Decimals
Adding and subtracting decimals
Line up the decimal points, not the ends of the numbers. Everything else is ordinary column arithmetic.
Line up the points
Write the calculation in columns with the decimal points directly under each other. The point in the answer goes directly under them too. If one number is shorter, fill the gap with zeros so every column is complete: 4.60 + 2.35 āāāā 6.95
Why the zeros help
12.4 + 3.75 looks awkward until you write 12.40. 12.40 + 3.75 āāāāā 16.15 Adding the zero changes nothing about the value, but it means every column has a digit to add.
Subtracting
Exactly the same: points lined up, gaps filled with zeros. 8.30 ā 2.65 āāāā 5.65 Without the zero on 8.3 it is easy to line the digits up wrongly and get 8.3 ā 2.65 = 6.35, which is too big by a whole 0.7.
Worked examples
4.6 + 2.35
- Line the decimal points up.
- Write 4.6 as 4.60 so every column is full.
- Add as usual.
Answer: 6.95
12.4 + 3.75
- Write 12.4 as 12.40.
- Line the points up and add.
Answer: 16.15
8.3 ā 2.65
- Write 8.3 as 8.30.
- Line the points up and subtract.
Answer: 5.65
What goes wrong without the zero
- Lining up the ends instead of the points.
- That gives 6.35, which is 0.7 too big.
Answer: Always line up the POINTS
Ā£9.22 + Ā£8.84
- Line up the points.
- Add the hundredths, then the tenths, then the pounds.
Answer: Ā£18.06
Where the point goes in the answer
- Directly below the points in the question.
Answer: In line with the others
Where you see this in real life
- Adding a Ā£4.60 sandwich and a Ā£2.35 drink is exactly this: line up the points, total Ā£6.95.
- Working out change from Ā£10 for Ā£3.45 of shopping means writing 10.00 ā 3.45, not 10 ā 3.45.
Key words
- Column method
- writing digits in place-value columns to calculate
- Placeholder zero
- a zero added to fill an empty column
- Decimal point
- the dot separating whole numbers from parts
- Sum
- the result of an addition
- Difference
- the result of a subtraction