Solve Vertical Addition: 743 + 259 Step-by-Step

$\begin{aligned} &743 \\ +& \\ &259 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

To solve this problem, we'll engage in vertical addition for the given numbers $743$ and $259$:

• Step 1: Align the numbers by their place value (units, tens, and hundreds).
• Step 2: Add each column starting from the right, taking care to carry over if needed.

Let's perform the addition:
Starting from the rightmost column (units):

• Add $3$ (from $743$) and $9$ (from $259$): $3 + 9 = 12$.
  Place $2$ in the units place and carry over $1$ to the tens column.
• Move to the tens column:
  Add $4$ (from $743$), $5$ (from $259$), and the carryover $1$: $4 + 5 + 1 = 10$.
  Place $0$ in the tens place and carry over $1$ to the hundreds column.
• Finally, add the hundreds column:
  Add $7$ (from $743$), $2$ (from $259$), and the carryover $1$: $7 + 2 + 1 = 10$.
  Place $0$ in the hundreds place and $1$ in the thousands place.

The final result of adding $743 + 259$ is $1002$.

Comparing this with the answer choices, the correct choice is (1): $1002$.

Therefore, the solution to the problem is $1002$.