Year 4: Column subtraction
Part of the Year 4 column addition and subtraction chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Column subtraction
In column subtraction the bigger number goes on top. This is the number you start with. You take the bottom number away from it, one column at a time, starting with the ones. Words that mean subtract are take away, minus, less than, fewer than and difference.
| Th | H | T | O | |
| 5 | 6 | 8 | 7 | |
| − | 2 | 3 | 5 | 4 |
| 3 | 3 | 3 | 3 |
Exchanging. Sometimes the top digit is smaller than the bottom digit, like 2 − 7 in the ones column. You cannot take 7 away from 2. So you exchange: swap 1 ten for 10 ones. The tens digit goes down by 1 and the ones digit goes up by 10. Now 12 − 7 = 5. Some people call this borrowing.
| Th | H | T | O | |
| 6 | 3 | 14 | 12 | |
| − | 2 | 1 | 8 | 7 |
| 4 | 2 | 6 | 5 |
Zeros are tricky. You cannot exchange from a 0, because there is nothing to swap. Go to the next column on the left that is not 0, and pass the exchange along one column at a time. In 5,003 − 1,847, the ones need help (3 − 7), but the tens and the hundreds are both 0. So 1 thousand becomes 10 hundreds, then 1 hundred becomes 10 tens, then 1 ten becomes 10 ones. Each 0 in the middle ends up as a 9.
| Th | H | T | O | |
| 4 | 9 | 9 | 13 | |
| − | 1 | 8 | 4 | 7 |
| 3 | 1 | 5 | 6 |
Different lengths. You can take a three-digit number from a four-digit number, like 4,326 − 758. Line the digits up on the right. Where the bottom number has no digit, there is nothing to take away.
Key words. To exchange is to swap 1 of a bigger unit for 10 of the next smaller unit. The difference between two numbers is how far apart they are. It is the answer to a subtraction.
Key ideas
- The bigger number goes on top. Line the digits up on the right.
- Take away the ones first, then the tens, hundreds and thousands.
- If the top digit is smaller than the bottom digit, exchange: take 1 from the column on the left and add 10 to this column.
- You cannot exchange from a 0. Go left to the first column that is not 0. Each 0 you pass becomes 9.
- Check with addition: the answer plus the number you took away gives the number you started with.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 5 6 8 7 − 2 3 5 4 - Subtract the ones. Always start with the ones, on the right.7 − 4 = 3
Th H T O 5 6 8 7 − 2 3 5 4 3 - Subtract the tens. Now the next column to the left.8 − 5 = 3
Th H T O 5 6 8 7 − 2 3 5 4 3 3 - Subtract the hundreds. Now the next column to the left.6 − 3 = 3
Th H T O 5 6 8 7 − 2 3 5 4 3 3 3 - Subtract the thousands. Now the next column to the left.5 − 2 = 3
Th H T O 5 6 8 7 − 2 3 5 4 3 3 3 3 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 5 6 8 7 − 2 3 5 4 3 3 3 3
5,687 − 2,354 = 3,333
Check. Use the opposite (inverse) operation: 3,333 + 2,354 = 5,687. ✓
Estimate: 6,000 − 2,000 = 4,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. The bigger number goes on top and the digits are taken away column by column, starting with the ones.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 6 4 5 2 − 2 1 8 7 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.2 ones is not enough to take away 7. We need to exchange.
Exchange 1 ten for 10 ones: 5 tens become 4 tens, and 2 ones become 12 ones.
12 − 7 = 5Th H T O 6 4 4 512 2− 2 1 8 7 5 - Exchange, then subtract the tens. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.4 tens is not enough to take away 8. We need to exchange.
(There were 5 tens to start with, but we gave one away in an earlier exchange.)
Exchange 1 hundred for 10 tens: 4 hundreds become 3 hundreds, and 4 tens become 14 tens.
14 − 8 = 6Th H T O 6 3 414 512 2− 2 1 8 7 6 5 - Subtract the hundreds. Now the next column to the left.(This digit is 3 now, not 4, because we exchanged from this column.)
3 − 1 = 2Th H T O 6 3 414 512 2− 2 1 8 7 2 6 5 - Subtract the thousands. Now the next column to the left.6 − 2 = 4
Th H T O 6 3 414 512 2− 2 1 8 7 4 2 6 5 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 6 3 414 512 2− 2 1 8 7 4 2 6 5
6,452 − 2,187 = 4,265
Check. Use the opposite (inverse) operation: 4,265 + 2,187 = 6,452. ✓
Estimate: 6,000 − 2,000 = 4,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. The bottom digit is always taken from the top digit. Do not turn it round: 3 − 7 is not 4. Exchange instead.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 7 3 0 5 − 1 4 6 8 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.5 ones is not enough to take away 8. We need to exchange.
The tens has 0, so there is nothing to exchange from there. We start further to the left, at the hundreds.
Exchange 1 hundred for 10 tens: 3 hundreds become 2 hundreds, and 0 tens become 10 tens.
Exchange 1 ten for 10 ones: 10 tens become 9 tens, and 5 ones become 15 ones.
15 − 8 = 7Th H T O 7 2 39 015 5− 1 4 6 8 7 - Subtract the tens. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 6 = 3Th H T O 7 2 39 015 5− 1 4 6 8 3 7 - Exchange, then subtract the hundreds. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.2 hundreds is not enough to take away 4. We need to exchange.
(There were 3 hundreds to start with, but we gave one away in an earlier exchange.)
Exchange 1 thousand for 10 hundreds: 7 thousands become 6 thousands, and 2 hundreds become 12 hundreds.
12 − 4 = 8Th H T O 6 712 39 015 5− 1 4 6 8 8 3 7 - Subtract the thousands. Now the next column to the left.(This digit is 6 now, not 7, because we exchanged from this column.)
6 − 1 = 5Th H T O 6 712 39 015 5− 1 4 6 8 5 8 3 7 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 6 712 39 015 5− 1 4 6 8 5 8 3 7
7,305 − 1,468 = 5,837
Check. Use the opposite (inverse) operation: 5,837 + 1,468 = 7,305. ✓
Estimate: 7,000 − 1,000 = 6,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. You cannot exchange from a 0. Look left for the first column that is not 0, then pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 5 0 0 3 − 1 8 4 7 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.3 ones is not enough to take away 7. We need to exchange.
