Operations and calculations
3. Subtraction
3.1. Long subtraction
Also known as the column method, long subtraction involves setting out larger numbers one above the other, then performing the subtraction operation on each column, working from right to left.
Long subtraction | Multiply Highland, 1:56
When we want to subtract one large number from another we can use a method called long subtraction.
To do this we first need to write the numbers out in a stack, with the number that is being subtracted sitting at the bottom. The place values need to be lined up in columns for units, tens, hundreds and so on.
We start with the units column on the right hand side. If the number on the bottom is smaller than the one on the top it should be subtracted. So here we can take away the six from the nine and write the answer three between the horizontal lines at the bottom.
Now we can move to the tens column to the left of the units column. We want to do the same as we did with the units column, but this time the top number is less than the one on the bottom. So here we will need to borrow from the hundreds column.
We do that by crossing out the five in the hundreds column and writing the remaining four next to it. Then we carry over the one that we've borrowed and write it next to the one in the tens column to become 11. Now we can subtract three from eleven and write the answer eight in the answer space for this column.
And finally in the hundreds column, we can subtract the two at the bottom from the four we have pencilled in at the top to give us two in the hundreds answer space. So now we have our answer 283.
Worked example
In the following steps we'll subtract 236 from 519.
Write out the numbers, with the number to be subtracted below the number it is to be subtracted from, keeping individual digits in columns according to place value (headings are included here as a reminder).
Starting in the units column, subtract the lower digit from the upper digit.
9 – 6 = 3
Write 3 below the line in the units column.
Moving to the tens column, you will notice that the number on the top (1) is smaller than the number to be subtracted (3). When this is the case, we take 10 from the next column on the left.
Remember: as you move from right to left, the numbers in each column are worth ten times (x 10) those in the preceding column.
So, we take 1 away from 5, to leave 4 (noting we have done so by crossing through the 5 and writing in 4). Then we add it (it’s worth 10 in this column) to the 1 to make 11.
Now that we have a larger number on top, we can subtract the number below.
11 – 3 = 8
Write 8 below the line in the tens column.
Moving to the next column on the left, subtract the lower digit from the upper digit (which is now 4).
4 – 2 = 2
Write 2 below the line in this column.
Following this process we find that 519 - 236 = 283.
Tip: We can check our answer is correct by adding the answer to the number subtracted, which should give the number we started with.
i.e. 283 + 236 = 519
In the next page we will look at an example where the number to be subtracted from contains zeros.