Year 5: Column subtraction with bigger numbers
Part of the Year 5 column addition and subtraction chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Column subtraction with bigger numbers
In column subtraction the bigger number goes on top. It 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.
| TTh | Th | H | T | O | |
| 7 | 6 | 8 | 4 | 5 | |
| − | 3 | 2 | 6 | 1 | 3 |
| 4 | 4 | 2 | 3 | 2 |
Exchanging. Sometimes the top digit is smaller than the bottom digit, like 2 − 7. You cannot take 7 away from 2. So you exchange: swap 1 from the next column on the left for 10 in this column. The digit on the left goes down by 1 and this digit goes up by 10. This works in every column. 1 hundred thousand is 10 ten thousands, and 1 ten thousand is 10 thousands.
| TTh | Th | H | T | O | |
| 5 | 13 | 3 | 14 | 12 | |
| − | 2 | 8 | 1 | 7 | 6 |
| 3 | 5 | 2 | 7 | 6 |
Zeros are tricky. You cannot exchange from a 0, because there is nothing to swap. Go left to the first column that is not 0, and pass the exchange along one column at a time. In 500,000 − 237,894 the ones need help, but every column on the left is 0 until the hundred thousands. So 1 hundred thousand becomes 10 ten thousands, then 1 ten thousand becomes 10 thousands, and so on. Each 0 in the middle ends up as a 9.
| HTh | TTh | Th | H | T | O | |
| 4 | 9 | 9 | 9 | 9 | 10 | |
| − | 2 | 3 | 7 | 8 | 9 | 4 |
| 2 | 6 | 2 | 1 | 0 | 6 |
Different lengths. You can take a four-digit number from a six-digit number, like 462,310 − 5,874. Line the digits up on the right. Where the bottom number has no digit, there is nothing to take away. And 1,000,000 is a seven-digit number: 1,000,000 − 468,325 works exactly like the 500,000 example, with six zeros to pass along.
Key words. To exchange is to swap 1 of a bigger unit for 10 of the next smaller unit (some people call it borrowing). 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 work left: tens, hundreds, thousands, ten thousands and so on.
- 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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
TTh Th H T O 7 6 8 4 5 − 3 2 6 1 3 - Subtract the ones. Always start with the ones, on the right.5 − 3 = 2
- Subtract the tens. Now the next column to the left.4 − 1 = 3
- Subtract the hundreds. Now the next column to the left.8 − 6 = 2
- Subtract the thousands. Now the next column to the left.6 − 2 = 4
- Subtract the ten thousands. Now the next column to the left.7 − 3 = 4
- Read the answer. Check that the answer has a sensible number of digits, then write it.
TTh Th H T O 7 6 8 4 5 − 3 2 6 1 3 4 4 2 3 2
76,845 − 32,613 = 44,232
Check. Use the opposite (inverse) operation: 44,232 + 32,613 = 76,845. ✓
Estimate: 77,000 − 33,000 = 44,000 (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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
TTh Th H T O 6 3 4 5 2 − 2 8 1 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.2 ones is not enough to take away 6. We need to exchange.
Exchange 1 ten for 10 ones: 5 tens become 4 tens, and 2 ones become 12 ones.
12 − 6 = 6TTh Th H T O 6 3 4 4 512 2− 2 8 1 7 6 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.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: 4 hundreds become 3 hundreds, and 4 tens become 14 tens.
14 − 7 = 7TTh Th H T O 6 3 3 414 512 2− 2 8 1 7 6 7 6 - 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 = 2TTh Th H T O 6 3 3 414 512 2− 2 8 1 7 6 2 7 6 - Exchange, then subtract the thousands. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.3 thousands is not enough to take away 8. We need to exchange.
Exchange 1 ten thousand for 10 thousands: 6 ten thousands become 5 ten thousands, and 3 thousands become 13 thousands.
13 − 8 = 5TTh Th H T O 5 613 33 414 512 2− 2 8 1 7 6 5 2 7 6 - Subtract the ten thousands. Now the next column to the left.(This digit is 5 now, not 6, because we exchanged from this column.)
5 − 2 = 3TTh Th H T O 5 613 33 414 512 2− 2 8 1 7 6 3 5 2 7 6 - Read the answer. Check that the answer has a sensible number of digits, then write it.
