14$. Write down $4$ and carry over $1$ to the hundreds place.
• Step 4: Add the hundreds place:
  $7 + 4 = 11$, and add the carry over $1$, getting $12$. Write down $2$ and carry over $1$ to the thousands place.
• Step 5: Add the thousands place:
  Since we only have $2$ and a carry of $1$, the result is $3$.
• Step 6: Compile the result across all columns:
  $3245$

Therefore, the solution to the addition problem is $3245$.

To solve the problem of adding the numbers 3267 and 1662, let's use vertical addition:

Step 1: Align the numbers by their place values, from right to left:

$\begin{aligned} &3267 \\ +& \\ &1662 \\ \end{aligned}$

Step 2: Begin adding from the units place (rightmost):

• Units place: $7 + 2 = 9$
• Tens place: $6 + 6 = 12$. Write 2, carry over 1.
• Hundreds place: $2 + 6 + 1$ (carried over) $= 9$
• Thousands place: $3 + 1 = 4$

The final sum by place value is 4929.

Therefore, the sum of 3267 and 1662 is $4929$.

The correct choice is option 4: 4929

To solve this addition problem, we will follow a systematic step-by-step approach:

• Step 1: Align the numbers vertically so that corresponding place values line up. We have:

$\begin{aligned} &3289 \\ + &2835 \\ \end{aligned}$

• Step 2: Start adding from the rightmost digit (units place).
• Units place: $9 + 5 = 14$. Write 4 and carry over 1 to the tens place.
• Step 3: Move to the next digit (tens place).
• Tens place: $8 + 3 = 11$. Add the carry 1: $11 + 1 = 12$. Write 2 and carry over 1 to the hundreds place.
• Step 4: Proceed to the hundreds place.
• Hundreds place: $2 + 8 = 10$. Add the carry 1: $10 + 1 = 11$. Write 1 and carry over 1 to the thousands place.
• Step 5: Finally, add the thousands place.
• Thousands place: $3 + 2 = 5$. Add the carry 1: $5 + 1 = 6$. Write 6.

By compiling these results, the sum is 6124.

Therefore, the solution to the problem is $6124$.

To solve this problem, we will utilize the vertical addition method as follows:

First, write the numbers one below the other, aligning them by their respective place values:

$\begin{aligned} &4652 \\ +& \\ &2161 \\ &\underline{\phantom{776}} \\ \end{aligned}$

Now, let's add the numbers column by column starting from the rightmost side (units place):
1. **Units Column**: $2 + 1 = 3$. Write 3 in the units place.
2. **Tens Column**: $5 + 6 = 11$. Write 1 in the tens place and carry over 1 to the hundreds place.
3. **Hundreds Column**: $6 + 1 + 1 = 8$. Write 8 in the hundreds place.
4. **Thousands Column**: $4 + 2 = 6$. Write 6 in the thousands place.

The sum is arranged as follows:

$\begin{aligned} &4652 \\ +& \\ &2161 \\ &\underline{6813} \\ \end{aligned}$

Therefore, the result of adding $4652$ and $2161$ is $\textbf{6813}$.

Checking against the choices provided, the correct answer is Choice 4: $6813$.

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

• Step 1: Align the numbers 4653 and 867 for vertical addition:
• Step 2: Add each digit column, starting from the right side (units place), and handle any necessary carrying over.

Let's proceed with the addition:

Step 1: Align the numbers as follows:
          4653
+         867

Step 2: Start with the rightmost column (units):

• Units: $3 + 7 = 10$. Place 0 and carry over 1 to the tens column.
• Tens: $5 + 6 = 11$, plus the carryover 1 gives us 12. Place 2 and carry over 1 to the hundreds column.
• Hundreds: $6 + 8 = 14$, plus the carryover 1 gives us 15. Place 5 and carry over 1 to the thousands column.
• Thousands: $4 + 0 = 4$, plus the carryover 1 gives us 5. Place 5.

Thus, the complete addition yields:
          5520

Therefore, the solution to the problem is $5520$.

To solve the problem of adding 5421 and 1657 using vertical addition, we will proceed through the following steps:

Step 1: Align the numbers vertically according to their place values:

$\begin{aligned} &5421 \\ + &1657 \\ \end{aligned}$

Step 2: Begin addition from the rightmost digit (units place):

• Units place: $1 + 7 = 8$. Write 8 in the units place.
• Tens place: $2 + 5 = 7$. Write 7 in the tens place.
• Hundreds place: $4 + 6 = 10$. Write 0 in the hundreds place and carry over 1 to the thousands place.
• Thousands place: $5 + 1 = 6$, plus the carried over 1 gives $6 + 1 = 7$. Write 7 in the thousands place.

Step 3: Write down the final result underneath the drawn line:

$\begin{aligned} &\underline{7078} \end{aligned}$

Therefore, the sum of 5421 and 1657 is $\textbf{7078}$.

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

• Step 1: Set up the numbers for vertical addition:

$\begin{aligned} &6324 \\ +&2798\\ \underline{\phantom{776}} & \\ \end{aligned}$

• Step 2: Add the digits in the units place: $4 + 8 = 12$, write down $2$, carry over $1$.

$\begin{aligned} &\phantom{1} \\ &\phantom{3} \;232 \\ \end{aligned}$

• Step 3: Add the digits in the tens place: $2 + 9 = 11$ plus carry $1$ makes $12$. Write down $2$, carry over $1$.

