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

To solve this problem, we'll perform the following steps:

• Step 1: Align the numbers vertically by their place values.
  $\begin{array}{c} 346 \\ + \ 62 \\ \underline{} \end{array}$
• Step 2: Start addition from the rightmost column (units place).
• Step 3: Add the units place: $6 + 2 = 8$. Write 8 in the units place of the answer.
• Step 4: Move to the tens place.
  $\begin{array}{c} \phantom{0}346 \\ + \phantom{0}62 \\ \underline{408} \end{array}$
• Step 5: Add the tens place: $4 + 6 = 10$. Write 0 in the tens place and carry over 1 to the hundreds place.
• Step 6: Move to the hundreds place. Add the hundreds, accounting for the carry: $3 + 1 = 4$.
• Step 7: Combine the results: The sum of the numbers is 408.

Therefore, the solution to the problem is $408$.

To solve this problem, we'll proceed with vertical addition of 257 and 51:

• Align the numbers by place values as follows:

Start adding from the right-most side (units column):

Units Column: $7 + 1 = 8$. There is no carrying over needed as the sum is below 10.
Tens Column: $5 + 5 = 10$. Here, we write down 0 and carry over 1 to the hundreds column.
Hundreds Column: $2 + 0 = 2$ from the original numbers plus the 1 carried over gives $3$.

The resulting sum is:

Therefore, the solution to the problem is $308$.

To solve this problem, we will perform the vertical addition of the numbers 367 and 41:

• Step 1: Write the numbers vertically and align them by their place values as follows: $\begin{aligned} & 367 \\ + & \underline{~~41} \\ \end{aligned}$
• Step 2: Start by adding the digits in the units column:
  The units column: $7 + 1 = 8$.
  Write 8 in the units place of the result.
• Step 3: Move to the tens column:
  The tens column: $6 + 4 = 10$.
  Since the sum is 10, write 0 in the tens place and carry over the 1 to the hundreds column.
• Step 4: Finally, add the digits in the hundreds column with the carryover:
  The hundreds column: $3 + 1 = 4$.
  Write 4 in the hundreds place. (There is no carryover here, as all is included.)
• Step 5: Combine the digits to form the final sum.
  The result after summing is 408.

Therefore, the solution to the sum of 367 and 41 is $408$.

To solve this problem, let's perform vertical addition:

• Step 1: Align the Numbers
       $871$
    +  $36$
    \underline{\phantom{7777}}

• Step 2: Add the Units
  Add the digits in the unit’s place: $1 + 6 = 7$. Write 7 in the unit’s position.

• Step 3: Add the Tens
  Add the digits in the tens place: $7 + 3 = 10$. Write 0 in the tens position and carry over 1 to the hundreds.

• Step 4: Add the Hundreds
  Add the digits in the hundreds place, including the carry over: $8 + 1 = 9$.

By combining these steps, the complete sum is $907$.

Therefore, the solution to this problem is $\boxed{907}$.

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

• Step 1: Identify the digits and add them from right to left.
• Step 2: Handle any carry-over between columns.
• Step 3: Record the final result.

Now, let's work through the addition:

Step 1: Add the ones digits: $2 + 7 = 9$. Place $9$ in the ones place of the result.
Step 2: Add the tens digits: $2 + 8 = 10$. Place $0$ in the tens place, and carry over $1$ to the hundreds place.
Step 3: Add the hundreds digit: $5 + 1 = 6$ (including the carry-over). Place $6$ in the hundreds place of the result.

Thus, the sum $522 + 87$ is $609$.

Therefore, the solution to the problem is $609$.

To solve this problem, let's perform vertical addition of the numbers 193 and 22:

• Step 1: Align the Numbers
       193
  +    22
       ------
• Step 2: Add the Units Column
  The rightmost column is the units place. Add the digits $3$ and $2$:
  $3 + 2 = 5$.
  Write down $5$ in the units place of the answer.
• Step 3: Add the Tens Column
  Move to the next column which is the tens place. Add the digits $9$ and $2$:
  $9 + 2 = 11$.
  Since it's 11 (which is greater than 10), we write $1$ under the tens column and carry over $1$ to the hundreds column.
• Step 4: Add the Hundreds Column
  Finally, add the digits in the hundreds place, considering the carryover:
  $1 + 1 = 2$.
  Write down $2$ in the hundreds place of the answer.
• Step 5: Write the Final Answer
  Combine the results from each column:
  215.

Therefore, the sum of 193 and 22 is $215$.

To solve this problem, we'll perform the following steps:

• Align the numbers vertically with the smaller number (54) beneath the larger number (276), ensuring correct placement according to place values (units under units, tens under tens).

• Add the units digits: $6 + 4 = 10$. Write down 0 in the units place and carry over 1 to the tens place.

• Add the tens digits: $7 + 5 = 12$, plus the carried-over 1 gives us $13$. Write down 3 in the tens place and carry over 1 to the hundreds place.