TTh Th H T O 5 613 33 414 512 2− 2 8 1 7 6 3 5 2 7 6
63,452 − 28,176 = 35,276
Check. Use the opposite (inverse) operation: 35,276 + 28,176 = 63,452. ✓
Estimate: 63,000 − 28,000 = 35,000 (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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
HTh TTh Th H T O 7 0 4 8 2 6 − 3 5 8 9 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.6 ones is not enough to take away 7. We need to exchange.
Exchange 1 ten for 10 ones: 2 tens become 1 ten, and 6 ones become 16 ones.
16 − 7 = 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.1 ten is not enough to take away 4. 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: 8 hundreds become 7 hundreds, and 1 ten become 11 tens.
11 − 4 = 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.7 hundreds is not enough to take away 9. We need to exchange.
(There were 8 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 7 hundreds become 17 hundreds.
17 − 9 = 8 - Exchange, then subtract the thousands. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.3 thousands is not enough to take away 8. We need to exchange.
(There were 4 thousands to start with, but we gave one away in an earlier exchange.)
The ten thousands has 0, so there is nothing to exchange from there. We start further to the left, at the hundred thousands.
Exchange 1 hundred thousand for 10 ten thousands: 7 hundred thousands become 6 hundred thousands, and 0 ten thousands become 10 ten thousands.
Exchange 1 ten thousand for 10 thousands: 10 ten thousands become 9 ten thousands, and 3 thousands become 13 thousands.
13 − 8 = 5 - Subtract the ten thousands. 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 hundred 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 that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 6 79 013 417 811 216 6− 3 5 8 9 4 7 3 4 5 8 7 9
704,826 − 358,947 = 345,879
Check. Use the opposite (inverse) operation: 345,879 + 358,947 = 704,826. ✓
Estimate: 700,000 − 360,000 = 340,000 (rounding to the nearest 10,000). 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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
TTh Th H T O 8 0 0 0 3 − 2 4 5 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.3 ones is not enough to take away 7. We need to exchange.
The tens, hundreds and thousands have 0, so there is nothing to exchange from there. We start further to the left, at the ten thousands.
Exchange 1 ten thousand for 10 thousands: 8 ten thousands become 7 ten thousands, and 0 thousands become 10 thousands.
Exchange 1 thousand for 10 hundreds: 10 thousands become 9 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 = 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 − 5 = 4 - Subtract the thousands. 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 ten thousands. Now the next column to the left.(This digit is 7 now, not 8, because we exchanged from this column.)
7 − 2 = 5 - Read the answer. Check that the answer has a sensible number of digits, then write it.
TTh Th H T O 7 89 09 09 013 3− 2 4 5 6 7 5 5 4 3 6
80,003 − 24,567 = 55,436
Check. Use the opposite (inverse) operation: 55,436 + 24,567 = 80,003. ✓
Estimate: 80,000 − 25,000 = 55,000 (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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
HTh TTh Th H T O 5 0 0 0 0 0 − 2 3 7 8 9 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, hundreds, thousands and ten thousands have 0, so there is nothing to exchange from there. We start further to the left, at the hundred thousands.
Exchange 1 hundred thousand for 10 ten thousands: 5 hundred thousands become 4 hundred thousands, and 0 ten thousands become 10 ten thousands.
Exchange 1 ten thousand for 10 thousands: 10 ten thousands become 9 ten thousands, and 0 thousands become 10 thousands.
Exchange 1 thousand for 10 hundreds: 10 thousands become 9 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 = 6HTh TTh Th H T O 4 59 09 09 09 010 0− 2 3 7 8 9 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 − 9 = 0HTh TTh Th H T O 4 59 09 09 09 010 0− 2 3 7 8 9 4 0 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 = 1HTh TTh Th H T O 4 59 09 09 09 010 0− 2 3 7 8 9 4 1 0 6 - Subtract the thousands. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 7 = 2HTh TTh Th H T O 4 59 09 09 09 010 0− 2 3 7 8 9 4 2 1 0 6 - Subtract the ten thousands. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 3 = 6HTh TTh Th H T O 4 59 09 09 09 010 0− 2 3 7 8 9 4 6 2 1 0 6 - Subtract the hundred thousands. Now the next column to the left.(This digit is 4 now, not 5, because we exchanged from this column.)