The tens and hundreds have 0, so there is nothing to exchange from there. We start further to the left, at the thousands.
Exchange 1 thousand for 10 hundreds: 5 thousands become 4 thousands, and 0 hundreds become 10 hundreds.
Exchange 1 hundred for 10 tens: 10 hundreds become 9 hundreds, and 0 tens become 10 tens.
Exchange 1 ten for 10 ones: 10 tens become 9 tens, and 3 ones become 13 ones.
13 − 7 = 6Th H T O 4 59 09 013 3− 1 8 4 7 6 - Subtract the tens. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 4 = 5Th H T O 4 59 09 013 3− 1 8 4 7 5 6 - Subtract the hundreds. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 8 = 1Th H T O 4 59 09 013 3− 1 8 4 7 1 5 6 - Subtract the thousands. Now the next column to the left.(This digit is 4 now, not 5, because we exchanged from this column.)
4 − 1 = 3Th H T O 4 59 09 013 3− 1 8 4 7 3 1 5 6 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 4 59 09 013 3− 1 8 4 7 3 1 5 6
5,003 − 1,847 = 3,156
Check. Use the opposite (inverse) operation: 3,156 + 1,847 = 5,003. ✓
Estimate: 5,000 − 2,000 = 3,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. You cannot exchange from a 0. Look left for the first column that is not 0, then pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 6 0 0 0 − 2 3 4 8 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.0 ones is not enough to take away 8. We need to exchange.
The tens and hundreds have 0, so there is nothing to exchange from there. We start further to the left, at the thousands.
Exchange 1 thousand for 10 hundreds: 6 thousands become 5 thousands, and 0 hundreds become 10 hundreds.
Exchange 1 hundred for 10 tens: 10 hundreds become 9 hundreds, and 0 tens become 10 tens.
Exchange 1 ten for 10 ones: 10 tens become 9 tens, and 0 ones become 10 ones.
10 − 8 = 2Th H T O 5 69 09 010 0− 2 3 4 8 2 - Subtract the tens. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 4 = 5Th H T O 5 69 09 010 0− 2 3 4 8 5 2 - Subtract the hundreds. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 3 = 6Th H T O 5 69 09 010 0− 2 3 4 8 6 5 2 - Subtract the thousands. Now the next column to the left.(This digit is 5 now, not 6, because we exchanged from this column.)
5 − 2 = 3Th H T O 5 69 09 010 0− 2 3 4 8 3 6 5 2 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 5 69 09 010 0− 2 3 4 8 3 6 5 2
6,000 − 2,348 = 3,652
Check. Use the opposite (inverse) operation: 3,652 + 2,348 = 6,000. ✓
Estimate: 6,000 − 2,000 = 4,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. You cannot exchange from a 0. Look left for the first column that is not 0, then pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 4 3 2 6 − 7 5 8 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.6 ones is not enough to take away 8. We need to exchange.
Exchange 1 ten for 10 ones: 2 tens become 1 ten, and 6 ones become 16 ones.
16 − 8 = 8Th H T O 4 3 1 216 6− 7 5 8 8 - Exchange, then subtract the tens. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.1 ten is not enough to take away 5. We need to exchange.
(There were 2 tens to start with, but we gave one away in an earlier exchange.)
Exchange 1 hundred for 10 tens: 3 hundreds become 2 hundreds, and 1 ten become 11 tens.
11 − 5 = 6Th H T O 4 2 311 216 6− 7 5 8 6 8 - Exchange, then subtract the hundreds. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.2 hundreds is not enough to take away 7. We need to exchange.
(There were 3 hundreds to start with, but we gave one away in an earlier exchange.)
Exchange 1 thousand for 10 hundreds: 4 thousands become 3 thousands, and 2 hundreds become 12 hundreds.
12 − 7 = 5Th H T O 3 412 311 216 6− 7 5 8 5 6 8 - Bring down the thousands digit. The bottom number has no digit in this column, so there is nothing to take away.(This digit is 3 now, not 4, because we exchanged from this column.)
Nothing to take away in this column, so the digit stays: 3.Th H T O 3 412 311 216 6− 7 5 8 3 5 6 8 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 3 412 311 216 6− 7 5 8 3 5 6 8
4,326 − 758 = 3,568
Check. Use the opposite (inverse) operation: 3,568 + 758 = 4,326. ✓
Estimate: 4,300 − 800 = 3,500 (rounding to the nearest 100). It is close to the exact answer. ✓
Watch out. The bottom digit is always taken from the top digit. Do not turn it round: 3 − 7 is not 4. Exchange instead.