$\begin{aligned} &\phantom{1} \\ &\phantom{3} \;32 \\ \end{aligned}$

• Step 4: Add the digits in the hundreds place: $3 + 7 = 10$ plus carry $1$ makes $11$. Write down $1$, carry over $1$.

$\begin{aligned} &\phantom{1} \\ &\phantom{2} \;1 \\ \end{aligned}$

• Step 5: Add the digits in the thousands place: $6 + 2 = 8$ plus carry $1$ makes $9$. Write down $9$.

$\begin{aligned} &\phantom{9}7122 \\ \end{aligned}$

Therefore, the sum of $6324$ and $2798$ is $\mathbf{9122}$.

To solve this problem, we will apply vertical addition:

Let's add the numbers 7256 and 1967 by arranging them in a column:

• First, arrange the numbers by place value:

7256

+1967

—

• Next, add the rightmost column (units place):
  **6 + 7 = 13**. Write down 3 and carry over 1 to the next column (tens place).
• Proceed to the tens place:
  **5 + 6 = 11**, plus the carry-over 1 gives **12**. Write down 2 and carry over 1.
• Now, add the hundreds place:
  **2 + 9 = 11**, plus the carry-over 1 gives **12**. Write down 2 and carry over 1.
• Finally, add the thousands place:
  **7 + 1 = 8**, plus the carry-over 1 gives **9**. Write down 9.

The sum of the numbers is written as:

Therefore, the correct sum of the numbers 7256 and 1967 is $9223$.

To solve the problem of finding the sum of 7351 and 2499, we will proceed with vertical addition. Here are the steps:

• Align the numbers with their rightmost digits: $\begin{array}{c} \phantom{0}7351 \\ +2499 \\ \underline{\phantom{0000}} \end{array}$
• Begin adding from the rightmost column (units):
  - Units column: $1 + 9 = 10$. Write 0, carry over 1.
• Next, move to the tens column:
  - Tens column: $5 + 9 = 14$, plus the carry of 1 gives $15$. Write 5, carry over 1.
• Proceed to the hundreds column:
  - Hundreds column: $3 + 4 = 7$, plus the carry of 1 gives $8$. Write 8.
• Finally, add the thousands column:
  - Thousands column: $7 + 2 = 9$. Write 9.

After completing these steps, the final sum is written as:

Therefore, the solution to the problem is $9850$.

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

• Step 1: Align the numbers by their place values:

$\begin{aligned} &7831 \\ +& \\ &~~673 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

• Step 2: Add the digits in each column, starting from the right (units) column.

The unit's column: $1 + 3 = 4$. Write 4 under the units column.

• Step 3: Move to the ten's column.

Add: $3 + 7 = 10$. Write 0 under the tens and carry 1 to the hundreds column.

• Step 4: Move to the hundred's column.

Add: $8 + 6 = 14$, and don't forget the carried 1, making it $15$.

Write 5 under the hundreds and carry 1 to the thousands.

• Step 5: Move to the thousand's column.

Add: $7 + 1 = 8$. Don't forget the carried 1, making it $8$.

Write 8 under the thousands.

The sum of the numbers is:

$\begin{aligned} &7831 \\ +& \\ &~~673 \\ &\underline{\phantom{776}} & \\ &8504 \\ \end{aligned}$

Therefore, the sum of 7831 and 673 is $\mathbf{8504}$.

This corresponds to the choice: :

8504

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

• Step 1: Align the numbers by their place values.
• Step 2: Add the digits starting from the rightmost column.
• Step 3: Handle any carryovers properly.
• Step 4: Write down the final result.

Now, let's work through each step:

Step 1: Align the numbers:

$8472$
$+ 5261$
$\_\_\_\_\_\_\_\_\_$

Step 2: Begin adding the digits starting from the rightmost side:

Units column: $2 + 1 = 3$.

Tens column: $7 + 6 = 13$. Write $3$ and carry over $1$.

Hundreds column: $4 + 2 + 1 \,(carry) = 7$.

Thousands column: $8 + 5 = 13$. Write $3$ and carry over $1$.

Step 3: Handle the extra thousands place from the carryover: $1$.

Thus, the full addition with carryovers corrected is:

$8472$
$+ 5261$
$\_\_\_\_\_\_\_\_=\_13733$

Therefore, the correct solution to the problem is $13733$.

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

• Step 1: Arrange the numbers vertically with 8974 on top and 264 below it.
• Step 2: Add the numbers column by column, starting from the rightmost (units) column.
• Step 3: Record the sum below the line, carrying over wherever necessary.

Let's perform the addition:

Step 1: Arrange the numbers vertically.

$\begin{array}{c} 8974 \\ +264 \\ \underline{\phantom{776}} \\ \end{array}$

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

• Units digit: $4 + 4 = 8$, so write 8 in the units place.
• Tens digit: $7 + 6 = 13$, write 3 and carry over 1 to the hundreds column.
• Hundreds digit: $9 + 2 + 1 = 12$, write 2 and carry over 1 to the thousands column.
• Thousands digit: $8 + 1 = 9$, write 9.

Step 3: Write the final result:

$\begin{array}{c} 8974 \\ +264 \\ \underline{9238} \\ \end{array}$

Therefore, the solution to the problem is $9238$.