4 − 2 = 2HTh TTh Th H T O 4 59 09 09 09 010 0− 2 3 7 8 9 4 2 6 2 1 0 6 - Read the answer. Check that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 4 59 09 09 09 010 0− 2 3 7 8 9 4 2 6 2 1 0 6
500,000 − 237,894 = 262,106
Check. Use the opposite (inverse) operation: 262,106 + 237,894 = 500,000. ✓
Estimate: 500,000 − 240,000 = 260,000 (rounding to the nearest 10,000). 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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on. The numbers have different lengths, so line them up on the right.
HTh TTh Th H T O 4 6 2 3 1 0 − 5 8 7 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.
Exchange 1 ten for 10 ones: 1 ten become 0 tens, and 0 ones become 10 ones.
10 − 4 = 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.0 tens is not enough to take away 7. 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: 3 hundreds become 2 hundreds, and 0 tens become 10 tens.
10 − 7 = 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.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: 2 thousands become 1 thousand, and 2 hundreds become 12 hundreds.
12 − 8 = 4 - Exchange, then subtract the thousands. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.1 thousand is not enough to take away 5. We need to exchange.
(There were 2 thousands to start with, but we gave one away in an earlier exchange.)
Exchange 1 ten thousand for 10 thousands: 6 ten thousands become 5 ten thousands, and 1 thousand become 11 thousands.
11 − 5 = 6 - Bring down the ten 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. - Bring down the hundred thousands digit. The bottom number has no digit in this column, so there is nothing to take away.Nothing to take away in this column, so the digit stays: 4.
- Read the answer. Check that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 4 5 611 212 310 110 0− 5 8 7 4 4 5 6 4 3 6
462,310 − 5,874 = 456,436
Check. Use the opposite (inverse) operation: 456,436 + 5,874 = 462,310. ✓
Estimate: 462,300 − 5,900 = 456,400 (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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on. The numbers have different lengths, so line them up on the right.
M HTh TTh Th H T O 1 0 0 0 0 0 0 − 4 6 8 3 2 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.
The tens, hundreds, thousands, ten thousands and hundred thousands have 0, so there is nothing to exchange from there. We start further to the left, at the millions.
Exchange 1 million for 10 hundred thousands: 1 million become 0 millions, and 0 hundred thousands become 10 hundred thousands.
Exchange 1 hundred thousand for 10 ten thousands: 10 hundred thousands become 9 hundred thousands, and 0 ten thousands become 10 ten thousands.
Exchange 1 ten thousand for 10 thousands: 10 ten thousands become 9 ten thousands, and 0 thousands become 10 thousands.
Exchange 1 thousand for 10 hundreds: 10 thousands become 9 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 − 5 = 5 - Subtract the tens. 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 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 9 now, not 0, because we exchanged from this column.)
9 − 8 = 1 - Subtract the ten thousands. 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 hundred thousands. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 4 = 5 - Bring down the millions digit. The bottom number has no digit in this column, so there is nothing to take away.(This digit is 0 now, not 1, because we exchanged from this column.)
Nothing to take away in this column, so the digit stays: 0.
We do not write a 0 at the front of an answer, so leave this space empty. - Read the answer. Check that the answer has a sensible number of digits, then write it.
M HTh TTh Th H T O 0 19 09 09 09 09 010 0− 4 6 8 3 2 5 5 3 1 6 7 5
1,000,000 − 468,325 = 531,675
Check. Use the opposite (inverse) operation: 531,675 + 468,325 = 1,000,000. ✓
Estimate: 1,000,000 − 470,000 = 530,000 (rounding to the nearest 10,000). 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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
TTh Th H T O 9 8 1 1 4 − 5 3 2 0 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.4 ones is not enough to take away 6. We need to exchange.
Exchange 1 ten for 10 ones: 1 ten become 0 tens, and 4 ones become 14 ones.
14 − 6 = 8 - Subtract the tens. Now the next column to the left.(This digit is 0 now, not 1, because we exchanged from this column.)
0 − 0 = 0 - 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 2. We need to exchange.
Exchange 1 thousand for 10 hundreds: 8 thousands become 7 thousands, and 1 hundred become 11 hundreds.
11 − 2 = 9 - Subtract the thousands. Now the next column to the left.(This digit is 7 now, not 8, because we exchanged from this column.)
7 − 3 = 4 - Subtract the ten thousands. Now the next column to the left.9 − 5 = 4
- Read the answer. Check that the answer has a sensible number of digits, then write it.