Watch out
Never turn the digits round! In 6,452 − 2,187 it is tempting to write 7 − 2 = 5 in the ones column because 2 − 7 is hard. That gives the wrong answer. The bottom digit is always taken away from the top digit, so exchange instead. And remember: you cannot exchange from a 0.Exercise 2B Column subtraction
Non-calculatorKey words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 5 6 8 7 − 2 3 5 4 - Subtract the ones. Always start with the ones, on the right.7 − 4 = 3
- Subtract the tens. Now the next column to the left.8 − 5 = 3
- Subtract the hundreds. Now the next column to the left.6 − 3 = 3
- Subtract the thousands. Now the next column to the left.5 − 2 = 3
- Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 5 6 8 7 − 2 3 5 4 3 3 3 3
5,687 − 2,354 = 3,333
Check. Use the opposite (inverse) operation: 3,333 + 2,354 = 5,687. ✓
Estimate: 6,000 − 2,000 = 4,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. The bigger number goes on top and the digits are taken away column by column, starting with the ones.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 7 9 4 8 − 3 2 1 5 - Subtract the ones. Always start with the ones, on the right.8 − 5 = 3
- Subtract the tens. Now the next column to the left.4 − 1 = 3
- Subtract the hundreds. Now the next column to the left.9 − 2 = 7
- Subtract the thousands. Now the next column to the left.7 − 3 = 4
- Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 7 9 4 8 − 3 2 1 5 4 7 3 3
7,948 − 3,215 = 4,733
Check. Use the opposite (inverse) operation: 4,733 + 3,215 = 7,948. ✓
Estimate: 8,000 − 3,000 = 5,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. The bigger number goes on top and the digits are taken away column by column, starting with the ones.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 9 6 7 5 − 4 3 5 2 - Subtract the ones. Always start with the ones, on the right.5 − 2 = 3
- Subtract the tens. Now the next column to the left.7 − 5 = 2
- Subtract the hundreds. Now the next column to the left.6 − 3 = 3
- Subtract the thousands. Now the next column to the left.9 − 4 = 5
- Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 9 6 7 5 − 4 3 5 2 5 3 2 3
9,675 − 4,352 = 5,323
Check. Use the opposite (inverse) operation: 5,323 + 4,352 = 9,675. ✓
Estimate: 10,000 − 4,000 = 6,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. The bigger number goes on top and the digits are taken away column by column, starting with the ones.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 8 4 0 9 − 6 1 0 8 - Subtract the ones. Always start with the ones, on the right.9 − 8 = 1
- Subtract the tens. Now the next column to the left.0 − 0 = 0
- Subtract the hundreds. Now the next column to the left.4 − 1 = 3
- Subtract the thousands. Now the next column to the left.8 − 6 = 2
- Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 8 4 0 9 − 6 1 0 8 2 3 0 1
8,409 − 6,108 = 2,301
Check. Use the opposite (inverse) operation: 2,301 + 6,108 = 8,409. ✓
Estimate: 8,000 − 6,000 = 2,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. The bigger number goes on top and the digits are taken away column by column, starting with the ones.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 4 7 3 2 − 1 5 1 9 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.2 ones is not enough to take away 9. We need to exchange.
Exchange 1 ten for 10 ones: 3 tens become 2 tens, and 2 ones become 12 ones.
12 − 9 = 3 - Subtract the tens. Now the next column to the left.(This digit is 2 now, not 3, because we exchanged from this column.)
2 − 1 = 1 - Subtract the hundreds. Now the next column to the left.7 − 5 = 2
- Subtract the thousands. Now the next column to the left.4 − 1 = 3
- Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 4 7 2 312 2− 1 5 1 9 3 2 1 3
4,732 − 1,519 = 3,213
Check. Use the opposite (inverse) operation: 3,213 + 1,519 = 4,732. ✓
Estimate: 5,000 − 2,000 = 3,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. The bottom digit is always taken from the top digit. Do not turn it round: 3 − 7 is not 4. Exchange instead.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 6 4 8 5 − 2 9 6 7 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.5 ones is not enough to take away 7. We need to exchange.
Exchange 1 ten for 10 ones: 8 tens become 7 tens, and 5 ones become 15 ones.
15 − 7 = 8 - Subtract the tens. Now the next column to the left.(This digit is 7 now, not 8, because we exchanged from this column.)
7 − 6 = 1 - Exchange, then subtract the hundreds. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.4 hundreds is not enough to take away 9. We need to exchange.
Exchange 1 thousand for 10 hundreds: 6 thousands become 5 thousands, and 4 hundreds become 14 hundreds.
14 − 9 = 5 - Subtract the thousands. Now the next column to the left.(This digit is 5 now, not 6, because we exchanged from this column.)
5 − 2 = 3 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 5 614 47 815 5− 2 9 6 7 3 5 1 8
6,485 − 2,967 = 3,518
Check. Use the opposite (inverse) operation: 3,518 + 2,967 = 6,485. ✓
Estimate: 6,000 − 3,000 = 3,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. The bottom digit is always taken from the top digit. Do not turn it round: 3 − 7 is not 4. Exchange instead.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 7 1 2 0 − 3 8 0 5 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.0 ones is not enough to take away 5. We need to exchange.
Exchange 1 ten for 10 ones: 2 tens become 1 ten, and 0 ones become 10 ones.
10 − 5 = 5 - Subtract the tens. Now the next column to the left.(This digit is 1 now, not 2, because we exchanged from this column.)
1 − 0 = 1 - Exchange, then subtract the hundreds. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.1 hundred is not enough to take away 8. We need to exchange.
Exchange 1 thousand for 10 hundreds: 7 thousands become 6 thousands, and 1 hundred become 11 hundreds.
11 − 8 = 3 - Subtract the thousands. Now the next column to the left.(This digit is 6 now, not 7, because we exchanged from this column.)
6 − 3 = 3 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 6 711 11 210 0− 3 8 0 5 3 3 1 5
7,120 − 3,805 = 3,315
Check. Use the opposite (inverse) operation: 3,315 + 3,805 = 7,120. ✓
Estimate: 7,000 − 4,000 = 3,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. The bottom digit is always taken from the top digit. Do not turn it round: 3 − 7 is not 4. Exchange instead.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 5 3 4 6 − 2 1 7 8 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.6 ones is not enough to take away 8. We need to exchange.
Exchange 1 ten for 10 ones: 4 tens become 3 tens, and 6 ones become 16 ones.
16 − 8 = 8 - Exchange, then subtract the tens. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.3 tens is not enough to take away 7. We need to exchange.
(There were 4 tens to start with, but we gave one away in an earlier exchange.)
Exchange 1 hundred for 10 tens: 3 hundreds become 2 hundreds, and 3 tens become 13 tens.
13 − 7 = 6 - Subtract the hundreds. Now the next column to the left.(This digit is 2 now, not 3, because we exchanged from this column.)
2 − 1 = 1 - Subtract the thousands. Now the next column to the left.5 − 2 = 3
- Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 5 2 313 416 6− 2 1 7 8 3 1 6 8
5,346 − 2,178 = 3,168
Check. Use the opposite (inverse) operation: 3,168 + 2,178 = 5,346. ✓
Estimate: 5,000 − 2,000 = 3,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. The bottom digit is always taken from the top digit. Do not turn it round: 3 − 7 is not 4. Exchange instead.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 8 3 5 2 − 4 8 7 9 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.2 ones is not enough to take away 9. We need to exchange.
