In times where an addition sum involves smaller numbers, the addition is usually quite straightforward and can be done quite quickly mentally.
But when there are larger numbers to be added together, such as the addition of 3 digit numbers and even some 2 digit numbers.
A better approach can be to write an addition sum down, and make use of what is known as column addition.
Adding Using Columns
We could have an addition sum such as: 314 + 265
This addition of 3 digit numbers sum can be written down in columns with column addition, where we have one number on top of the other number.
Also leaving a space lower down for the answer to the addition sum.
Here the arranged columns are UNITS, TENS and HUNDREDS.
Starting with the “UNITS” on the right hand side.
314 is made up of 3 hundreds, 1 tens and 4 units.
265 is made up of 2 hundreds, 6 tens and 5 units.
\begin{array}{r} &{\scriptsize{H}} \space {\scriptsize{T}}\space {\scriptsize{U}}\\ &3\space1\space4\\ + &2\space6\space5\\ \hline \\ \end{array}
From here we look to add up each individual column, and placing each addition result in the correct column below.
Working from the right side to the left side adding the UNITS column together first.
HUNDREDS TENS UNITS
3 + 2 = 5 1 + 6 = 7 4 + 5 = 9
=> \begin{array}{r} &3\space1\space4\\ + &2\space6\space5\\ \hline &5\space7\space9 \end{array} 314 + 265 = 559
Addition of 3 Digit Numbers,
Adding with Columns Examples
(1.1)
203 + 45
Solution
Here the HUNDREDS column for 45 is empty, so for the columns we just have a 0 present, or it could be left blank.
\begin{array}{r} &2\space0\space3\\ + &\space\space\space4\space5\\ \hline &2\space4\space8 \end{array}
(1.2)
168 + 527
Solution
This example is look a bit trickier, abecause the UNITS column will add up to a number that is 2 digits in size, a number that is greater than 9.
In this situation, when we’re left with for example 15 in the UNITS column.
The 5 is placed as the answer for the UNITS column, and the 1 will then be added to the answer in the next column, which here will be the HUNDREDS.
\begin{array}{r} &1\space6\space8\\ + &5\space2\space7\\ \hline \\ \end{array} => \begin{array}{r} &{\tiny{1}}\\ &1\space6\space8\\ + &5\space2\space7\\ \hline &\space\space\space\space\space\space2\\ \end{array} => \begin{array}{r} &{\tiny{1}}\\ &1\space6\space8\\ + &5\space2\space7\\ \hline &6\space9\space5\\ \end{array}
In the UNITS column, 8 + 7 = 15.
The 2 is placed in the usual answer spot below.
But the 1 is carried over left, and written above to be added on to the TENS column.
Thus the TENS column becomes 1 + 4 + 2 = 7.
(1.3)
686 + 245
Solution
Here both the UNITS and the TENS columns add up to a number that is 2 digits in size.
Like in example (1.3), an extra 1 will be added on to the TENS column, and an extra 1 will also be onto the HUNDREDS column.
\begin{array}{r} &{\tiny{1}}\space\space{\tiny{1}}\space\space\space\\ &6\space8\space6\\ + &2\space4\space5\\ \hline &9\space3\space1\\ \end{array}
(1.4)
823 + 546
Solution
Here the HUNDREDS column is the column addition that will produce an extra digit.
This extra digit still carry’s over to the left. But it will create a new THOUSANDS column in the answer section.
\begin{array}{r} &8\space2\space3\\ + &5\space4\space6\\ \hline &1\space3\space6\space9\space\space\space\\ \end{array}
(1.5)
224 + 35 + 603
Solution
There’s an addition of 3 digit numbers involved here with 3 different numbers to add together.
Now the addition sum will be set up as normal, but with 3 rows.
\begin{array}{r} &{\tiny{1}}\\ &2\space2\space4\\ &6\space0\space3\\ + &\space\space\space3\space5\\ \hline &8\space3\space2\\ \end{array}
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