Column decimals
You learn to add, subtract and multiply decimals in columns.
How to work it out
- Line up decimal points.
- Calculate as whole numbers, bringing the decimal point straight down.
11
12.45
+3.78
16.23
A worked example
12.45 + 3.78
- Line up the decimal points.
- Hundredths: 5 + 8 = 13, write 3 and carry 1.
- Tenths: 4 + 7 + 1 = 12, write 2 and carry 1.
- Ones and tens: 12 + 3 + 1 = 16.
- The answer is 16.23.
11
1245
+378
1623
More examples
8.32 − 4.57
- Line up the decimal points.
- Hundredths: 2 − 7 does not work, so exchange: 12 − 7 = 5.
- Tenths: the 3 has become 2, and 2 − 5 does not work, so exchange: 12 − 5 = 7.
- Ones: the 8 has become 7, and 7 − 4 = 3.
- The answer is 3.75.
71212
832
−457
375
3.45 × 6
- Work without the decimal point: 345 × 6 = 2070.
- 3.45 has 2 digits after the decimal point.
- Give the answer 2 as well: 20.70.
345
×6
2070
Watch out
You line the numbers up on the right instead of lining up the decimal points: for 2.7 + 1.45 you add the 7 to the 5.
Fill empty places with a 0: 2.70 + 1.45. Then all the digits are lined up correctly.
Tips
- Fill empty places after the decimal point with a 0.
- When you multiply, work without the decimal point, then count the digits after it.
Exceptions
- When you multiply, the decimal points do not need to be lined up.
Why it works
Lining up the decimal points puts tenths under tenths and ones under ones. Then you work just as you do with whole numbers. When you multiply, it does not matter where the decimal point is: work without it, then count how many digits go after it.