The method for working out subtraction sums with column subtraction, is fairly similar to performing column addition sums.
Like with addition, in learning how to do column subtraction we again set up individual rows and columns for the numbers in the sum, but how we use columns does differ.
Subtraction with Columns
If we have for example:859 − 231
In the case of addition, it doesn’t matter in which order the numbers are placed from top to bottom, but it does matter with column subtraction.
9 + 8 is the same as 8 + 9
But 9 − 8 is NOT the same as 8 − 9 ( So it’s key to pay attention to order. )
Looking at the sum shown above, we layout the same way as addition, also working from right to left.
The number being subtracted from goes in the top row, and we look to subtract the lower number from the top in each of the columns.
H T U
\begin{array}{r} &8\space5\space9\\ - &2\space3\space1\\ \hline \\ \end{array}
HUNDREDS TENS UNITS
8 − 2 = 6 5 − 3 = 2 9 − 1 = 8
\begin{array}{r} &8\space5\space9\\ - &2\space3\space1\\ \hline &6\space2\space8 \end{array} 859 − 231 = 628
How to do Column Subtraction,
Examples
1.1
653 − 237
Solution
\begin{array}{r} &6\space5\space3\\ - &2\space3\space7\\ \hline \\ \end{array}
With this subtraction sum there is an issue with the “UNITS” column.
As the top number is smaller than the lower number.
How to do column subtraction in a situation like this, we need to borrow a digit from the next column on the left, in this example the “TENS” column.
So the 5 in the “TENS” with 1 digit removed will become 4, and we will now have 13 in the “UNITS” column, which 7 can be subtracted from.
\begin{array}{r} &{\tiny{4}}\\ &\space6\space{\bcancel{5}}\space{\tiny{1}}3\\ - &\space2\space3\space\space7\\ \hline &\space4\space1\space\space6 \end{array}
6 − 2 = 4 4 − 3 = 1 13 − 7 = 6
653 − 237 = 416
1.2
742 − 65
Solution
\begin{array}{r} &\space\space\space\space{\tiny{3}}\space\space\space\\ &\space7\space{\bcancel{4}}\space{\tiny{1}}2\\ - &\space\space\space\space6\space\space5\\ \hline &\space\space\space\space\space\space\space\space7 \end{array} => \begin{array}{r} &{\tiny{6}}\space\space{\tiny{13}}\space\space\space\\ &\space{\bcancel{7}}\space{\bcancel{4}}\space{\tiny{1}}2\\ - &\space\space\space\space6\space\space5\\ \hline &\space\space\space\space7\space\space7 \end{array} => \begin{array}{r} &{\tiny{6}}\space\space{\tiny{13}}\space\space\space\\ &\space{\bcancel{7}}\space{\bcancel{4}}\space{\tiny{1}}2\\ - &\space\space\space\space6\space\space5\\ \hline &\space6\space7\space\space7 \end{array}
This time we had 2 columns where we needed to borrow from the next.
The first borrow was to take 1 from the “TENS”, leaving 3 there, and cresting 12 in the “UNITS” column.
The second borrow was taking 1 from the “HUNDREDS” column, leaving 6 there, and cresting 13 in the “TENS” column.
1.3
748 − 263 − 157
Solution
With a subtraction sum like this we set up the sum with 3 rows.
\begin{array}{r} &7\space4\space8\\ &2\space6\space3\\ - &1\space5\space7\\ \hline \end{array}
But focus heavily on the numbers at the top.
Borrow digits where needed to make sure that each top number becomes a big enough size so that we can subtract the lower numbers, and still get an answer that is either positive or 0.
\begin{array}{r} &{\tiny{3}}\\ &7\space{\bcancel{4}}\space{\tiny{1}}8\\ &2\space6\space\space3\\ - &1\space5\space\space7\\ \hline &\space\space\space\space\space\space\space8 \end{array} => \begin{array}{r} &{\tiny{6}}\space\space{\tiny{13}}\space\space\space\space\\ &{\bcancel{7}}\space{\bcancel{4}}\space{\tiny{1}}8\\ &2\space6\space\space3\\ - &1\space5\space\space7\\ \hline &\space\space\space2\space\space8 \end{array} => \begin{array}{r} &{\tiny{6}}\space\space{\tiny{13}}\space\space\space\space\\ &{\bcancel{7}}\space{\bcancel{4}}\space{\tiny{1}}8\\ &2\space6\space\space3\\ - &1\space5\space\space7\\ \hline &3\space2\space\space8 \end{array}
The first action was to take 1 from the “TENS”, leaving 3 there, and making 18 in the “UNITS” column.
The second action was to borrow 1 from the “HUNDREDS” column, leaving 6 there, and making 13 in the “TENS” column.
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