Write the answer under the line and move one column left.
Before this page: the column layout from column addition, and what each digit is worth in integers and decimals.
Subtracting in columns
Column subtraction takes one place value at a time. In 876 − 342 the ones ask 6 − 2 = 4, the tens ask 7 − 4 = 3 and the hundreds ask 8 − 3 = 5.
Each answer is written under the column it came from, and reading them together gives 534.
The layout works because every column of 876 − 342 holds enough to pay what is asked of it. 872 − 346 is set out the same way, but the ones column asks 2 − 6, and 2 ones cannot give 6.
100s
10s
1s
8
7
2
−
3
4
6
?
One of the 7 tens is ten ones. Exchanging it gives 6 tens and 12 ones, and the total is still 872.
Exchanging without changing the value
872 = 800 + 70 + 2
872 = 800 + 60 + 12
Swapping a £10 note for ten £1 coins changes what can be paid, not how much money there is. An exchange does that, and it is available in every column: one hundred for ten tens, one tenth for ten hundredths.
The ones column now holds 12, and 12 − 6 = 6. The other two columns need no exchange: 6 − 4 = 2 and 8 − 3 = 5.
Two marks record the swap. Cross out the 7 and write 6 above it, because the tens gave one away. Write a small 1 in front of the 2, because the ones received it.
100s
10s
1s
6
8
7
12
−
3
4
6
5
2
6
Every column asks the same question
Is the top digit big enough to take the digit below it?
Lower the column on the left by one, add ten to this column, then subtract.
Setting out a subtraction
Addition can be written either way round; subtraction cannot, because 8 − 3 and 3 − 8 are different questions. For the non-negative subtractions here, the larger number is written on top. If the number underneath is the larger one, the answer is negative, which adding and subtracting negatives covers.
Writing 14.6 as 14.60 makes the hundredths column explicit. There are zero hundredths before we exchange, so the 5 hundredths in 8.35 must be subtracted from an exchanged amount, not copied into the answer.
14.60
Whole numbers and decimals
In 6,145 − 2,978 the hundreds column gives its last hundred away, and then needs one from the thousands.
6,145 − 2,978
Align equal place values
Ones under ones, tens under tens, hundreds under hundreds.
Once the points are lined up, the columns carry on past them, and the answer's point goes beneath them.
14.6 − 8.35
Align equal place values
Points beneath points; 14.6 written as 14.60 so the hundredths column has a 0.
Finding what is left or how far apart
Removing 8.35 m from 14.6 m asks what remains. Comparing 2.4 m with 1.75 m asks for the distance between them. Both structures lead to subtraction.
What is left
A roll holds 14.6 m of cable and 8.35 m is cut off it. What remains is 14.60 − 8.35 = 6.25 m.
Change from a payment is the same shape of question: the money handed over is the starting amount, and the price comes out of it.
How far apart
One shelf is 2.4 m long and another is 1.75 m. Nothing is cut; the question is the gap between them, which is 2.40 − 1.75 = 0.65 m.
0.65 m
1.75 m
2.4 m
For these problems, subtract the smaller amount from the larger to find the gap. Decide what the amounts represent before choosing the calculation.
Explore column subtraction
The second number is the larger one, so the answer falls below zero. Lower it, or read adding and subtracting negatives.
Align equal place values
Points beneath points; 4,351.2 written as 4,351.20 so the hundredths column has a 0.
Key points
- Line up the decimal points and fill empty decimal places with zeros.
- Work from right to left. Exchange one unit of the next place for ten of the current place when needed.
- Record both sides of an exchange; the original number has not changed.
- Check by adding the answer to the amount subtracted.