Step-by-step Maths Level 4: Column subtraction with exchange
Part of the Step-by-step Maths Level 4 column addition and subtraction chapter. Chapter overview · whole chapter on one page
Column subtraction with exchange
Subtract the ones first. If the top digit is too small, exchange 1 ten from the tens column for 10 ones.
If a column is too small, exchange again from the column on its left. Work from the ones to the thousands.
Key ideas
- Work from the ones, column by column.
- Exchange 1 from the column on the left when the top digit is too small.
- Subtract the bottom digit from the top digit in each column.
Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.
- Exchange in the tens column. The ones digit is too small, so exchange 1 ten for 10 ones.tens: 7 to 6; ones: 1 to 11
- Subtract the ones column. Take the bottom digit from the top digit.11 - 5 = 6
- Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.hundreds: 2 to 1; tens: 6 to 16
- Subtract the tens column. Take the bottom digit from the top digit.16 - 8 = 8
- Exchange in the thousands column. The hundreds digit is too small, so exchange 1 thousand for 10 hundreds.thousands: 5 to 4; hundreds: 1 to 11
- Subtract the hundreds column. Take the bottom digit from the top digit.11 - 3 = 8
- Subtract the thousands column. Take the bottom digit from the top digit.4 - 2 = 2
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.2886
Check. Check: 2886 + 2385 = 5271.
Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.
Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.
- Exchange in the tens column. The ones digit is too small, so exchange 1 ten for 10 ones.tens: 6 to 5; ones: 2 to 12
- Subtract the ones column. Take the bottom digit from the top digit.12 - 5 = 7
- Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.hundreds: 4 to 3; tens: 5 to 15
- Subtract the tens column. Take the bottom digit from the top digit.15 - 7 = 8
- Exchange in the thousands column. The hundreds digit is too small, so exchange 1 thousand for 10 hundreds.thousands: 3 to 2; hundreds: 3 to 13
- Subtract the hundreds column. Take the bottom digit from the top digit.13 - 8 = 5
- Subtract the thousands column. Take the bottom digit from the top digit.2 - 1 = 1
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.1587
Check. Check: 1587 + 1875 = 3462.
Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.
Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.
- Exchange in the tens column. The ones digit is too small, so exchange 1 ten for 10 ones.tens: 3 to 2; ones: 5 to 15
- Subtract the ones column. Take the bottom digit from the top digit.15 - 8 = 7
- Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.hundreds: 1 to 0; tens: 2 to 12
- Subtract the tens column. Take the bottom digit from the top digit.12 - 4 = 8
- Exchange in the thousands column. The hundreds digit is too small, so exchange 1 thousand for 10 hundreds.thousands: 6 to 5; hundreds: 0 to 10
- Subtract the hundreds column. Take the bottom digit from the top digit.10 - 7 = 3
- Subtract the thousands column. Take the bottom digit from the top digit.5 - 2 = 3
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.3387
Check. Check: 3387 + 2748 = 6135.
Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.
Watch out
Watch out. Exchange before you subtract. In 5271 - 2385, the ones 1 is too small for 5, so exchange a ten first.
Exam tip
Grown-up tip. Ask: “Is the top digit big enough? If not, what can you exchange?” Let the child check by adding back.
Exercise 3C Practice: column subtraction with exchange
Non-calculatorMethod. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.
- Subtract the ones column. Take the bottom digit from the top digit.9 - 4 = 5
- Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.hundreds: 2 to 1; tens: 0 to 10
- Subtract the tens column. Take the bottom digit from the top digit.10 - 7 = 3
- Exchange in the thousands column. The hundreds digit is too small, so exchange 1 thousand for 10 hundreds.thousands: 9 to 8; hundreds: 1 to 11
- Subtract the hundreds column. Take the bottom digit from the top digit.11 - 6 = 5
- Subtract the thousands column. Take the bottom digit from the top digit.8 - 7 = 1
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.1535
Check. Check: 1535 + 7674 = 9209.
Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.
Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.
- Exchange in the tens column. The ones digit is too small, so exchange 1 ten for 10 ones.tens: 3 to 2; ones: 0 to 10
- Subtract the ones column. Take the bottom digit from the top digit.10 - 6 = 4
- Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.hundreds: 6 to 5; tens: 2 to 12
- Subtract the tens column. Take the bottom digit from the top digit.12 - 9 = 3
- Subtract the hundreds column. Take the bottom digit from the top digit.5 - 4 = 1
- Subtract the thousands column. Take the bottom digit from the top digit.5 - 5 = 0
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.134
Check. Check: 134 + 5496 = 5630.
Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.
Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.