TTh Th H T O 9 7 811 10 114 4− 5 3 2 0 6 4 4 9 0 8
98,114 − 53,206 = 44,908
Check. Use the opposite (inverse) operation: 44,908 + 53,206 = 98,114. ✓
Estimate: 98,000 − 53,000 = 45,000 (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.
Watch out
Never turn the digits round! In 63,452 − 28,176 it is tempting to write 8 − 2 = 6 in the ones column because 2 − 6 is hard. That is wrong. 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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
TTh Th H T O 7 6 8 4 5 − 3 2 6 1 3 - Subtract the ones. Always start with the ones, on the right.5 − 3 = 2
- Subtract the tens. Now the next column to the left.4 − 1 = 3
- Subtract the hundreds. Now the next column to the left.8 − 6 = 2
- Subtract the thousands. Now the next column to the left.6 − 2 = 4
- Subtract the ten thousands. Now the next column to the left.7 − 3 = 4
- Read the answer. Check that the answer has a sensible number of digits, then write it.
TTh Th H T O 7 6 8 4 5 − 3 2 6 1 3 4 4 2 3 2
76,845 − 32,613 = 44,232
Check. Use the opposite (inverse) operation: 44,232 + 32,613 = 76,845. ✓
Estimate: 77,000 − 33,000 = 44,000 (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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
TTh Th H T O 9 8 7 6 5 − 5 4 3 2 1 - Subtract the ones. Always start with the ones, on the right.5 − 1 = 4
- Subtract the tens. Now the next column to the left.6 − 2 = 4
- Subtract the hundreds. Now the next column to the left.7 − 3 = 4
- Subtract the thousands. Now the next column to the left.8 − 4 = 4
- Subtract the ten thousands. Now the next column to the left.9 − 5 = 4
- Read the answer. Check that the answer has a sensible number of digits, then write it.
TTh Th H T O 9 8 7 6 5 − 5 4 3 2 1 4 4 4 4 4
98,765 − 54,321 = 44,444
Check. Use the opposite (inverse) operation: 44,444 + 54,321 = 98,765. ✓
Estimate: 99,000 − 54,000 = 45,000 (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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
HTh TTh Th H T O 8 4 5 2 9 0 − 5 2 3 1 7 0 - Subtract the ones. Always start with the ones, on the right.0 − 0 = 0
- Subtract the tens. Now the next column to the left.9 − 7 = 2
- Subtract the hundreds. Now the next column to the left.2 − 1 = 1
- Subtract the thousands. Now the next column to the left.5 − 3 = 2
- Subtract the ten thousands. Now the next column to the left.4 − 2 = 2
- Subtract the hundred thousands. Now the next column to the left.8 − 5 = 3
- Read the answer. Check that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 8 4 5 2 9 0 − 5 2 3 1 7 0 3 2 2 1 2 0
845,290 − 523,170 = 322,120
Check. Use the opposite (inverse) operation: 322,120 + 523,170 = 845,290. ✓
Estimate: 850,000 − 520,000 = 330,000 (rounding to the nearest 10,000). 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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
HTh TTh Th H T O 9 6 7 4 8 1 − 3 0 5 2 6 0 - Subtract the ones. Always start with the ones, on the right.1 − 0 = 1
- Subtract the tens. Now the next column to the left.8 − 6 = 2
- Subtract the hundreds. Now the next column to the left.4 − 2 = 2
- Subtract the thousands. Now the next column to the left.7 − 5 = 2
- Subtract the ten thousands. Now the next column to the left.6 − 0 = 6
- Subtract the hundred thousands. Now the next column to the left.9 − 3 = 6
- Read the answer. Check that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 9 6 7 4 8 1 − 3 0 5 2 6 0 6 6 2 2 2 1
967,481 − 305,260 = 662,221
Check. Use the opposite (inverse) operation: 662,221 + 305,260 = 967,481. ✓
Estimate: 970,000 − 310,000 = 660,000 (rounding to the nearest 10,000). 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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
TTh Th H T O 6 3 4 5 2 − 2 8 1 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.2 ones is not enough to take away 6. We need to exchange.
Exchange 1 ten for 10 ones: 5 tens become 4 tens, and 2 ones become 12 ones.
12 − 6 = 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.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: 4 hundreds become 3 hundreds, and 4 tens become 14 tens.
14 − 7 = 7 - 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 = 2 - Exchange, then subtract the thousands. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.3 thousands is not enough to take away 8. We need to exchange.
