Vertical Addition: Addition of 3-digit and 1-digit numbers with the regrouping of tens

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

• Step 1: Arrange the numbers vertically with digits aligned by place value.
• Step 2: Start adding from the rightmost column (ones place).
• Step 3: Move to the next column to the left if necessary.
• Step 4: Record the result above the underscore line.

Now, let's add the numbers:

$\begin{aligned} & 175 \\ + &~~~5 \\ \underline{\phantom{180}} \\ \end{aligned}$

Step 1: Add the ones place digits: $5 + 5 = 10$

• Write 0 in the ones place and carry over 1 to the tens place.

Step 2: Add the tens place digits, including the carry: $7 + 0 + 1 = 8$

• Write 8 in the tens place. There's no carryover to the hundreds place in this case.

Step 3: Add the hundreds place digits: $1 + 0 = 1$

• Write 1 in the hundreds place.

Thus, the sum of 175 and 5 is 180.

Therefore, the solution to the problem is $180$.

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

• Step 1: Align the numbers vertically so that the digits of each place value line up:
  $\begin{array}{c} 289 \\ +1 \\ \underline{\phantom{776}} \\ \end{array}$
• Step 2: Start adding from the rightmost column, the units place:
  $9 + 1 = 10$. Write $0$ in the units place and carry over $1$ to the tens place.
• Step 3: Move to the tens column, add the tens digits and the carry-over $1$:
  $8 + 0 + 1 = 9$. Place $9$ in the tens place.
• Step 4: Move to the hundreds column, add the remaining numbers:
  $2 + 0 = 2$. Place $2$ in the hundreds place.

The total sum reflects in the alignment:

$\begin{array}{c} 289 \\ +1 \\ \underline{\phantom{776}} \\ 290 \end{array}$

Therefore, the solution to the problem is $290$.

Let's solve this problem by performing vertical addition:

• Step 1: Write the numbers vertically, aligning the digits by place value.

$\begin{array}{c} 377 \\ + \\ \phantom{0}3 \\ \underline{\phantom{776}} \\ \end{array}$

• Step 2: Start with the units place. Add $7$ (from 377) and $3$, getting $10$.
• Step 3: Since $10$ is greater than $9$, we write down $0$ in the units place and carry over $1$ to the tens place.
• Step 4: Move to the tens place. Add $7$ (from 377 in tens place) plus the carried over $1$, resulting in $8$.
• Step 5: Move to the hundreds place. Since there is no additional value to add, it remains $3$.

Thus, the computed sum is:

$\begin{array}{c} 377 \\ + 3 \\ \underline{\phantom{776}} \\ 380 \\ \end{array}$

Therefore, the sum of $377$ and $3$ is $\mathbf{380}$.

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

• Step 1: Align the numbers vertically based on their place values:
       $456$
  +   $004$
  $\underline{\phantom{457}}$

• Step 2: Start adding from the rightmost column (units place):
          6 (from 456) + 4 = 10.
  The result is 10, so we place 0 in the units place under the line, and carry over 1 to the next column (tens place).

• Step 3: Move to the tens place, including the carry over:
          5 (from 456) + 0 (from 004) + 1 (carry over) = 6.
  Place 6 in the tens place under the line.

• Step 4: Move to the hundreds place:
          4 (from 456) + 0 = 4.
  Place 4 in the hundreds place under the line.

The complete sum would look like this:
        $456$
+    $004$
$\phantom{460} \underline{460}$

Therefore, the solution to the problem is $460$, which corresponds to choice 4.

To solve this problem, we'll perform vertical addition for the numbers 631 and 9, handling any necessary carrying.

Align the numbers based on their place value:

$\begin{aligned} &631 \\ +& \\ &~~~9 \\ \end{aligned}$

• Step 1: Add the units place (rightmost column).
  - We have 1 (from 631) + 9 = 10.
  - Write 0 and carry over 1 to the tens place.
• Step 2: Add the tens place (second column from the right).
  - We have 3 (from 31) + 0 + 1 (carry-over) = 4.
  - Write 4 in the tens place.
• Step 3: Add the hundreds place (leftmost column).
  - We have 6 only (as there’s nothing else to add).
  - Write 6 in the hundreds place.

Thus, the final sum of 631 and 9 is 640.

Therefore, the solution to the problem is $\textbf{640}$.

To solve the problem, we will perform vertical addition of the numbers $545$ and $45$, as follows:

Step 1: Align the numbers correctly, placing the digits in each number in their appropriate columns:

$\begin{array}{c} \phantom{1}545 \\ \phantom{+}45\phantom{0} \\ \underline{\phantom{999}} \end{array}$

Step 2: Perform the addition column by column, starting from the rightmost column (the units place):

• Units place: $5 + 5 = 10$. Write down $0$ and carry over $1$ to the tens column.
• Tens place: $4 + 4 = 8$, plus the carry-over $1$ gives $9$. Write $9$ in the tens column.
• Hundreds place: The only digit is $5$. So, write $5$ in the hundreds column.

Step 3: Write down the complete sum:

$\begin{array}{c} \phantom{1}545 \\ \phantom{+}45\phantom{0} \\ \underline{\phantom{999}} \\ \phantom{99}590 \end{array}$

Therefore, the sum of $545$ and $45$ is $590$.