• Add the hundreds digits: $2 + 0 = 2$, plus the carried-over 1 gives us $3$.

The numbers aligned look like this:

$\begin{aligned} & \phantom{1} 276 \\ + & \phantom{1} \underline{\phantom{0}54} \\ & \phantom{1} 330 \\ \end{aligned}$

Therefore, the solution to the problem is $330$.

To solve this problem, we will perform vertical addition, which involves aligning the numbers based on their place values and adding them column by column, starting from the right.

Step 1: Write the problem in vertical format:
$\begin{array}{c} \phantom{~}331 \\ +\phantom{~}89 \\ \hline \phantom{~} \end{array}$

Step 2: Add the units (rightmost) column:
$1 + 9 = 10$ We write 0 in the units position and carry over 1 to the tens column.

Step 3: Add the tens column including the carry over:
$\begin{aligned} 3 (from ~331) + 8 (from ~89) + 1 (carry over) &= 12. \end{aligned}$ Write 2 in the tens place and carry 1 over to the hundreds column.

Step 4: Add the hundreds column including the carry over:
$3 (from ~331) + 0 (from ~89) + 1 (carry over) = 4.$ Write 4 in the hundreds place.

The result of the addition is:
$\begin{array}{c} \phantom{0}\\ \phantom{~}331 \\ +\phantom{~}89 \\ \hline \phantom{~}420 \end{array}$

Therefore, the solution to the problem is $420$, corresponding to choice 4.

The key steps to solve this addition problem using vertical addition are as follows:

• First, write the numbers vertically, ensuring the alignment by place value. The problem is set up as:

$\begin{array}{c} 489 \\ +37 \\ \underline{\phantom{776}} \\ \end{array}$

• Step 1: Add the digits in the ones column: $9 + 7 = 16$. Write 6 in the ones place and carry over 1 to the tens column.
• Step 2: Add the digits in the tens column, including the carryover: $8 + 3 + 1 = 12$. Write 2 in the tens place and carry over 1 to the hundreds column.
• Step 3: Add the digits in the hundreds column, including the carryover: $4 + 1 = 5$. Write 5 in the hundreds place.

The calculation looks like:

$\begin{array}{c} 489 \\ +37 \\ \underline{526} \\ \end{array}$

Therefore, the sum of 489 and 37 is $\textbf{526}$.

To solve this problem, we'll add the numbers 597 and 65 using vertical addition.

Write the numbers vertically, aligning them by their place values (units, tens, hundreds):

• 597
• + 65

Step 1: Add the units column:

• Add 7 (from 597) and 5 (from 65) to get 12. Write 2 in the units column and carry over 1 to the tens column.

Step 2: Add the tens column:

• Add 9 (from 597), 6 (from 65), and the carried over 1 to get 16. Write 6 in the tens column and carry over 1 to the hundreds column.

Step 3: Add the hundreds column:

• Add 5 (from 597) and the carried over 1 to get 6. Write 6 in the hundreds column.

Therefore, the sum of 597 and 65 is $662$.

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

• Step 1: Set up the addition problem vertically, aligning the numbers by their place values.
• Step 2: Add the digits column by column, starting from the rightmost position (units place).
• Step 3: If the sum in any column is 10 or more, carry over to the next column.

Now, let's work through each step:

Given numbers are:

$\begin{aligned} & 847 \\ + & \phantom{} 77 \\ \end{aligned}$

Step 1: Start with the units place.

$7 + 7 = 14$. Write down 4 in the units place, and carry over 1 to the tens place.

Step 2: Move to the tens place.

$4 + 7 = 11$, plus the carried over 1 makes it 12. Write down 2 in the tens place, and carry over 1 to the hundreds place.

Step 3: Finally, add the hundreds place.

$8 + 0 = 8$, plus the 1 carried over makes it 9. Write down 9 in the hundreds place.

The sum is:

$\begin{aligned} & 847 \\ + & \phantom{} 77 \\ \hline & 924 \\ \end{aligned}$

Therefore, the solution to the problem is $924$.

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

• Step 1: Align the numbers 746 and 68 by place value. Since 68 is a 2-digit number, place it beneath the 746 aligning to the right.
• Step 2: Add the digits in the units place: 6 (from 746) + 8 (from 68) equals 14. Write down 4 and carry over 1 to the tens place.
• Step 3: Add the digits in the tens place plus the carried over 1: 4 (from 746) + 6 (from 68) + 1 (carried over) equals 11. Write down 1 and carry over 1 to the hundreds place.
• Step 4: Add the digits in the hundreds place plus any carry: 7 (from 746) + 0 (from 68 as there's no hundreds place in 68) + 1 (carried over) equals 8.

Thus, the complete sum is formed by reading down the digits you have written from top to bottom in each column after handling carries: 814.

Therefore, the solution to the problem is $814$.