Exchange 1 ten thousand for 10 thousands: 6 ten thousands become 5 ten thousands, and 3 thousands become 13 thousands.
13 − 8 = 5 - Subtract the ten 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 that the answer has a sensible number of digits, then write it.
TTh Th H T O 5 613 33 414 512 2− 2 8 1 7 6 3 5 2 7 6
63,452 − 28,176 = 35,276
Check. Use the opposite (inverse) operation: 35,276 + 28,176 = 63,452. ✓
Estimate: 63,000 − 28,000 = 35,000 (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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
TTh Th H T O 8 4 2 7 0 − 5 1 8 3 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: 7 tens become 6 tens, and 0 ones become 10 ones.
10 − 5 = 5 - Subtract the tens. Now the next column to the left.(This digit is 6 now, not 7, because we exchanged from this column.)
6 − 3 = 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.2 hundreds is not enough to take away 8. We need to exchange.
Exchange 1 thousand for 10 hundreds: 4 thousands become 3 thousands, and 2 hundreds become 12 hundreds.
12 − 8 = 4 - 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 - Subtract the ten thousands. Now the next column to the left.8 − 5 = 3
- Read the answer. Check that the answer has a sensible number of digits, then write it.
TTh Th H T O 8 3 412 26 710 0− 5 1 8 3 5 3 2 4 3 5
84,270 − 51,835 = 32,435
Check. Use the opposite (inverse) operation: 32,435 + 51,835 = 84,270. ✓
Estimate: 84,000 − 52,000 = 32,000 (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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
HTh TTh Th H T O 5 9 2 3 1 6 − 2 3 8 4 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.6 ones is not enough to take away 9. We need to exchange.
Exchange 1 ten for 10 ones: 1 ten become 0 tens, and 6 ones become 16 ones.
16 − 9 = 7 - 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 7. 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: 3 hundreds become 2 hundreds, and 0 tens become 10 tens.
10 − 7 = 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.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: 2 thousands become 1 thousand, and 2 hundreds become 12 hundreds.
12 − 4 = 8 - Exchange, then subtract the thousands. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.1 thousand is not enough to take away 8. We need to exchange.
(There were 2 thousands to start with, but we gave one away in an earlier exchange.)
Exchange 1 ten thousand for 10 thousands: 9 ten thousands become 8 ten thousands, and 1 thousand become 11 thousands.
11 − 8 = 3 - Subtract the ten thousands. Now the next column to the left.(This digit is 8 now, not 9, because we exchanged from this column.)
8 − 3 = 5 - Subtract the hundred thousands. Now the next column to the left.5 − 2 = 3
- Read the answer. Check that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 5 8 911 212 310 116 6− 2 3 8 4 7 9 3 5 3 8 3 7
592,316 − 238,479 = 353,837
Check. Use the opposite (inverse) operation: 353,837 + 238,479 = 592,316. ✓
Estimate: 590,000 − 240,000 = 350,000 (rounding to the nearest 10,000). 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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
HTh TTh Th H T O 7 3 0 4 5 8 − 4 1 5 1 9 2 - Subtract the ones. Always start with the ones, on the right.8 − 2 = 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.5 tens is not enough to take away 9. We need to exchange.
Exchange 1 hundred for 10 tens: 4 hundreds become 3 hundreds, and 5 tens become 15 tens.
15 − 9 = 6 - 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 = 2 - Exchange, then subtract the thousands. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.0 thousands is not enough to take away 5. We need to exchange.
Exchange 1 ten thousand for 10 thousands: 3 ten thousands become 2 ten thousands, and 0 thousands become 10 thousands.
10 − 5 = 5 - Subtract the ten thousands. 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 hundred thousands. Now the next column to the left.7 − 4 = 3
- Read the answer. Check that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 7 2 310 03 415 58 − 4 1 5 1 9 2 3 1 5 2 6 6
730,458 − 415,192 = 315,266
Check. Use the opposite (inverse) operation: 315,266 + 415,192 = 730,458. ✓
Estimate: 730,000 − 420,000 = 310,000 (rounding to the nearest 10,000). 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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
TTh Th H T O 5 2 3 4 1 − 2 7 6 8 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.1 one is not enough to take away 5. We need to exchange.
Exchange 1 ten for 10 ones: 4 tens become 3 tens, and 1 one become 11 ones.
11 − 5 = 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.3 tens is not enough to take away 8. 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 − 8 = 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.2 hundreds is not enough to take away 6. 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: 2 thousands become 1 thousand, and 2 hundreds become 12 hundreds.