Exchange 1 ten for 10 ones: 5 tens become 4 tens, and 2 ones become 12 ones.
12 − 9 = 3 - Exchange, then subtract the tens. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.4 tens is not enough to take away 7. We need to exchange.
(There were 5 tens to start with, but we gave one away in an earlier exchange.)
Exchange 1 hundred for 10 tens: 3 hundreds become 2 hundreds, and 4 tens become 14 tens.
14 − 7 = 7 - Exchange, then subtract the hundreds. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.2 hundreds is not enough to take away 8. We need to exchange.
(There were 3 hundreds to start with, but we gave one away in an earlier exchange.)
Exchange 1 thousand for 10 hundreds: 8 thousands become 7 thousands, and 2 hundreds become 12 hundreds.
12 − 8 = 4 - Subtract the thousands. Now the next column to the left.(This digit is 7 now, not 8, because we exchanged from this column.)
7 − 4 = 3 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 7 812 314 512 2− 4 8 7 9 3 4 7 3
8,352 − 4,879 = 3,473
Check. Use the opposite (inverse) operation: 3,473 + 4,879 = 8,352. ✓
Estimate: 8,000 − 5,000 = 3,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. The bottom digit is always taken from the top digit. Do not turn it round: 3 − 7 is not 4. Exchange instead.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 6 2 3 4 − 2 9 5 8 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.4 ones is not enough to take away 8. We need to exchange.
Exchange 1 ten for 10 ones: 3 tens become 2 tens, and 4 ones become 14 ones.
14 − 8 = 6 - Exchange, then subtract the tens. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.2 tens is not enough to take away 5. We need to exchange.
(There were 3 tens to start with, but we gave one away in an earlier exchange.)
Exchange 1 hundred for 10 tens: 2 hundreds become 1 hundred, and 2 tens become 12 tens.
12 − 5 = 7 - Exchange, then subtract the hundreds. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.1 hundred is not enough to take away 9. We need to exchange.
(There were 2 hundreds to start with, but we gave one away in an earlier exchange.)
Exchange 1 thousand for 10 hundreds: 6 thousands become 5 thousands, and 1 hundred become 11 hundreds.
11 − 9 = 2 - Subtract the thousands. Now the next column to the left.(This digit is 5 now, not 6, because we exchanged from this column.)
5 − 2 = 3 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 5 611 212 314 4− 2 9 5 8 3 2 7 6
6,234 − 2,958 = 3,276
Check. Use the opposite (inverse) operation: 3,276 + 2,958 = 6,234. ✓
Estimate: 6,000 − 3,000 = 3,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. The bottom digit is always taken from the top digit. Do not turn it round: 3 − 7 is not 4. Exchange instead.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 9 1 4 1 − 5 8 7 6 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.1 one is not enough to take away 6. We need to exchange.
Exchange 1 ten for 10 ones: 4 tens become 3 tens, and 1 one become 11 ones.
11 − 6 = 5 - Exchange, then subtract the tens. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.3 tens is not enough to take away 7. We need to exchange.
(There were 4 tens to start with, but we gave one away in an earlier exchange.)
Exchange 1 hundred for 10 tens: 1 hundred become 0 hundreds, and 3 tens become 13 tens.
13 − 7 = 6 - Exchange, then subtract the hundreds. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.0 hundreds is not enough to take away 8. We need to exchange.
(There were 1 hundreds to start with, but we gave one away in an earlier exchange.)
Exchange 1 thousand for 10 hundreds: 9 thousands become 8 thousands, and 0 hundreds become 10 hundreds.
10 − 8 = 2 - Subtract the thousands. Now the next column to the left.(This digit is 8 now, not 9, because we exchanged from this column.)
8 − 5 = 3 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 8 910 113 411 1− 5 8 7 6 3 2 6 5
9,141 − 5,876 = 3,265
Check. Use the opposite (inverse) operation: 3,265 + 5,876 = 9,141. ✓
Estimate: 9,000 − 6,000 = 3,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. The bottom digit is always taken from the top digit. Do not turn it round: 3 − 7 is not 4. Exchange instead.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 7 0 0 7 − 2 3 4 9 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.7 ones is not enough to take away 9. We need to exchange.
The tens and hundreds have 0, so there is nothing to exchange from there. We start further to the left, at the thousands.
Exchange 1 thousand for 10 hundreds: 7 thousands become 6 thousands, and 0 hundreds become 10 hundreds.
Exchange 1 hundred for 10 tens: 10 hundreds become 9 hundreds, and 0 tens become 10 tens.
Exchange 1 ten for 10 ones: 10 tens become 9 tens, and 7 ones become 17 ones.
17 − 9 = 8 - Subtract the tens. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 4 = 5 - Subtract the hundreds. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 3 = 6 - Subtract the thousands. Now the next column to the left.(This digit is 6 now, not 7, because we exchanged from this column.)
6 − 2 = 4 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 6 79 09 017 7− 2 3 4 9 4 6 5 8
7,007 − 2,349 = 4,658
Check. Use the opposite (inverse) operation: 4,658 + 2,349 = 7,007. ✓
Estimate: 7,000 − 2,000 = 5,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. You cannot exchange from a 0. Look left for the first column that is not 0, then pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 4 2 0 5 − 1 3 6 8 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.5 ones is not enough to take away 8. We need to exchange.
The tens has 0, so there is nothing to exchange from there. We start further to the left, at the hundreds.
Exchange 1 hundred for 10 tens: 2 hundreds become 1 hundred, and 0 tens become 10 tens.
Exchange 1 ten for 10 ones: 10 tens become 9 tens, and 5 ones become 15 ones.
15 − 8 = 7 - Subtract the tens. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 6 = 3 - Exchange, then subtract the hundreds. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.1 hundred is not enough to take away 3. We need to exchange.
(There were 2 hundreds to start with, but we gave one away in an earlier exchange.)
Exchange 1 thousand for 10 hundreds: 4 thousands become 3 thousands, and 1 hundred become 11 hundreds.
