Rule: Line up the decimal points, pad with zeros, then add column by column
To add decimals, line up the decimal points in a column so digits of the same place value sit above one another, padding shorter numbers with zeros where needed. Then add from right to left exactly as with whole numbers, carrying any extra ten into the next column.
Example 1 — Calculate \(3.47 + 12.6\)
Step 1
Write in columns with decimal points aligned. Pad 12.6 as 12.60.
⚠ Common mistake: Not aligning decimal points. Always write the decimal point in the same column for every number, then pad shorter numbers with zeros.
✓ Quick Check 1 — Adding Decimals
Question 1 of 10
Subtracting Decimals — Column Method with Borrowing
Subtracting decimals uses the same column approach. Align the decimal points, pad with zeros, then subtract from right to left — borrowing (exchanging) when a digit on top is smaller than the one below.
Example 3 — Calculate \(10.00 - 3.47\)
Step 1
Set up in columns: 10.00 on top, 03.47 below. Decimal points aligned.
Step 2
Hundredths: \(0 - 7\) — can't do it. Borrow from tenths. Tenths is 0, so borrow from units. Units is 0, so borrow from tens. Chain borrow: tens becomes 0, units becomes 9, tenths becomes 9, hundredths becomes 10.
Real-Life Applications — Shopping, Change and Bank Statements
Adding and subtracting decimals is essential for everyday money and measurement calculations. The method is always the same: align the decimal point and work in columns.
Example 5 — Shopping total and change
Step 1
Items cost £1.20, £0.89, £1.45, £2.30. Align decimal points and add in columns.
Work through these without a calculator. Type your answer, then click Check.
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Question
Answer
Result
1
A plank is 2.45 m long. You cut off 0.8 m. How much is left (m)?
2
You buy items costing £4.99, £1.35 and £2.60. What is the total (£)?
3
Balance £56.40. You spend £12.75 then receive £30.00. New balance (£)?
4
£15.60 + £3.45 = ?
5
8.7 − 3.25 = ?
6
You buy 3 items: £2.15, £0.99 and £4.50. What is the total (£)?
7
You have £100. You spend £34.75. How much change (£)?
8
12.6 + 3.47 = ?
9
10.00 − 3.47 = ?
10
A recipe needs 1.25 kg flour. You have 0.6 kg. How much more do you need (kg)?
⚠ Things to Watch Out For
Not aligning the decimal points: Always write numbers with decimal points directly below each other. This is the single most common error — misalignment means wrong column values.
Not padding with zeros: 12.6 + 3.47 — write 12.60 + 3.47 so both have the same number of decimal places. This prevents misreading the hundredths column.
Moving the decimal point: The decimal point stays in the same column throughout the calculation. It does not move.
Subtraction from zero: 10.00 − 3.47: you must borrow through the zeros. Work carefully column by column — don't subtract 0 from 4 and write 4.
Dropping the decimal in the answer: Always include the decimal point in the answer, aligned exactly with the decimal points in the calculation.