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

To solve this problem, we'll perform vertical addition:

• Write the numbers 157 and 264 in a column, aligning the digits by place value. Start from right (units) to left (hundreds).
• Step 1: Add the digits in the units place $7 + 4 = 11$. Write down 1 and carry over 1 to the tens column.
• Step 2: Add the digits in the tens place $5 + 6 = 11$, plus the carried 1 from the previous step, giving a total of 12. Write down 2 and carry over 1 to the hundreds column.
• Step 3: Add the digits in the hundreds place $1 + 2 = 3$, plus the carried 1 from the previous step, resulting in 4. Write down 4.

After adding each column and managing the carries appropriately, the resulting sum of these numbers is 421.

Therefore, the solution to the problem is $421$.

To solve the problem of adding 285 and 146, we'll use vertical addition with regrouping. Here are the steps:

Step 1: Write the numbers vertically, aligning by their place values:

$\begin{aligned} & 285 \\ + & 146 \\ & \underline{\phantom{776}} \end{aligned}$

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

$\begin{aligned} \text{Units:} & \, 5 + 6 = 11 \quad (\text{write 1, carry over 1}) \\ \end{aligned}$

Step 3: Move to the tens column, adding the carry:

$\begin{aligned} \text{Tens:} & \, 8 + 4 + 1 = 13 \quad (\text{write 3, carry over 1}) \\ \end{aligned}$

Step 4: Finally, add the hundreds column:

$\begin{aligned} \text{Hundreds:} & \, 2 + 1 + 1 = 4 \quad (\text{write 4}) \\ \end{aligned}$

The final sum reads:

$\begin{aligned} & 431 \\ \end{aligned}$

Therefore, the sum of 285 and 146 is $431$, which matches choice 2 in the provided multiple-choice options.

Therefore, the solution to the problem is $431$.

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

• Step 1: Align the numbers vertically by place value, which are the units, tens, and hundreds places.
• Step 2: Begin adding from the far right (units place), moving left.
• Step 3: Regroup if a column sum is 10 or greater.

Now, let's work through each step:

Step 1: Align numbers:

$\begin{aligned} & \phantom{0}378 \\ + & \\ & \phantom{0}455 \\ \end{aligned}$

Step 2: Begin with the units place:
8 (units from 378) + 5 (units from 455) = 13.
Write down 3 in the units place, and carry over 1 to the tens place.

Step 3: Move to the tens place:
7 (tens from 378) + 5 (tens from 455) + 1 (carried over) = 13.
Write down 3 in the tens place, and carry over 1 to the hundreds place.

Step 4: Finally, add the hundreds place:
3 (hundreds from 378) + 4 (hundreds from 455) + 1 (carried over) = 8.
Write down 8 in the hundreds place.

The final sum is, therefore:

$\begin{aligned} & \phantom{0}378 \\ + & \\ & \phantom{0}455 \\ \hline & \phantom{0}833 \end{aligned}$

Therefore, the solution to the problem is $833$.

To solve this problem, we will perform vertical addition on the two numbers, 589 and 263:

• Step 1: Add the units place.
  The units digits are 9 (from 589) and 3 (from 263).
  9 + 3 = 12. Write down 2 in the units place and carry over 1 to the tens place.
• Step 2: Add the tens place.
  The tens digits are 8 (from 589) and 6 (from 263), plus the carry-over 1 from the previous step.
  8 + 6 + 1 = 15. Write down 5 in the tens place and carry over 1 to the hundreds place.
• Step 3: Add the hundreds place.
  The hundreds digits are 5 (from 589) and 2 (from 263), plus the carry-over 1 from the previous step.
  5 + 2 + 1 = 8. Write down 8 in the hundreds place.

Combining our results, the sum of 589 and 263 is $852$.

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

• Step 1: Write the numbers one under the other, aligning their digits by place value.

• Step 2: Add the digits from the rightmost column to the left, carrying over where needed.

Detailed Steps:
Step 1: Begin with the units place. Add the digits in the units column: $7 + 4 = 11$. Write down 1 in the units column and carry over the 1 to the tens column.

Step 2: Move to the tens column. Add the digits along with the carried over value: $7 + 3 + 1 = 11$. Again, write down 1 in the tens column and carry over the 1 to the hundreds column.

Step 3: In the final hundreds column, add: $6 + 2 + 1 = 9$. Write down the 9 in the hundreds column as there are no more digits to add.

The final result by putting all these together is: $911$ .

Therefore, the sum of 677 and 234 is$911$