11 − 3 = 8 - Subtract the thousands. Now the next column to the left.(This digit is 3 now, not 4, because we exchanged from this column.)
3 − 1 = 2 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 3 411 29 015 5− 1 3 6 8 2 8 3 7
4,205 − 1,368 = 2,837
Check. Use the opposite (inverse) operation: 2,837 + 1,368 = 4,205. ✓
Estimate: 4,000 − 1,000 = 3,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. You cannot exchange from a 0. Look left for the first column that is not 0, then pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 6 3 0 8 − 2 7 4 5 - Subtract the ones. Always start with the ones, on the right.8 − 5 = 3
- Exchange, then subtract the tens. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.0 tens is not enough to take away 4. We need to exchange.
Exchange 1 hundred for 10 tens: 3 hundreds become 2 hundreds, and 0 tens become 10 tens.
10 − 4 = 6 - Exchange, then subtract the hundreds. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.2 hundreds is not enough to take away 7. We need to exchange.
(There were 3 hundreds to start with, but we gave one away in an earlier exchange.)
Exchange 1 thousand for 10 hundreds: 6 thousands become 5 thousands, and 2 hundreds become 12 hundreds.
12 − 7 = 5 - Subtract the thousands. Now the next column to the left.(This digit is 5 now, not 6, because we exchanged from this column.)
5 − 2 = 3 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 5 612 310 08 − 2 7 4 5 3 5 6 3
6,308 − 2,745 = 3,563
Check. Use the opposite (inverse) operation: 3,563 + 2,745 = 6,308. ✓
Estimate: 6,000 − 3,000 = 3,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. The bottom digit is always taken from the top digit. Do not turn it round: 3 − 7 is not 4. Exchange instead.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 7 0 4 0 − 3 2 5 7 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.0 ones is not enough to take away 7. We need to exchange.
Exchange 1 ten for 10 ones: 4 tens become 3 tens, and 0 ones become 10 ones.
10 − 7 = 3 - Exchange, then subtract the tens. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.3 tens is not enough to take away 5. We need to exchange.
(There were 4 tens to start with, but we gave one away in an earlier exchange.)
The hundreds has 0, so there is nothing to exchange from there. We start further to the left, at the thousands.
Exchange 1 thousand for 10 hundreds: 7 thousands become 6 thousands, and 0 hundreds become 10 hundreds.
Exchange 1 hundred for 10 tens: 10 hundreds become 9 hundreds, and 3 tens become 13 tens.
13 − 5 = 8 - Subtract the hundreds. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 2 = 7 - Subtract the thousands. Now the next column to the left.(This digit is 6 now, not 7, because we exchanged from this column.)
6 − 3 = 3 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 6 79 013 410 0− 3 2 5 7 3 7 8 3
7,040 − 3,257 = 3,783
Check. Use the opposite (inverse) operation: 3,783 + 3,257 = 7,040. ✓
Estimate: 7,000 − 3,000 = 4,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. You cannot exchange from a 0. Look left for the first column that is not 0, then pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 8 1 0 6 − 4 3 1 9 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.6 ones is not enough to take away 9. We need to exchange.
The tens has 0, so there is nothing to exchange from there. We start further to the left, at the hundreds.
Exchange 1 hundred for 10 tens: 1 hundred become 0 hundreds, and 0 tens become 10 tens.
Exchange 1 ten for 10 ones: 10 tens become 9 tens, and 6 ones become 16 ones.
16 − 9 = 7 - Subtract the tens. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 1 = 8 - Exchange, then subtract the hundreds. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.0 hundreds is not enough to take away 3. We need to exchange.
(There were 1 hundreds to start with, but we gave one away in an earlier exchange.)
Exchange 1 thousand for 10 hundreds: 8 thousands become 7 thousands, and 0 hundreds become 10 hundreds.
10 − 3 = 7 - Subtract the thousands. Now the next column to the left.(This digit is 7 now, not 8, because we exchanged from this column.)
7 − 4 = 3 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 7 810 19 016 6− 4 3 1 9 3 7 8 7
8,106 − 4,319 = 3,787
Check. Use the opposite (inverse) operation: 3,787 + 4,319 = 8,106. ✓
Estimate: 8,000 − 4,000 = 4,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. You cannot exchange from a 0. Look left for the first column that is not 0, then pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 5 0 0 0 − 2 4 6 8 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.0 ones is not enough to take away 8. We need to exchange.
The tens and hundreds have 0, so there is nothing to exchange from there. We start further to the left, at the thousands.
Exchange 1 thousand for 10 hundreds: 5 thousands become 4 thousands, and 0 hundreds become 10 hundreds.
Exchange 1 hundred for 10 tens: 10 hundreds become 9 hundreds, and 0 tens become 10 tens.
Exchange 1 ten for 10 ones: 10 tens become 9 tens, and 0 ones become 10 ones.
10 − 8 = 2 - Subtract the tens. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 6 = 3 - Subtract the hundreds. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 4 = 5 - Subtract the thousands. Now the next column to the left.(This digit is 4 now, not 5, because we exchanged from this column.)
4 − 2 = 2 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 4 59 09 010 0− 2 4 6 8 2 5 3 2
5,000 − 2,468 = 2,532
Check. Use the opposite (inverse) operation: 2,532 + 2,468 = 5,000. ✓
Estimate: 5,000 − 2,000 = 3,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. You cannot exchange from a 0. Look left for the first column that is not 0, then pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 7 0 0 6 − 3 4 5 8 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.6 ones is not enough to take away 8. We need to exchange.
The tens and hundreds have 0, so there is nothing to exchange from there. We start further to the left, at the thousands.
Exchange 1 thousand for 10 hundreds: 7 thousands become 6 thousands, and 0 hundreds become 10 hundreds.
Exchange 1 hundred for 10 tens: 10 hundreds become 9 hundreds, and 0 tens become 10 tens.
Exchange 1 ten for 10 ones: 10 tens become 9 tens, and 6 ones become 16 ones.
