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

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 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 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 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 $290$.

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 $590$.