Column Addition
Addition of 3 Digit Numbers

Addition sums are where learning arithmetic often begins. The type of sums that many people do almost daily.
When addition sums involve smaller numbers, they are generally fairly straightforward and can be done quickly in ones head.

But at times when there are larger numbers to be added, such as the addition of 3 digit numbers and 2 digit numbers.
It can be better to write an addition sum down with what is known as column addition.

Addition with Columns

If we had an addition sum to work out such as:     213 + 346


We can write this addition of 3 digit numbers sum down in appropriate columns with column addition, having one number on top of the other number.
While leaving a space below for the answer to the addition.


Here the arranged columns are UNITS, TENS and HUNDREDS.

Starting with the “UNITS” on the right hand side.

213  is made up of   2 hundreds, 1 tens and 3 units.
346  is made up of   3 hundreds, 4 tens and 6 units.

\begin{array}{r} &{\scriptsize{H}} \space {\scriptsize{T}}\space {\scriptsize{U}}\\ &2\space1\space3\\ + &3\space4\space6\\ \hline \\ \end{array}


Now we look to add up each column separately, placing each addition result below in the correct column. Working from the right side to the left side adding the UNITS column together first.

HUNDREDS           TENS                  UNITS
2 + 3 = 5                 1 + 4 = 5              3 + 6 = 9

=>     \begin{array}{r} &2\space1\space3\\ + &3\space4\space6\\ \hline &5\space5\space9 \end{array}                 213 + 346  =  559

Addition of 3 Digit Numbers,
Column Addition Examples

1.1

251 + 626

Solution

\begin{array}{r} &2\space5\space1\\ + &6\space2\space6\\ \hline &8\space7\space7 \end{array}



1.2

304 + 25

Solution

Here the HUNDREDS column for 25 is empty, so for the columns we just have a 0 present, or it could be left blank.

\begin{array}{r} &3\space0\space4\\ + &\space\space\space2\space5\\ \hline &3\space2\space9 \end{array}



1.3

148 + 724

Solution

Here things look a little bit trickier, as the “UNITS” column will add up to a number that contains 2 digits, a number that is larger than 9.
When this happens, and we’re left with for example 13 in the “UNITS” column.

The 3 gets placed as the answer for the “UNITS” column, while the 1 will get added to the answer in the next column, which is the “HUNDREDS”.

\begin{array}{r} &1\space4\space8\\ + &7\space2\space4\\ \hline \\ \end{array}       =>       \begin{array}{r} &{\tiny{1}}\\ &1\space4\space8\\ + &7\space2\space4\\ \hline &\space\space\space\space\space\space2\\ \end{array}       =>       \begin{array}{r} &{\tiny{1}}\\ &1\space4\space8\\ + &7\space2\space4\\ \hline &8\space7\space2\\ \end{array}

In the “UNITS” column, 8 + 4 = 12.

The 2 is placed in the same answer position below.
But the 1 is carried over to the left, and written above to be added on to the “TENS” column.

So the “TENS” column becomes  1 + 4 + 2 = 7.




1.4

578 + 156

Solution

We have here both the “UNITS” and the “TENS” columns adding up to a number that is 2 digits.
Like with example (1.3), we will be adding an extra 1 on to the “TENS” column, but also be adding an extra 1 onto the “HUNDREDS” column.
\begin{array}{r} &{\tiny{1}}\space\space{\tiny{1}}\space\space\space\\ &5\space7\space8\\ + &1\space5\space6\\ \hline &7\space3\space4\\ \end{array}



1.5

812 + 734

Solution

This time the “HUNDREDS” column will have an extra digit.
This digit will still carry over to the left as usual. But here it will create a new “THOUSANDS” column in the answer section.

\begin{array}{r} &8\space1\space2\\ + &7\space3\space4\\ \hline &1\space5\space4\space6\space\space\space\\ \end{array}




1.6

213 + 52 + 509

Solution

Here there’s an addition of 3 digit numbers involved where there are 3 different numbers to add together, the addition sum will be set up as normal, but with 3 rows.

\begin{array}{r} &{\tiny{1}}\\ &2\space1\space3\\ &5\space0\space9\\ + &\space\space\space5\space2\\ \hline &7\space7\space4\\ \end{array}

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