Step-by-step Maths Level 4: Subtraction with a zero in the middle
Part of the Step-by-step Maths Level 4 column addition and subtraction chapter. Chapter overview · whole chapter on one page
Subtraction with a zero in the middle
A zero cannot give a ten. In 5004 - 2378 there are no tens and no hundreds to exchange from.
Go left to the first column that is not zero. Exchange 1 from there, then make each zero 9 as you go along.
Key ideas
- A zero cannot be exchanged from.
- Exchange from the first column on the left that is not zero.
- Each zero that you pass becomes 9.
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: 5 to 4; 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: 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.9 - 7 = 2
- 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.4 - 2 = 2
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.2626
Check. Check: 2626 + 2378 = 5004.
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: 3 to 2; 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: 1 to 11
- Subtract the ones column. Take the bottom digit from the top digit.11 - 5 = 6
- Subtract the tens column. Take the bottom digit from the top digit.9 - 4 = 5
- Subtract the hundreds column. Take the bottom digit from the top digit.9 - 2 = 7
- 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.1756
Check. Check: 1756 + 1245 = 3001.
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: 5 to 4; 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 - 8 = 2
- Subtract the tens column. Take the bottom digit from the top digit.9 - 6 = 3
- Subtract the hundreds column. Take the bottom digit from the top digit.4 - 2 = 2
- Subtract the thousands column. Take the bottom digit from the top digit.4 - 1 = 3
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.3232
Check. Check: 3232 + 1268 = 4500.
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. 5004 - 2378 is 2626, not 2636. Each zero becomes 9 after the exchange, and the last column gets 10 more.
Exam tip
Grown-up tip. Ask the child to point to the first non-zero digit on the left before exchanging.
Exercise 3D Practice: subtraction across zeros
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.8 - 3 = 5
- Exchange in the thousands column. The hundreds are 0, so exchange from further left: exchange 1 thousand for 10 hundreds.thousands: 4 to 3; hundreds: 0 to 10
- Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.hundreds: 10 to 9; tens: 7 to 17
- Subtract the tens column. Take the bottom digit from the top digit.17 - 9 = 8
- 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.3 - 3 = 0
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.185
Check. Check: 185 + 3893 = 4078.
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
- Exchange in the thousands column. The hundreds are 0, so exchange from further left: exchange 1 thousand for 10 hundreds.thousands: 2 to 1; hundreds: 0 to 10
- Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.hundreds: 10 to 9; tens: 6 to 16
- Subtract the tens column. Take the bottom digit from the top digit.16 - 8 = 8
- Subtract the hundreds column. Take the bottom digit from the top digit.9 - 7 = 2
- 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.288
Check. Check: 288 + 1782 = 2070.
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.8 - 8 = 0
- Exchange in the thousands column. The hundreds are 0, so exchange from further left: exchange 1 thousand for 10 hundreds.thousands: 5 to 4; hundreds: 0 to 10
- Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.hundreds: 10 to 9; tens: 4 to 14
- Subtract the tens column. Take the bottom digit from the top digit.14 - 8 = 6
- Subtract the hundreds column. Take the bottom digit from the top digit.9 - 2 = 7
- Subtract the thousands column. Take the bottom digit from the top digit.4 - 4 = 0
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.760
Check. Check: 760 + 4288 = 5048.
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: 2 to 12
- Subtract the ones column. Take the bottom digit from the top digit.12 - 5 = 7
- Exchange in the thousands column. The hundreds are 0, so exchange from further left: exchange 1 thousand for 10 hundreds.thousands: 9 to 8; hundreds: 0 to 10
- Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.hundreds: 10 to 9; tens: 6 to 16
- Subtract the tens column. Take the bottom digit from the top digit.16 - 8 = 8
- Subtract the hundreds column. Take the bottom digit from the top digit.9 - 1 = 8
- 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.6887
Check. Check: 6887 + 2185 = 9072.
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.2 - 1 = 1
- Exchange in the thousands column. The hundreds are 0, so exchange from further left: exchange 1 thousand for 10 hundreds.thousands: 9 to 8; hundreds: 0 to 10
- Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.hundreds: 10 to 9; tens: 7 to 17
- Subtract the tens column. Take the bottom digit from the top digit.17 - 9 = 8
- Subtract the hundreds column. Take the bottom digit from the top digit.9 - 1 = 8
- Subtract the thousands column. Take the bottom digit from the top digit.8 - 1 = 7
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.7881
Check. Check: 7881 + 1191 = 9072.
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: 5 to 4; ones: 0 to 10
- Subtract the ones column. Take the bottom digit from the top digit.10 - 7 = 3
- Exchange in the thousands column. The hundreds are 0, so exchange from further left: exchange 1 thousand for 10 hundreds.thousands: 5 to 4; hundreds: 0 to 10
- Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.hundreds: 10 to 9; tens: 4 to 14
- Subtract the tens column. Take the bottom digit from the top digit.14 - 5 = 9
- Subtract the hundreds column. Take the bottom digit from the top digit.9 - 7 = 2
- Subtract the thousands column. Take the bottom digit from the top digit.4 - 4 = 0
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.293
Check. Check: 293 + 4757 = 5050.
