How to add and subtract decimals

• To add or subtract decimals, an understanding of place value is useful.

• The ability to sum single digits makes this a quick way to get the total of a list of decimals.

• In subtraction, regrouping may be necessary to complete the process.

To add decimals:

1. Write the numbers in a vertical list, lining up the decimal points.

2. If the numbers have a different amount of digits, there may be some gaps in the columns. Fill in any gaps with a zero so that each number has the same number of decimal places.

3. Add a decimal point in the answer space, lined up with the others.

4. Start at the right, the column with the least place value. Add the digits in the column.

- If the total is less than 10, enter the digit in the answer space.

- If the total is 10 or more, enter the units digit in the answer space for the column and carry the tens digit to the next column on the left.

5. Move left to the next place value column. Add the digits in the column and add any digit that was carried to this column. Repeat the addition process in each column until the calculation is complete.

To subtract decimals:

• Write the larger number above the smaller number in a vertical list, lining up the decimal points.

• Column subtraction works from right to left.

• Starting with the column on the right, the bottom digit is subtracted from the top digit and the answer is written in the answer space.

• Move left to the next column. Complete this subtraction process for each column until the calculation is complete.

If the top digit is smaller than the bottom digit, regroup the number. Regrouping is a process where groups of 10 are borrowed from one column and given to another. It is also known as exchanging.

Look through the examples to see how to follow the regrouping process. The first example is a normal subtraction, while the second requires regrouping.

To subtract decimals:

1. Write the larger number above the smaller number in a vertical list, lining up the decimal points.

2. Fill in any gaps after the decimal point with zeros so that each number has the same number of decimal places. Add a decimal point in the answer space, lined up with the others.

3. Start with the column on the right, the column with the least place value.

4. Subtract the bottom digit from the top digit.

• When the top digit is greater or equal to the bottom digit, the answer is entered in the answer space.

• When the top digit is less than the bottom digit, regroup the number to make the top digit bigger by 10. Sometimes regrouping is carried out across more than one column.

5. Move left to the next place value column.

6. Repeat the subtraction process for each column until the calculation is complete.

Practise adding and subtracting decimals in this quiz. You might need a pen and paper for your working out.

Calculations that involve money use the addition and subtraction of decimals.

• Subtraction of decimals can be used to work out how much change is needed. For example, if an item worth £17.75 is bought with a £20 note, subtraction is used to find the change required. 20 – 17.75 = 2.25. £2.25 in change is owed.

• Addition of decimals can be used to total the amount of money spent on several different items. It is useful to keep track of spending when on a budget.