Operations and calculations
3. Subtraction
3.2. Long subtraction from value containing zeros
Long subtraction with zeros | Multiply Highland, 2:04
When we want to subtract one large number from another we can use a method called long subtraction, but the process can seem a little more challenging if the larger number contains zeros, for example 500 - 236.
To calculate the answer 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. The bottom number, six, is larger than the top number, 0, so we need to take one from the tens column. However the tens column also has a 0, so we need to take one from the hundreds column.
We therefore cross out the 5 in the hundreds column and write the remaining 4 next to it. We then turn the tens column 0 into 10. Next we take one from this 10, crossing it out to make it 9, and turning the units column 0 into 10.
Now we can subtract 6 from 10 in the units column and write the answer 4 between the horizontal lines at the bottom.
Next we move to the tens column. We now have 9 in the tens column and we need to subtract 3 from the 9. We do this and write 6 in the answer space for this column.
Finally, in the hundreds column, we subtract 2 from the 4 that remains, which gives us 2 in the hundred's answer space. So we now have our answer 264.
Worked example
If the number above is lower than the number to be subtracted, we take 1 from the number immediately to its left (reducing that number by 1) but what if the number to its left is a 0 (zero)?
This is slightly more complicated. Let’s work through an example.
500 – 236
Starting on the right, at the units (U) column, the upper number is 0 (zero). We can't subtract 6 from 0, so we will need to add ten, which we will 'take' from the tens (T) column on the left.
Looking at the tens (T) column however, the upper number is also 0, so we will need to add ten here first, by taking from the column to its left.
Moving to the hundreds (H) column, the upper number is 5, so we can take 1 from this, noting we have done so by crossing through the 5 and replacing it with a 4.
Remember: as you move from right to left, the numbers in each column are worth ten times (x 10) those in the preceding column.
Moving back to the tens column, we can now add 10 to the 0 to make 10, however we then need to take 1 from this to add to the units column, which we do by crossing through 10 and replacing it with 9.
Moving back to the units column, we add 10 to the 0 to make 10. Now we can take 6 from 10 which leaves 4, which we write below the line in this column.
Moving on to the tens column, we take 3 from 9 which leaves 6, which we write below the line in this column.
Finally, in the hundreds column, we take 2 from 4 which leaves 2, which we write below the line in this column.
Following this process, we can see that:
500 – 236 = 264
