Operations and calculations
2. Addition
2.1. Adding decimals
When working with decimal values, it is important to ensure that the decimal point is always in the same position (column) in each row of 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, we use two decimal places to hold values up to 99 pence, so, if we are working with mixed values of pounds and pence, we can include a decimal point and two decimal places for each. Two zeros after the decimal indicate ‘no pence’ and a zero before the decimal point indicates ‘no pounds’.
For example to sum the following amounts:
- Two pounds (£2)
- 99 pence (99p)
- Thirteen pounds (£13)
- Six pounds and five pence (£6.05)
Set them out, one above the other, with the decimal point always in the same position.
Then, working from right to left, add the digits in each column, carrying over as required, as outlined in ‘long addition’ on the previous page.
Starting on the far right: 0 + 9 + 0 + 5 = 14. Write 4 below this column and carry the ten over to the column on the left, by marking 1 below the bottom line.
Moving left: 0 + 9 + 0 + 0 = 9, plus the 1 carried over, is 10. Write 0 in this column and carry the ten over to the next column on the left, by marking 1 below.
Moving to the column on the left of the decimal point: 2 + 0 + 3 + 6 = 11, plus the 1 carried over, is 12. Write 2 in this column and carry the ten over, by marking 1 below.
Next column on the left: there's only one digit, so add this to the 1 carried over. 1 + 2 = 2, so write 2 below the line.
Keeping the decimal point in the same position, £22.04 is our total.
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 each value in the calculation, inserting zeros in any which are not required.
For example to sum the following amounts:
- 22
- 17.5
- 33.333
- 0.1257
- 15
Set them out, one above the other, with the decimal point always in the same position:
Then, working from right to left, add the digits in each column, carrying over as required, as outlined in ‘long addition’ on the previous page.
Ignoring the 0s (as they are of no value) add the digits in each columns:
Far right column: 7
Moving left: 3 + 5 = 8
Next left: 3 + 2 = 5
Left again: 5 + 3 + 1 = 9
Left again: add the decimal point
Column to the left of the decimal point: 2 + 7 + 3 + 5 = 17. Write 7 in this column and carry over the 10 by writing 1 below.
Final column: 2 + 1 + 3 + 1 = 7, plus the 1 carried over = 8
