Operations and calculations

3. Subtraction

3.4. Subtracting decimals

When working with decimal values, it is important to ensure that the decimal point remains in the same position (column) throughout the calculation. This is easier if the same number of decimal places (i.e. positions to the right of the decimal point) are used for each value in the calculation.


Money

When working with money, in mixed values of pounds and pence, include a decimal point and two decimal places in each line of the calculation.

Two zeros after the decimal indicate ‘no pence’ and a zero before the decimal point indicates ‘no pounds’.

For example, to subtract £6.05 (six pounds and five pence) from £13 (thirteen pounds):

  1. Include a decimal point and two zeros, in the first line of the calculation (£13.00) to indicate thirteen pounds and no pence.
  2. Write the value to be subtracted (£6.05) in the line below, ensuring the decimal point is in the same position as in the line above.
  3. Ensuring the decimal point remains in the same position, subtract the lower value from the one above, using the long subtraction (column) process.
13.00 written over 6.05 with decimals points in same column position ready for subtraction

worked solution showing 6.05 subtracted from 13.00 with answer 6.95 and decimal point always in same position
  1. Starting in the far right (2nd decimal place) column, 0 is less than 5, so we need to take 1 over from the column on the left.
  2. The next left (1st decimal place) column also contains 0, however, so we need to take 1 from the next left (units) column, to the left of the decimal point.
  3. In the units column take 1 from 3 (cross through 3 and mark as 2).

    4. Remember that 1 in any position is worth 10 when added to the column immediately to its right.

  4. Carrying right (1st decimal place) 10 + 0 = 10, but we need to take 1 from this to carry right again (cross through 10 and mark as 9).
  5. Carrying right (2nd decimal place), 10 + 0 = 10, and 10 – 5 = 5
  6. Moving left (1st decimal place), 9 – 0 = 9
  7. Left again (units column), 2 is less than 6, so we need to take 1 over from the (tens) column to the left (cross through 1, and mark as 0).
  8. Carrying right, 10 + 2 = 12, and 12 – 6 = 6

The tens column now only contains 0, so this is the end of the process.


Mixed decimals

It is easier to ensure an accurate result if you use the same number of decimal places (positions to the right of the decimal point) for both values in the calculation, inserting zeros in any which are not required.

For example to subtract 17.5 from 24.247:

  1. Write 24.247 on the first line
  2. Write 17.500 (which includes two additional zeros to match the decimal places in the value above).
  3. Ensuring the decimal point remains in the same position, subtract the lower value from the one above, using the long subtraction (column) process.
24.247 written above 17.500, with decimal points in same column position in both rows.

The worked solution as described, which comes to 6.747
  1. Far right (3rd decimal place) column, 7 - 0 = 7
  2. Moving left (2nd decimal place), 4 - 0 = 4
  3. Moving left (1st decimal place), 2 is less than 5, so take 1 from the next (units) column to the left (cross through 4 and mark as 3).
  4. Carrying right, 10 + 2 = 12, and 12 - 5 = 7
  5. Left again (units column), 3 is less than 7, so take 1 from the (tens) column to the left (cross through 2 and mark as 1).
  6. Carrying right, 10 + 3 = 13, and 13 - 7 = 6
  7. Left again (tens column), 1 - 1 = 0, and as whole numbers can't start with 0, leave this column blank.