16 − 8 = 8 - Subtract the tens. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 5 = 4 - Subtract the hundreds. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 4 = 5 - Subtract the thousands. Now the next column to the left.(This digit is 6 now, not 7, because we exchanged from this column.)
6 − 3 = 3 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 6 79 09 016 6− 3 4 5 8 3 5 4 8
7,006 − 3,458 = 3,548
Check. Use the opposite (inverse) operation: 3,548 + 3,458 = 7,006. ✓
Estimate: 7,000 − 3,000 = 4,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. You cannot exchange from a 0. Look left for the first column that is not 0, then pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 3 0 0 0 − 1 2 6 4 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.0 ones is not enough to take away 4. We need to exchange.
The tens and hundreds have 0, so there is nothing to exchange from there. We start further to the left, at the thousands.
Exchange 1 thousand for 10 hundreds: 3 thousands become 2 thousands, and 0 hundreds become 10 hundreds.
Exchange 1 hundred for 10 tens: 10 hundreds become 9 hundreds, and 0 tens become 10 tens.
Exchange 1 ten for 10 ones: 10 tens become 9 tens, and 0 ones become 10 ones.
10 − 4 = 6 - Subtract the tens. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 6 = 3 - Subtract the hundreds. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 2 = 7 - Subtract the thousands. Now the next column to the left.(This digit is 2 now, not 3, because we exchanged from this column.)
2 − 1 = 1 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 2 39 09 010 0− 1 2 6 4 1 7 3 6
3,000 − 1,264 = 1,736
Check. Use the opposite (inverse) operation: 1,736 + 1,264 = 3,000. ✓
Estimate: 3,000 − 1,000 = 2,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. You cannot exchange from a 0. Look left for the first column that is not 0, then pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 9 0 0 0 − 4 9 9 9 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.0 ones is not enough to take away 9. We need to exchange.
The tens and hundreds have 0, so there is nothing to exchange from there. We start further to the left, at the thousands.
Exchange 1 thousand for 10 hundreds: 9 thousands become 8 thousands, and 0 hundreds become 10 hundreds.
Exchange 1 hundred for 10 tens: 10 hundreds become 9 hundreds, and 0 tens become 10 tens.
Exchange 1 ten for 10 ones: 10 tens become 9 tens, and 0 ones become 10 ones.
10 − 9 = 1 - Subtract the tens. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 9 = 0 - Subtract the hundreds. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 9 = 0 - Subtract the thousands. Now the next column to the left.(This digit is 8 now, not 9, because we exchanged from this column.)
8 − 4 = 4 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 8 99 09 010 0− 4 9 9 9 4 0 0 1
9,000 − 4,999 = 4,001
Check. Use the opposite (inverse) operation: 4,001 + 4,999 = 9,000. ✓
Estimate: 9,000 − 5,000 = 4,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. You cannot exchange from a 0. Look left for the first column that is not 0, then pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 4 5 6 2 − 7 8 3 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.2 ones is not enough to take away 3. We need to exchange.
Exchange 1 ten for 10 ones: 6 tens become 5 tens, and 2 ones become 12 ones.
12 − 3 = 9 - Exchange, then subtract the tens. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.5 tens is not enough to take away 8. We need to exchange.
(There were 6 tens to start with, but we gave one away in an earlier exchange.)
Exchange 1 hundred for 10 tens: 5 hundreds become 4 hundreds, and 5 tens become 15 tens.
15 − 8 = 7 - Exchange, then subtract the hundreds. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.4 hundreds is not enough to take away 7. We need to exchange.
(There were 5 hundreds to start with, but we gave one away in an earlier exchange.)
Exchange 1 thousand for 10 hundreds: 4 thousands become 3 thousands, and 4 hundreds become 14 hundreds.
14 − 7 = 7 - Bring down the thousands digit. The bottom number has no digit in this column, so there is nothing to take away.(This digit is 3 now, not 4, because we exchanged from this column.)
Nothing to take away in this column, so the digit stays: 3. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 3 414 515 612 2− 7 8 3 3 7 7 9
4,562 − 783 = 3,779
Check. Use the opposite (inverse) operation: 3,779 + 783 = 4,562. ✓
Estimate: 4,600 − 800 = 3,800 (rounding to the nearest 100). It is close to the exact answer. ✓
Watch out. The bottom digit is always taken from the top digit. Do not turn it round: 3 − 7 is not 4. Exchange instead.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 3 2 0 5 − 4 6 8 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.5 ones is not enough to take away 8. We need to exchange.
The tens has 0, so there is nothing to exchange from there. We start further to the left, at the hundreds.
Exchange 1 hundred for 10 tens: 2 hundreds become 1 hundred, and 0 tens become 10 tens.
Exchange 1 ten for 10 ones: 10 tens become 9 tens, and 5 ones become 15 ones.
15 − 8 = 7 - Subtract the tens. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 6 = 3 - Exchange, then subtract the hundreds. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.1 hundred is not enough to take away 4. We need to exchange.
(There were 2 hundreds to start with, but we gave one away in an earlier exchange.)
Exchange 1 thousand for 10 hundreds: 3 thousands become 2 thousands, and 1 hundred become 11 hundreds.
11 − 4 = 7 - Bring down the thousands digit. The bottom number has no digit in this column, so there is nothing to take away.(This digit is 2 now, not 3, because we exchanged from this column.)
Nothing to take away in this column, so the digit stays: 2. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 2 311 29 015 5− 4 6 8 2 7 3 7
3,205 − 468 = 2,737
Check. Use the opposite (inverse) operation: 2,737 + 468 = 3,205. ✓
Estimate: 3,200 − 500 = 2,700 (rounding to the nearest 100). It is close to the exact answer. ✓
Watch out. You cannot exchange from a 0. Look left for the first column that is not 0, then pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 6 1 4 0 − 9 9 5 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.0 ones is not enough to take away 5. We need to exchange.
Exchange 1 ten for 10 ones: 4 tens become 3 tens, and 0 ones become 10 ones.
10 − 5 = 5 - Exchange, then subtract the tens. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.3 tens is not enough to take away 9. We need to exchange.
(There were 4 tens to start with, but we gave one away in an earlier exchange.)
