12.40
+03.75
The decimal points line up, so 4 tenths sits over 7 tenths and 0 hundredths over 5 hundredths.
Before this page: know what each digit is worth in integers and decimals, and be able to add two single digits without writing anything down.
Adding in columns
Adding a long number does not need one long mental calculation. Place value lets us add the ones, tens and hundreds separately, keeping track of each part.
Column addition gives each place its own column. In 342 + 526 no column reaches ten, so every column total is a single digit:
100s
10s
1s
3
4
2
+
5
2
6
8
6
8
The columns are added in this direction
- Place-value columns The 3 and the 5 both count hundreds, the 4 and the 2 tens, the 2 and the 6 ones.
- One column at a time 2 + 6 = 8 first, then 4 + 2 = 6, then 3 + 5 = 8.
- Answer line Every column total is written beneath the line, in the column it came from.
Lining up the place values
In 12.4 + 3.75 a digit in the tens column counts groups of ten and a digit in the hundredths column counts groups of one hundredth: each column holds quantities of one size.
12.4
+3.75
Aligning the final digits puts 5 hundredths beneath 4 tenths and 3 ones beneath 1 ten, so each column of the calculation adds two different sizes.
Carrying into the next column
When a column totals ten or more, exchange ten units for one in the next column. For example, 14 tens become 1 hundred and 4 tens. The amount stays the same; we have just regrouped it.
10 ones
1 ten
In 4,687 + 2,759 the tens column holds 8 and 5 with a regrouped 1 above it, so the column totals 14:
Tens column
18514
4is written in the tens column
1is regrouped into the hundreds column, where it joins the next addition
Add one place-value column at a time
- 1
Align equal place values.
- 2
Begin with the furthest column to the right.
- 3
Write the result digit and regroup any tens.
- 4
Continue left, including every regrouped amount.
Adding whole numbers
4,687 + 2,759 is four columns, and three of them regroup:
4,687 + 2,759
Align equal place values
Ones under ones, tens under tens, hundreds under hundreds.
Adding decimals
In 18.75 + 6.9 the columns carry on past the point: tenths, then hundredths. The point sits between ones and tenths in every row, so the answer's point goes directly beneath the two above:
18.75 + 6.9
Align equal place values
Points beneath points; 6.9 written as 6.90 so the hundredths column has a 0.
Adding amounts
Pounds, metres or minutes: every quantity is converted to the same unit before the columns are set out, and the unit goes with the answer.
Money
A book costs £18.75 and a notebook costs £6.90. Their total cost is £18.75 + £6.90 = £25.65.
Measure
A 2.35 m length is joined to an 85 cm length. 85 cm is 0.85 m, so the total is 2.35 m + 0.85 m = 3.20 m, or 3.2 m.
Three numbers are added in the same columns as two, and a column can now total twenty or more, so 2 is regrouped rather than 1.
Example: add three prices, £18.75 + £6.90 + £4.85
Add the three prices in columns.
- Hundredths: 5 + 0 + 5 = 10 Write 0, and regroup 1 into the tenths.
- Tenths: 7 + 9 + 8 + 1 = 25 Write 5, and regroup 2 into the ones: twenty-five tenths is two ones and five tenths.
- Ones: 8 + 6 + 4 + 2 = 20 Write 0, and regroup 2 into the tens.
- Tens: 1 + 2 = 3, so the total is £30.50 The final zero stays, because prices are written to the penny.
Explore column addition
Align equal place values
Points beneath points; 956.7 written as 956.70 so the hundredths column has a 0.
Key points
- Line up equal place values, including decimal points. Add zeros to empty decimal places if helpful.
- Work from right to left, including every carried amount in the next column.
- Use the same unit for all amounts, and keep the unit with the answer.