Solve Vertical Addition: 1547 + 7656 Step-by-Step

$\begin{aligned} &1547 \\ +& \\ &7656 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Let's solve the problem by completing an addition of the numbers vertically.

• Write the numbers vertically, aligning them by their place values:
  \begin{array}{c@{}c@{}c@{}c@{}c} & 1 & 5 & 4 & 7 \\ + & & 7 & 6 & 5 & 6 \\ \end{array}

• Add the digits starting from the rightmost (units place):

• Units Place: $7 + 6 = 13$. Write 3 and carry over 1 to the tens place.

• Tens Place: $4 + 5 = 9$, plus 1 from the carry-over equals 10. Write 0 and carry over 1 to the hundreds place.

• Hundreds Place: $5 + 6 = 11$, plus 1 from the carry-over equals 12. Write 2 and carry over 1 to the thousands place.

• Thousands Place: $1 + 7 = 8$, plus 1 from the carry-over equals 9. Write 9.

• The final addition gives us:
  $\begin{array}{c} 9 \quad 2 \quad 0 \quad 3 \\ \end{array}$

Thus, the sum of 1547 and 7656 is $\boxed{9203}$.