- Subtract the ones column. Take the bottom digit from the top digit.6 - 4 = 2
- Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.hundreds: 7 to 6; tens: 1 to 11
- Subtract the tens column. Take the bottom digit from the top digit.11 - 7 = 4
- Subtract the hundreds column. Take the bottom digit from the top digit.6 - 6 = 0
- Subtract the thousands column. Take the bottom digit from the top digit.7 - 5 = 2
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.2042
Check. Check: 2042 + 5674 = 7716.
Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.
Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.
- Subtract the ones column. Take the bottom digit from the top digit.9 - 7 = 2
- Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.hundreds: 2 to 1; tens: 2 to 12
- Subtract the tens column. Take the bottom digit from the top digit.12 - 4 = 8
- Exchange in the thousands column. The hundreds digit is too small, so exchange 1 thousand for 10 hundreds.thousands: 5 to 4; hundreds: 1 to 11
- Subtract the hundreds column. Take the bottom digit from the top digit.11 - 8 = 3
- Subtract the thousands column. Take the bottom digit from the top digit.4 - 2 = 2
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.2382
Check. Check: 2382 + 2847 = 5229.
Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.
Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.
- Exchange in the tens column. The ones digit is too small, so exchange 1 ten for 10 ones.tens: 7 to 6; ones: 0 to 10
- Subtract the ones column. Take the bottom digit from the top digit.10 - 2 = 8
- Subtract the tens column. Take the bottom digit from the top digit.6 - 5 = 1
- Subtract the hundreds column. Take the bottom digit from the top digit.5 - 3 = 2
- Subtract the thousands column. Take the bottom digit from the top digit.8 - 2 = 6
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.6218
Check. Check: 6218 + 2352 = 8570.
Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.
Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.
- Exchange in the tens column. The ones digit is too small, so exchange 1 ten for 10 ones.tens: 8 to 7; ones: 4 to 14
- Subtract the ones column. Take the bottom digit from the top digit.14 - 9 = 5
- Subtract the tens column. Take the bottom digit from the top digit.7 - 0 = 7
- Subtract the hundreds column. Take the bottom digit from the top digit.4 - 0 = 4
- Subtract the thousands column. Take the bottom digit from the top digit.8 - 6 = 2
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.2475
Check. Check: 2475 + 6009 = 8484.
Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.
Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.
- Subtract the ones column. Take the bottom digit from the top digit.9 - 0 = 9
- Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.hundreds: 6 to 5; tens: 4 to 14
- Subtract the tens column. Take the bottom digit from the top digit.14 - 6 = 8
- Exchange in the thousands column. The hundreds digit is too small, so exchange 1 thousand for 10 hundreds.thousands: 8 to 7; hundreds: 5 to 15
- Subtract the hundreds column. Take the bottom digit from the top digit.15 - 7 = 8
- Subtract the thousands column. Take the bottom digit from the top digit.7 - 7 = 0
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.889
Check. Check: 889 + 7760 = 8649.
Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.
Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.
- Subtract the ones column. Take the bottom digit from the top digit.6 - 0 = 6
- Subtract the tens column. Take the bottom digit from the top digit.9 - 7 = 2
- Exchange in the thousands column. The hundreds digit is too small, so exchange 1 thousand for 10 hundreds.thousands: 7 to 6; hundreds: 0 to 10
- Subtract the hundreds column. Take the bottom digit from the top digit.10 - 7 = 3
- Subtract the thousands column. Take the bottom digit from the top digit.6 - 2 = 4
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.4326
Check. Check: 4326 + 2770 = 7096.
Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.
Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.
- Exchange in the thousands column. The hundreds are 0, so exchange from further left: exchange 1 thousand for 10 hundreds.thousands: 7 to 6; hundreds: 0 to 10
- Exchange in the hundreds column. The tens are 0, so exchange from further left: exchange 1 hundred for 10 tens.hundreds: 10 to 9; tens: 0 to 10
- Exchange in the tens column. The ones digit is too small, so exchange 1 ten for 10 ones.tens: 10 to 9; ones: 0 to 10
- Subtract the ones column. Take the bottom digit from the top digit.10 - 1 = 9
- Subtract the tens column. Take the bottom digit from the top digit.9 - 9 = 0
- Subtract the hundreds column. Take the bottom digit from the top digit.9 - 8 = 1
- Subtract the thousands column. Take the bottom digit from the top digit.6 - 1 = 5
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.5109
Check. Check: 5109 + 1891 = 7000.
Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.
Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.