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: 8 to 18
- Subtract the ones column. Take the bottom digit from the top digit.18 - 9 = 9
- Exchange in the thousands column. The hundreds are 0, so exchange from further left: exchange 1 thousand for 10 hundreds.thousands: 8 to 7; hundreds: 0 to 10
- Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.hundreds: 10 to 9; tens: 6 to 16
- Subtract the tens column. Take the bottom digit from the top digit.16 - 9 = 7
- Subtract the hundreds column. Take the bottom digit from the top digit.9 - 5 = 4
- Subtract the thousands column. Take the bottom digit from the top digit.7 - 1 = 6
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.6479
Check. Check: 6479 + 1599 = 8078.
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: 4 to 3; 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: 2 to 12
- Subtract the ones column. Take the bottom digit from the top digit.12 - 8 = 4
- Subtract the tens column. Take the bottom digit from the top digit.9 - 8 = 1
- Subtract the hundreds column. Take the bottom digit from the top digit.9 - 4 = 5
- Subtract the thousands column. Take the bottom digit from the top digit.3 - 1 = 2
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.2514
Check. Check: 2514 + 1488 = 4002.
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: 6 to 5; 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: 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.9 - 7 = 2
- Subtract the hundreds column. Take the bottom digit from the top digit.9 - 5 = 4
- Subtract the thousands column. Take the bottom digit from the top digit.5 - 1 = 4
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.4429
Check. Check: 4429 + 1576 = 6005.
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.2 - 0 = 2
- Exchange in the thousands column. The hundreds are 0, so exchange from further left: exchange 1 thousand for 10 hundreds.thousands: 2 to 1; hundreds: 0 to 10
- Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.hundreds: 10 to 9; tens: 0 to 10
- Subtract the tens column. Take the bottom digit from the top digit.10 - 9 = 1
- Subtract the hundreds column. Take the bottom digit from the top digit.9 - 5 = 4
- 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.412
Check. Check: 412 + 1590 = 2002.
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: 1 to 0; ones: 2 to 12
- Subtract the ones column. Take the bottom digit from the top digit.12 - 8 = 4
- Subtract the tens column. Take the bottom digit from the top digit.0 - 0 = 0
- 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 - 4 = 6
- 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.604
Check. Check: 604 + 1408 = 2012.
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.1 - 0 = 1
- Exchange in the thousands column. The hundreds are 0, so exchange from further left: exchange 1 thousand for 10 hundreds.thousands: 3 to 2; hundreds: 0 to 10
- Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.hundreds: 10 to 9; tens: 4 to 14
- Subtract the tens column. Take the bottom digit from the top digit.14 - 6 = 8
- Subtract the hundreds column. Take the bottom digit from the top digit.9 - 1 = 8
- Subtract the thousands column. Take the bottom digit from the top digit.2 - 2 = 0
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.881
Check. Check: 881 + 2160 = 3041.
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.8 - 3 = 5
- Exchange in the thousands column. The hundreds are 0, so exchange from further left: exchange 1 thousand for 10 hundreds.thousands: 8 to 7; hundreds: 0 to 10
- Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.hundreds: 10 to 9; tens: 3 to 13
- Subtract the tens column. Take the bottom digit from the top digit.13 - 4 = 9
- Subtract the hundreds column. Take the bottom digit from the top digit.9 - 5 = 4
- Subtract the thousands column. Take the bottom digit from the top digit.7 - 6 = 1
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.1495
Check. Check: 1495 + 6543 = 8038.
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 - 3 = 3
- Exchange in the thousands column. The hundreds are 0, so exchange from further left: exchange 1 thousand for 10 hundreds.thousands: 2 to 1; hundreds: 0 to 10
- Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.hundreds: 10 to 9; tens: 6 to 16
- Subtract the tens column. Take the bottom digit from the top digit.16 - 8 = 8
- Subtract the hundreds column. Take the bottom digit from the top digit.9 - 6 = 3
- 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.383
Check. Check: 383 + 1683 = 2066.
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: 2 to 1; ones: 2 to 12
- Subtract the ones column. Take the bottom digit from the top digit.12 - 5 = 7
- Exchange in the thousands column. The hundreds are 0, so exchange from further left: exchange 1 thousand for 10 hundreds.thousands: 8 to 7; hundreds: 0 to 10
- Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.hundreds: 10 to 9; tens: 1 to 11
- Subtract the tens column. Take the bottom digit from the top digit.11 - 8 = 3
- Subtract the hundreds column. Take the bottom digit from the top digit.9 - 0 = 9
- Subtract the thousands column. Take the bottom digit from the top digit.7 - 3 = 4
- Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.4937
Check. Check: 4937 + 3085 = 8022.
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: 4 to 3; ones: 1 to 11
- Subtract the ones column. Take the bottom digit from the top digit.11 - 3 = 8
- Subtract the tens column. Take the bottom digit from the top digit.3 - 0 = 3
- 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 - 8 = 2
- 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.2238
Check. Check: 2238 + 3803 = 6041.
Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.