Exchange 1 hundred for 10 tens: 1 hundred become 0 hundreds, and 3 tens become 13 tens.
13 − 9 = 4 - Exchange, then subtract the hundreds. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.0 hundreds is not enough to take away 9. We need to exchange.
(There were 1 hundreds to start with, but we gave one away in an earlier exchange.)
Exchange 1 thousand for 10 hundreds: 6 thousands become 5 thousands, and 0 hundreds become 10 hundreds.
10 − 9 = 1 - Bring down the thousands digit. The bottom number has no digit in this column, so there is nothing to take away.(This digit is 5 now, not 6, because we exchanged from this column.)
Nothing to take away in this column, so the digit stays: 5. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 5 610 113 410 0− 9 9 5 5 1 4 5
6,140 − 995 = 5,145
Check. Use the opposite (inverse) operation: 5,145 + 995 = 6,140. ✓
Estimate: 6,100 − 1,000 = 5,100 (rounding to the nearest 100). It is close to the exact answer. ✓
Watch out. The bottom digit is always taken from the top digit. Do not turn it round: 3 − 7 is not 4. Exchange instead.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 5 0 0 0 − 7 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.0 ones is not enough to take away 7. We need to exchange.
The tens and hundreds have 0, so there is nothing to exchange from there. We start further to the left, at the thousands.
Exchange 1 thousand for 10 hundreds: 5 thousands become 4 thousands, and 0 hundreds become 10 hundreds.
Exchange 1 hundred for 10 tens: 10 hundreds become 9 hundreds, and 0 tens become 10 tens.
Exchange 1 ten for 10 ones: 10 tens become 9 tens, and 0 ones become 10 ones.
10 − 7 = 3 - Bring down the tens digit. The bottom number has no digit in this column, so there is nothing to take away.(This digit is 9 now, not 0, because we exchanged from this column.)
Nothing to take away in this column, so the digit stays: 9. - Bring down the hundreds digit. The bottom number has no digit in this column, so there is nothing to take away.(This digit is 9 now, not 0, because we exchanged from this column.)
Nothing to take away in this column, so the digit stays: 9. - Bring down the thousands digit. The bottom number has no digit in this column, so there is nothing to take away.(This digit is 4 now, not 5, because we exchanged from this column.)
Nothing to take away in this column, so the digit stays: 4. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 4 59 09 010 0− 7 4 9 9 3
5,000 − 7 = 4,993
Check. Use the opposite (inverse) operation: 4,993 + 7 = 5,000. ✓
Estimate: 5,000 − 10 = 4,990 (rounding to the nearest 10). It is close to the exact answer. ✓
Watch out. You cannot exchange from a 0. Look left for the first column that is not 0, then pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 6 2 1 4 − 3 8 5 9 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.4 ones is not enough to take away 9. We need to exchange.
Exchange 1 ten for 10 ones: 1 ten become 0 tens, and 4 ones become 14 ones.
14 − 9 = 5 - Exchange, then subtract the tens. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.0 tens is not enough to take away 5. We need to exchange.
(There were 1 tens to start with, but we gave one away in an earlier exchange.)
Exchange 1 hundred for 10 tens: 2 hundreds become 1 hundred, and 0 tens become 10 tens.
10 − 5 = 5 - Exchange, then subtract the hundreds. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.1 hundred is not enough to take away 8. We need to exchange.
(There were 2 hundreds to start with, but we gave one away in an earlier exchange.)
Exchange 1 thousand for 10 hundreds: 6 thousands become 5 thousands, and 1 hundred become 11 hundreds.
11 − 8 = 3 - Subtract the thousands. Now the next column to the left.(This digit is 5 now, not 6, because we exchanged from this column.)
5 − 3 = 2 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 5 611 210 114 4− 3 8 5 9 2 3 5 5
6,214 − 3,859 = 2,355
Check. Use the opposite (inverse) operation: 2,355 + 3,859 = 6,214. ✓
Estimate: 6,000 − 4,000 = 2,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. The bottom digit is always taken from the top digit. Do not turn it round: 3 − 7 is not 4. Exchange instead.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 5 0 0 0 − 2 5 4 3 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.0 ones is not enough to take away 3. We need to exchange.
The tens and hundreds have 0, so there is nothing to exchange from there. We start further to the left, at the thousands.
Exchange 1 thousand for 10 hundreds: 5 thousands become 4 thousands, and 0 hundreds become 10 hundreds.
Exchange 1 hundred for 10 tens: 10 hundreds become 9 hundreds, and 0 tens become 10 tens.
Exchange 1 ten for 10 ones: 10 tens become 9 tens, and 0 ones become 10 ones.
10 − 3 = 7 - Subtract the tens. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 4 = 5 - Subtract the hundreds. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 5 = 4 - Subtract the thousands. Now the next column to the left.(This digit is 4 now, not 5, because we exchanged from this column.)
4 − 2 = 2 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 4 59 09 010 0− 2 5 4 3 2 4 5 7
5,000 − 2,543 = 2,457
Check. Use the opposite (inverse) operation: 2,457 + 2,543 = 5,000. ✓
Estimate: 5,000 − 3,000 = 2,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. You cannot exchange from a 0. Look left for the first column that is not 0, then pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.
- Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O 7 1 0 5 − 4 9 8 8 - Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.5 ones is not enough to take away 8. We need to exchange.
The tens has 0, so there is nothing to exchange from there. We start further to the left, at the hundreds.
Exchange 1 hundred for 10 tens: 1 hundred become 0 hundreds, and 0 tens become 10 tens.
Exchange 1 ten for 10 ones: 10 tens become 9 tens, and 5 ones become 15 ones.
15 − 8 = 7 - Subtract the tens. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 8 = 1 - Exchange, then subtract the hundreds. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.0 hundreds is not enough to take away 9. We need to exchange.
(There were 1 hundreds to start with, but we gave one away in an earlier exchange.)
Exchange 1 thousand for 10 hundreds: 7 thousands become 6 thousands, and 0 hundreds become 10 hundreds.
