The approach for working out answers to subtraction sums with column subtraction, is quite similar to carrying out column addition.
Like with the case of addition, with column subtraction we again set up individual rows and columns for the numbers in the sum, but how we use columns does differ.
We’ll see how this works on this page, along with how to subtract with borrowing.
Subtracting with Columns
We could have for example:
587 − 341
In the case of adding with columns, it doesn’t matter in which order the numbers are positioned from top to bottom.
But order it does matter when subtracting with columns.
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. )
So looking at the subtraction sum shown above, we first layout the columns in the same way as with addition, also working from right to left.
The number that is being subtracted from goes in the top row, and we then subtract the lower number from the top, in each column.
H T U
\begin{array}{r} &5\space8\space7\\ - &3\space4\space1\\ \hline \\ \end{array}
HUNDREDS TENS UNITS
5 − 3 = 2 8 − 4 = 4 7 − 1 = 6
\begin{array}{r} &5\space8\space7\\ - &3\space4\space1\\ \hline &2\space4\space6 \end{array} 587 − 341 = 246
How to Subtract with Borrowing
Examples
(1.1)
584 − 236
Solution
\begin{array}{r} &5\space8\space4\\ - &2\space3\space6\\ \hline \\ \end{array}
In this subtraction sum we have a bit of an issue with the “UNITS” column.
Because the top number is of lesser value than the lower number.
This is where we introduce how to subtract with borrowing.
Where we look to borrow a digit from the next column in the sum on the left, so here the “TENS” column.
The 8 in the “TENS” column with 1 digit removed will become 7, and we will now have 14 in the “UNITS” column, which will be able to subtract 6 from.
\begin{array}{r} &{\tiny{7}}\\ &\space5\space{\bcancel{8}}\space{\tiny{1}}4\\ - &\space2\space3\space\space6\\ \hline &\space3\space4\space\space8 \end{array}
5 − 2 = 3 7 − 3 = 4 14 − 6 = 8
653 − 237 = 416
(1.2)
852 − 73
Solution
\begin{array}{r} &\space\space\space\space{\tiny{4}}\space\space\space\\ &\space8\space{\bcancel{5}}\space{\tiny{1}}2\\ - &\space\space\space\space7\space\space3\\ \hline &\space\space\space\space\space\space\space\space9 \end{array} => \begin{array}{r} &{\tiny{7}}\space\space{\tiny{14}}\space\space\space\\ &\space{\bcancel{8}}\space{\bcancel{5}}\space{\tiny{1}}2\\ - &\space\space\space\space7\space\space3\\ \hline &\space\space\space\space7\space\space9 \end{array} => \begin{array}{r} &{\tiny{7}}\space\space{\tiny{14}}\space\space\space\\ &\space{\bcancel{8}}\space{\bcancel{5}}\space{\tiny{1}}2\\ - &\space\space\space\space7\space\space3\\ \hline &\space7\space7\space\space9 \end{array}
Here we had 2 columns that needed to borrow a digit from the next.
The first borrow was to take 1 from the “TENS”, leaving 4 there, giving us 12 in the “UNITS” column.
The second borrow was bringing 1 from the “HUNDREDS” column, leaving 7 there, and creating 14 in the “TENS” column.
(1.3)
759 − 364 − 147
Solution
For a subtraction sum such as this we set up the sum with 3 rows from top downward.
\begin{array}{r} &7\space5\space9\\ &3\space6\space4\\ - &1\space4\space7\\ \hline \end{array}
We concentrate on the numbers at the top.
Borrow digits where necessary in order to ensure that each top number becomes large enough in size so that we are able to subtract the lower numbers, and still get a result that is either a positive number or 0.
\begin{array}{r} &{\tiny{4}}\\ &7\space{\bcancel{5}}\space{\tiny{1}}9\\ &3\space6\space\space4\\ - &1\space4\space\space7\\ \hline &\space\space\space\space\space\space\space8 \end{array} => \begin{array}{r} &{\tiny{6}}\space\space{\tiny{14}}\space\space\space\space\\ &{\bcancel{7}}\space{\bcancel{5}}\space{\tiny{1}}9\\ &3\space6\space\space4\\ - &1\space4\space\space7\\ \hline &\space\space\space4\space\space8 \end{array} => \begin{array}{r} &{\tiny{6}}\space\space{\tiny{14}}\space\space\space\space\\ &{\bcancel{7}}\space{\bcancel{5}}\space{\tiny{1}}9\\ &3\space6\space\space4\\ - &1\space4\space\space7\\ \hline &2\space4\space\space8 \end{array}
The first step was to take a 1 from the “TENS” column, leaving 3 there, and creating 18 in the “UNITS” column.
The second step was to borrow a 1 from the “HUNDREDS” column, leaving 6 there, and making 13 in the “TENS” column.
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