Solve Vertical Addition: 257 + 51 Step-by-Step

To solve this problem, we'll proceed with vertical addition of 257 and 51:

• Align the numbers by place values as follows:

$\begin{aligned} & 257 \\ +& ~~51 \\ \hline \end{aligned}$

Start adding from the right-most side (units column):

Units Column: $7 + 1 = 8$. There is no carrying over needed as the sum is below 10.
Tens Column: $5 + 5 = 10$. Here, we write down 0 and carry over 1 to the hundreds column.
Hundreds Column: $2 + 0 = 2$ from the original numbers plus the 1 carried over gives $3$.

The resulting sum is:

$\begin{aligned} & 257 \\ +& ~~51 \\ \hline & 308 \\ \end{aligned}$

Therefore, the solution to the problem is $308$.