10 − 9 = 1 - Subtract the thousands. Now the next column to the left.(This digit is 6 now, not 7, because we exchanged from this column.)
6 − 4 = 2 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 6 710 19 015 5− 4 9 8 8 2 1 1 7
7,105 − 4,988 = 2,117
Check. Use the opposite (inverse) operation: 2,117 + 4,988 = 7,105. ✓
Estimate: 7,000 − 5,000 = 2,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. You cannot exchange from a 0. Look left for the first column that is not 0, then pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Method. Draw a bar model to see what is happening. Decide whether to add or subtract, then use a written method.
- Draw a bar model. A picture shows what we know and what we need to find.
- Choose the operation. We are finding what is left, or the difference, so we subtract.£8,400 − £5,675
- Work it out. Use the column method if the numbers are big.£8,400 − £5,675 = £2,725
Th H T O 7 813 49 010 0− 5 6 7 5 2 7 2 5 - Write the answer. £2,725
Check. Use the opposite operation: £2,725 + £5,675 = £8,400. ✓
Watch out. Read the question again at the end. Does your answer make sense, and does it answer what was asked?
Method. Draw a bar model to see what is happening. Decide whether to add or subtract, then use a written method.
- Draw a bar model. A picture shows what we know and what we need to find.
- Choose the operation. We are finding what is left, or the difference, so we subtract.3,000 km − 1,876 km
- Work it out. Use the column method if the numbers are big.3,000 km − 1,876 km = 1,124 km
Th H T O 2 39 09 010 0− 1 8 7 6 1 1 2 4 - Write the answer. 1,124 km
Check. Use the opposite operation: 1,124 km + 1,876 km = 3,000 km. ✓
Watch out. Read the question again at the end. Does your answer make sense, and does it answer what was asked?
Method. Draw a bar model to see what is happening. Decide whether to add or subtract, then use a written method.
- Draw a bar model. A picture shows what we know and what we need to find.
- Choose the operation. We are finding what is left, or the difference, so we subtract.6,000 − 2,468
- Work it out. Use the column method if the numbers are big.6,000 − 2,468 = 3,532
Th H T O 5 69 09 010 0− 2 4 6 8 3 5 3 2 - Write the answer. 3,532 books
Check. Use the opposite operation: 3,532 + 2,468 = 6,000. ✓
Watch out. Read the question again at the end. Does your answer make sense, and does it answer what was asked?
Method. Do the calculation again with the column method and compare it with Leo’s answer.
- Work out the correct answer. Use the column method carefully.
Th H T O 5 613 411 215 5− 2 7 8 8 3 6 3 7
6,425 − 2,788 = 3,637 - Compare with Leo’s answer. Leo wrote 4,363.3,637 is not 4,363, so Leo made a mistake.
- Find the mistake. When the top digit is smaller than the bottom digit, he took the small digit from the big one. That is the wrong way round. He needed to exchange.The ones, tens and hundreds columns should have used an exchange.
Check. Use the opposite operation: 3,637 + 2,788 = 6,425. ✓
Watch out. In subtraction the order matters. Never take the top digit from the bottom digit. Exchange instead.
Key words. A counter-example is one example that shows a rule is not always true.
Method. To show Dev is wrong, find one subtraction with a zero in the top number that does not need an exchange.
- Try a subtraction with a zero on top. We want the bottom digits to be small enough in every column.5,030 − 2,010
5,030 − 2,010 = 3,020Th H T O 5 0 3 0 − 2 0 1 0 3 0 2 0 - Check each column. An exchange is only needed when a top digit is smaller than the bottom digit.ones: 0 − 0 = 0 tens: 3 − 1 = 2 hundreds: 0 − 0 = 0 thousands: 5 − 2 = 3
No column needs an exchange. - Answer Dev. Dev is not always right. Sometimes a zero does need an exchange, as in 5,030 − 2,060, but not always.No. 5,030 − 2,010 = 3,020 has a 0 on top but needs no exchange.
Check. Check with addition: 3,020 + 2,010 = 5,030. ✓
Watch out. One example is enough to show that a rule that says “always” is wrong. This is called a counter-example.
Method. Look at the digits in each column. An exchange is needed when a top digit is smaller than the bottom digit.
- Compare the digits in each subtraction. Check ones, tens, hundreds and thousands.A: 4 ≥ 1, 7 ≥ 3, 5 ≥ 4, 6 ≥ 2 → no exchange
B: 6 < 9 → exchange
C: 0 < 5 → exchange
D: 3 < 6 → exchange - Choose the one with no exchanges. A
Check. Work out A: 4,143. Each column is just a simple subtraction. ✓
Watch out. Look at every column, not just the ones.
Key words. A pattern is something that repeats or follows a rule.
Method. Follow the rule carefully each time. Each step is a column subtraction.
- Do the rule once. Put the digits in order, biggest first for the top number and smallest first for the bottom number.Start with 1,002. Biggest: 2,100. Smallest: 12.
2,100 − 12 = 2,088Th H T O 2 0 19 010 0− 1 2 2 0 8 8 - Do the rule again with the new answer. Use the answer as the new starting number.Start with 2,088. Biggest: 8,820. Smallest: 288.
8,820 − 288 = 8,532Th H T O 8 7 811 210 0− 2 8 8 8 5 3 2
Start with 8,532. Biggest: 8,532. Smallest: 2,358.
8,532 − 2,358 = 6,174Th H T O 8 4 512 312 2− 2 3 5 8 6 1 7 4 - Keep going and look for a pattern. After 3 steps we reach 6,174. Do the rule once more:Start with 6,174. Biggest: 7,641. Smallest: 1,467.
7,641 − 1,467 = 6,174Th H T O 7 5 613 411 1− 1 4 6 7 6 1 7 4 - Say what you notice. The numbers go 1,002 → 2,088 → 8,532 → 6,174 and then stay at 6,174 for ever.
Check. Every four-digit number that has at least two different digits ends up at 6,174 if you keep doing this. It is called Kaprekar’s constant. ✓
Watch out. If the smallest number starts with 0 (like 0,468), it is just a three-digit number. Write 468.