Vertical Addition: Addition of 3-digit and 2-digit numbers with regrouping beyond 1000

To solve this problem, we will use vertical addition, adding each column digit separately starting from the rightmost column forming the following arrangement:

• Align the numbers:

     916
    + 95
    ----
     

• Start with the rightmost column (units):
  • The units digit of $916$ is $6$, and the units digit of $95$ is $5$.
  • Adding these gives $6 + 5 = 11$.
  • Place the $1$ in the units column and carry over the $1$ to the tens column.
• Move to the tens column:
  • The tens digit of $916$ is $1$, and the tens digit of $95$ is $9$. Add these together with the carried over $1$: $1 + 9 + 1 = 11$.
  • Place the $1$ in the tens column and carry over the $1$ to the hundreds column.
• Finally, address the hundreds column:
  • The hundreds digit of $916$ is $9$, and there is no hundreds digit in $95$, so it is $0$. Add these along with any carried over number: $9 + 0 + 1 = 10$.
  • Place the $0$ in the hundreds column, and $1$ will become the new thousands digit.
• The final sum is then:

     1011
     

Therefore, the solution to the addition problem is $\mathbf{1011}$.

To solve this problem, we'll proceed with vertical addition:

• Step 1: Align the numbers.

Align the numbers so that their place values line up:

$\begin{array}{c} & 936 \\ + & 79 \\ \hline \end{array}$

• Step 2: Add the rightmost column (Units).

Add the units digits: $6 + 9 = 15$. Place the 5 in the units column and carry over the 1 to the tens column.

• Step 3: Add the next column (Tens), including any carried-over value.

Add the tens digits and the carried-over 1: $3 + 7 + 1 = 11$. Place 1 in the tens column and carry over the 1 to the hundreds column.

• Step 4: Add the final column (Hundreds), including any carried-over value.

Add the hundreds digits and the carried-over 1: $9 + 1 = 10$. Since this is the leftmost column, write down the entire value as it is.

• Final sum:

The resulting sum is:

$\begin{array}{c} & 936 \\ + & 79 \\ \hline & 1015 \\ \end{array}$

Therefore, the correct answer is $1015$.

To solve this problem, we employ vertical addition as follows:

• Align the numbers according to their place values:

   945
+    88
_______

We'll add column by column, starting from the right (units place):

• Units (right-most) Column:
  Add 5 and 8 to get 13. Write down 3 and carry over 1 to the next column.
• Tens Column:
  Add 4 and 8 to get 12, plus the carry-over 1 equals 13. Write down 3 and carry over 1 to the hundreds column.
• Hundreds Column:
  Add 9 and the carry-over 1 to get 10. Write down 0, and carry over 1 to the thousands column (or simply add since it's the last position in this sum).

Adding these values gives us the final result:

   945
+    88
_______
 1033

Therefore, the solution to the addition problem is $1033$.

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

• Step 1: Start with the units' column addition.
• Step 2: Add the tens' column, accounting for any carryover from the units' column.
• Step 3: Add the hundreds' column, accounting for any carryover from the tens' column.

Now, let's work through each step:

Step 1: Add the units' place:
The units' place in 954 is 4, and in 72, it is 2. Add these together: $4 + 2 = 6$.
Place 6 in the units' position of our result.

Step 2: Add the tens' place:
The tens' place in 954 is 5, and in 72, it is 7. Add these together: $5 + 7 = 12$.
Since 12 is greater than 9, place 2 in the tens' position and carry over 1 to the hundreds' column.

Step 3: Add the hundreds' place:
The hundreds' place in 954 is 9. Add the carry over 1 from the tens' addition: $9 + 1 = 10$.
This gives us 0 in the hundreds' position, with another carry over 1 to the next column which becomes a thousand.
This forms 1 in the thousand's position of our result.

Therefore, the sum of 954 and 72 is $1026$.

Among the provided choices, choice 4 corresponds to this solution.

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

• Step 1: Align the numbers 978 and 53 by their place value, where 53 is written below 978, making sure that the rightmost digits are in the same column. This means placing 978 over 53.

Align the numbers:
$\begin{array}{c} 978 \\ + \\ \underline{~53} \\ \end{array}$

• Step 2: Add the units place. Add 8 (from 978) and 3 (from 53). The sum is 8 + 3 = 11. Write 1 in the units place of the answer and carry over 1 to the tens place.

• Step 3: Add the tens place. Add 7 (from 978) and 5 (from 53), also add the carryover of 1 from the previous step. The sum is 7 + 5 + 1 = 13. Write 3 in the tens place of the answer and carry over 1 to the hundreds place.

• Step 4: Add the hundreds place. Add 9 (from 978) and the carryover 1 (from the tens calculation). The sum is 9 + 1 = 10. Write 0 in the hundreds place of the answer and carry over 1 to the thousands place.

• Step 5: Since we have a carryover for the thousands place, write 1.

Thus, the complete sum is $1031$.

The solution to the problem is $1031$, which matches choice 2.