Let's solve thirty-three plus seventy-seven using the vertical addition method. First, we write the numbers vertically, aligning the digits by place value. The units digits go in the same column, and the tens digits go in the same column.
Now we add the units digits. Three plus seven equals ten. Since ten is a two-digit number, we write zero in the units place and carry the one to the tens place.
Now we add the tens digits, including the carry-over. Three plus seven plus one equals eleven. We write eleven to complete our answer, giving us one hundred and ten.
The complete solution shows that thirty-three plus seventy-seven equals one hundred and ten. We added the units digits to get ten, wrote zero and carried one. Then we added the tens digits including the carry-over to get eleven, giving us our final answer of one hundred and ten.
To summarize vertical addition: align digits by place value, add from right to left starting with units, carry over when the sum exceeds nine, and include the carry-over in the next column calculation.