Operations and calculations

3. Subtraction

3.3. Long subtraction with a negative result

It is important to note that the long subtraction, or column, method does not work when a smaller value is placed above a larger value.

If it is clear that a subtraction will provide a negative value (i.e. less than 0), swap the order of the numbers, placing the larger number above the smaller number, before carrying out the operation.

This will provide the negative answer required.

Let's look at an example.


Long subtraction with a negative result | Multiply Highland, 2:39

When we want to subtract one large number from another we can use a method called long subtraction, but what if we want to subtract a larger number from a smaller one?

In this video we will calculate 365 minus 420, recognising that 420 is larger than 365 so the result will be negative.

To simplify the process, we can switch the numbers around and subtract the smaller number from the larger one. At the end, we will mark the answer as negative.

Next we write the numbers out in a stack with the larger number, 420, on top and the smaller number, 365, on 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, 5, is larger than the top number, 0, so we need to take one from the tens column.

We cross out the 2 in the tens column and write the remaining 1 next to it. Then we carry over the 1 that we've taken and write it next to the 0 in the units column to become 10. Now we can subtract 5 from 10 and write the answer, 5, between the horizontal lines at the bottom.

Next we move on to the tens column. We need to subtract 6 from the 1 that remains. Since 1 is less than 6 we need to take from the hundreds column.

We cross out the 4 in the hundreds column and write the remaining 3 next to it. Then we carry over the 1 that we've taken and write it next to the 1 in the tens column to become 11. Now we can subtract 6 from 11 and write 5 in the answer space for this column.

Finally, in the hundreds column, we subtract 3 from the 3 that remains which gives us 0 in the hundreds answer space.

So we now have our answer of 55, but remember since we've reversed the numbers to recognize that 420 is larger than 365, our final result is negative therefore the final answer is - 55.


Worked example

365 – 420

As 420 is larger than 365, this operation will result in a value less than 0, so we will swap the numbers before carrying out the operation.

Place the larger number (420) over the smaller number (365) and use the column (long subtraction) method to subtract 365 from 420.

  1. Units (U) column

    2. 0 is less than 5, so we take 1 from the column to the left, (crossing out 2, and making this 1) and add it to the 0 to make 10.

    Now we can take the number below (5) from this: 10 – 5 = 5

    Write 5 below the line, in the same column.

  2. Tens (T) column

    3. 1 is less than 6, so we take 1 from the column to the left (crossing out 4, and making this 3) and add it to the 1 to make 11.

    Now we can take the number below (6) from this: 11 – 6 = 5

    Write 5 below the line in the same column.

  3. Hundreds (H) column

    4. 3 – 3 = 0 but as this is the furthest left column, you don't need to write this below the line.

420 written over 365 for column method of subtraction

So the answer to 365 - 420 is -55 (minus 55).