- Subtract the ones column. Take the bottom digit from the top digit.5 - 0 = 5
- Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.hundreds: 1 to 0; tens: 4 to 14
- Subtract the tens column. Take the bottom digit from the top digit.14 - 7 = 7
- Exchange in the thousands column. The hundreds digit is too small, so exchange 1 thousand for 10 hundreds.thousands: 2 to 1; hundreds: 0 to 10
- Subtract the hundreds column. Take the bottom digit from the top digit.10 - 1 = 9
- Subtract the thousands column. Take the bottom digit from the top digit.1 - 1 = 0
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.975
Check. Check: 975 + 1170 = 2145.
Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.
Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.
- Exchange in the tens column. The ones digit is too small, so exchange 1 ten for 10 ones.tens: 9 to 8; ones: 0 to 10
- Subtract the ones column. Take the bottom digit from the top digit.10 - 4 = 6
- Subtract the tens column. Take the bottom digit from the top digit.8 - 1 = 7
- Exchange in the thousands column. The hundreds digit is too small, so exchange 1 thousand for 10 hundreds.thousands: 5 to 4; hundreds: 5 to 15
- Subtract the hundreds column. Take the bottom digit from the top digit.15 - 9 = 6
- Subtract the thousands column. Take the bottom digit from the top digit.4 - 2 = 2
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.2676
Check. Check: 2676 + 2914 = 5590.
Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.
Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.
- Exchange in the tens column. The ones digit is too small, so exchange 1 ten for 10 ones.tens: 9 to 8; ones: 4 to 14
- Subtract the ones column. Take the bottom digit from the top digit.14 - 8 = 6
- Subtract the tens column. Take the bottom digit from the top digit.8 - 3 = 5
- Subtract the hundreds column. Take the bottom digit from the top digit.9 - 3 = 6
- Subtract the thousands column. Take the bottom digit from the top digit.5 - 3 = 2
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.2656
Check. Check: 2656 + 3338 = 5994.
Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.
Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.
- Subtract the ones column. Take the bottom digit from the top digit.9 - 9 = 0
- Subtract the tens column. Take the bottom digit from the top digit.1 - 1 = 0
- Exchange in the thousands column. The hundreds digit is too small, so exchange 1 thousand for 10 hundreds.thousands: 9 to 8; hundreds: 4 to 14
- Subtract the hundreds column. Take the bottom digit from the top digit.14 - 8 = 6
- Subtract the thousands column. Take the bottom digit from the top digit.8 - 5 = 3
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.3600
Check. Check: 3600 + 5819 = 9419.
Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.
Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.
- Exchange in the hundreds column. The tens are 0, so exchange from further left: exchange 1 hundred for 10 tens.hundreds: 3 to 2; tens: 0 to 10
- Exchange in the tens column. The ones digit is too small, so exchange 1 ten for 10 ones.tens: 10 to 9; ones: 4 to 14
- Subtract the ones column. Take the bottom digit from the top digit.14 - 6 = 8
- Subtract the tens column. Take the bottom digit from the top digit.9 - 7 = 2
- Subtract the hundreds column. Take the bottom digit from the top digit.2 - 1 = 1
- Subtract the thousands column. Take the bottom digit from the top digit.9 - 8 = 1
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.1128
Check. Check: 1128 + 8176 = 9304.
Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.
Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.
- Exchange in the hundreds column. The tens are 0, so exchange from further left: exchange 1 hundred for 10 tens.hundreds: 3 to 2; tens: 0 to 10
- Exchange in the tens column. The ones digit is too small, so exchange 1 ten for 10 ones.tens: 10 to 9; ones: 5 to 15
- Subtract the ones column. Take the bottom digit from the top digit.15 - 7 = 8
- Subtract the tens column. Take the bottom digit from the top digit.9 - 5 = 4
- Exchange in the thousands column. The hundreds digit is too small, so exchange 1 thousand for 10 hundreds.thousands: 9 to 8; hundreds: 2 to 12
- Subtract the hundreds column. Take the bottom digit from the top digit.12 - 7 = 5
- Subtract the thousands column. Take the bottom digit from the top digit.8 - 8 = 0
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.548
Check. Check: 548 + 8757 = 9305.
Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.
Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.
- Exchange in the tens column. The ones digit is too small, so exchange 1 ten for 10 ones.tens: 6 to 5; ones: 5 to 15
- Subtract the ones column. Take the bottom digit from the top digit.15 - 6 = 9
- Subtract the tens column. Take the bottom digit from the top digit.5 - 5 = 0
- Subtract the hundreds column. Take the bottom digit from the top digit.8 - 6 = 2
- Subtract the thousands column. Take the bottom digit from the top digit.7 - 7 = 0
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.209
Check. Check: 209 + 7656 = 7865.
Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.