Adding Whole Numbers

To add several large numbers together, place them one below the other and make sure to line up the digits according to their place value.

Example: |\begin{align} 364+75\ \rightarrow\quad &364 \\ +&\underline{\ \ 75} \end{align}|

The line under 75 means equals |(=).| Write the sum below this line. 

Then, add the numbers one position at a time, starting from the right and taking into account the regrouped values.

Add the numbers |574| and |65.|

1) Align the digits according to their place value

||\begin{align} &574 \\ +\ &\underline{\phantom{5} 65} \end{align}||

2) Add the ones

||\begin{align} &57\color{red}{4} \\ +\ &\underline{\phantom{5} 6\color{red}{5}} \\ &\phantom{56}\color{red}{9} \end{align}||

3) Next, add the tens

Adding |7| and |6| equals |13.| Place the number |3| below the line and regroup the |1| above the digit in the hundreds position of the addition.

||\begin{align}&\it{\color{blue}{1}} \\ &5\color{red}{7}4 \\ +\ &\underline{\phantom{5} \color{red}{6}5} \\ &\phantom{5}\color{red}{3}9 \end{align}||

4) Finish by adding the hundreds

All that remains is to add the regrouped value with the number in the hundreds position, i.e. the |5.|

||\begin{align}&\it{\color{red}{1}} \\ &\color{red}{5}74 \\ +\ &\underline{\phantom{5} 65} \\ &\color{red}{6}39 \end{align}||

The result is |\bf{639}.|

Add the numbers |2\ 548| and |869.|

1) Align the digits according to their place value

||\begin{align} &2\ 548 \\ +\ &\underline{\phantom{2\ }869} \end{align}||

2) Add the ones

Adding |8| and |9| equals |17.| Place the |7| below the line and regroup the |1| above the digit in the tens position of the addition.

||{\begin{align} &\phantom{2\ 5}\it{\color{blue}{1}} \\&2\ 54\color{red}{8} \\ +\ &\underline{\phantom{2\ }86\color{red}{9}} \\ &\phantom{2\ 54}\color{red}{7} \end{align}}||

3) Add the tens

|1, 4,| and |6| added together equal |11.| Place the |1| below the line and regroup the |1| above the digit in the hundreds position of the addition.

||\begin{align} &\phantom{2\ }\it{\color{blue}{1}}\it{\color{red}{1}} \\&2\ 5\color{red}{4}8 \\ +\ &\underline{\phantom{2\ }8\color{red}{6}9} \\ &\phantom{2\ 5}\color{red}{1}7 \end{align}||

4) Add the hundreds

|1, 5,| and |8| added together equal |14.| Place the number  |4| below the line and regroup the |1| above the digit in the thousands position of the addition.

||\begin{align} &\it{\color{blue}{1}}\ \it{\color{red}{1}}\it{1} \\&2\ \color{red}{5}48 \\ +\ &\underline{\phantom{2\ }\color{red}{8}69} \\ &\phantom{2\ }\color{red}{4}17 \end{align}||

5) Finish by adding the thousands 

All that remains is to add the regrouped value to the number in the thousands position, the number |2.|

||\begin{align} &\it{\color{red}{1}}\ \it{1}\it{1} \\&\color{red}{2}\ 548 \\ +\ &\underline{\phantom{2\ }869} \\ &\color{red}{3}\ 417 \end{align}||

The result is |\bf{3\ 417}.|