Money
A £27.68 purchase is paid for with £50. In 50.00 − 27.68 one ten is exchanged, passes through the ones and tenths, and the change is £22.32.
Before this page: setting a subtraction out in columns and exchanging one unit from the column on the left, both from column subtraction.
Exchanging across zeros
In 3,000 − 847, the top line holds a 0 in every column but the thousands. One thousand can be renamed as 10 hundreds, then one hundred as 10 tens, then one ten as 10 ones.
1,000s
100s
10s
1s
3
0
0
0
−
0
8
4
7
?
A thousand comes apart without anything being lost:
1000 = 900 + 90 + 10
3000 = 2000 + 900 + 90 + 10
Written down, the 3, 0, 0, 0 becomes 2, 9, 9 and 10. A run of 9s above the top line shows an exchange that had to travel.
3,000 − 847
Align equal place values
Ones under ones, tens under tens, hundreds under hundreds.
Explore exchanging across zeros
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
Ones under ones, tens under tens, hundreds under hundreds.
Across zeros in decimals
In 4.03 − 1.276, writing 4.03 as 4.030 creates a zero of the same kind as the zeros in 3,000: the first exchange is ordinary and the second has to travel.
4.03 − 1.276
Align equal place values
Points beneath points; 4.03 written as 4.030 so the thousandths column has a 0.
In 12 − 3.475, every decimal column of the whole number 12 starts at 0, so the exchange travels from the ones to the thousandths.
12 − 3.475
Align equal place values
Points beneath points; 12 written as 12.000 so the tenths, hundredths and thousandths columns each have a 0.
Change and lengths
£50 − £27.68 is the same subtraction as 50.00 − 27.68: the whole quantity is written to match the decimal, and the unit only says what the answer counts.
Measure
A 2.675 m piece is cut from a 5 m length. The 5 is written 5.000, and 5.000 − 2.675 = 2.325 m.
Key points
- Find the first non-zero digit to the left and reduce it by one.
- Each empty column passed through receives ten, passes one on, and keeps nine.
- Subtract using the rewritten digits, including any zeros added after a decimal point.