12 − 6 = 6 - Exchange, then subtract the thousands. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.1 thousand is not enough to take away 7. We need to exchange.
(There were 2 thousands to start with, but we gave one away in an earlier exchange.)
Exchange 1 ten thousand for 10 thousands: 5 ten thousands become 4 ten thousands, and 1 thousand become 11 thousands.
11 − 7 = 4 - Subtract the ten 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 that the answer has a sensible number of digits, then write it.
TTh Th H T O 4 511 212 313 411 1− 2 7 6 8 5 2 4 6 5 6
52,341 − 27,685 = 24,656
Check. Use the opposite (inverse) operation: 24,656 + 27,685 = 52,341. ✓
Estimate: 52,000 − 28,000 = 24,000 (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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
HTh TTh Th H T O 8 3 6 2 5 2 − 4 7 8 9 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.2 ones is not enough to take away 8. We need to exchange.
Exchange 1 ten for 10 ones: 5 tens become 4 tens, and 2 ones become 12 ones.
12 − 8 = 4 - 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 6. 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: 2 hundreds become 1 hundred, and 4 tens become 14 tens.
14 − 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.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 - Exchange, then subtract the thousands. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.5 thousands is not enough to take away 8. We need to exchange.
(There were 6 thousands to start with, but we gave one away in an earlier exchange.)
Exchange 1 ten thousand for 10 thousands: 3 ten thousands become 2 ten thousands, and 5 thousands become 15 thousands.
15 − 8 = 7 - Exchange, then subtract the ten thousands. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.2 ten thousands is not enough to take away 7. We need to exchange.
(There were 3 ten thousands to start with, but we gave one away in an earlier exchange.)
Exchange 1 hundred thousand for 10 ten thousands: 8 hundred thousands become 7 hundred thousands, and 2 ten thousands become 12 ten thousands.
12 − 7 = 5 - Subtract the hundred 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 that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 7 812 315 611 214 512 2− 4 7 8 9 6 8 3 5 7 2 8 4
836,252 − 478,968 = 357,284
Check. Use the opposite (inverse) operation: 357,284 + 478,968 = 836,252. ✓
Estimate: 840,000 − 480,000 = 360,000 (rounding to the nearest 10,000). 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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
HTh TTh Th H T O 7 0 0 8 1 2 − 3 5 4 6 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.2 ones is not enough to take away 9. We need to exchange.
Exchange 1 ten for 10 ones: 1 ten become 0 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.0 tens is not enough to take away 9. 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: 8 hundreds become 7 hundreds, and 0 tens become 10 tens.
10 − 9 = 1 - Subtract the hundreds. 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 thousands. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.0 thousands is not enough to take away 4. We need to exchange.
The ten thousands has 0, so there is nothing to exchange from there. We start further to the left, at the hundred thousands.
Exchange 1 hundred thousand for 10 ten thousands: 7 hundred thousands become 6 hundred thousands, and 0 ten thousands become 10 ten thousands.
Exchange 1 ten thousand for 10 thousands: 10 ten thousands become 9 ten thousands, and 0 thousands become 10 thousands.
10 − 4 = 6 - Subtract the ten thousands. 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 hundred 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 that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 6 79 010 07 810 112 2− 3 5 4 6 9 9 3 4 6 1 1 3
700,812 − 354,699 = 346,113
Check. Use the opposite (inverse) operation: 346,113 + 354,699 = 700,812. ✓
Estimate: 700,000 − 350,000 = 350,000 (rounding to the nearest 10,000). 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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
HTh TTh Th H T O 9 1 3 4 2 7 − 5 6 8 7 3 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.
Exchange 1 ten for 10 ones: 2 tens become 1 ten, and 7 ones become 17 ones.
17 − 9 = 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 3. 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: 4 hundreds become 3 hundreds, and 1 ten become 11 tens.
11 − 3 = 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.3 hundreds is not enough to take away 7. We need to exchange.
(There were 4 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 3 hundreds become 13 hundreds.
13 − 7 = 6 - Exchange, then subtract the thousands. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.2 thousands is not enough to take away 8. We need to exchange.
(There were 3 thousands to start with, but we gave one away in an earlier exchange.)
Exchange 1 ten thousand for 10 thousands: 1 ten thousand become 0 ten thousands, and 2 thousands become 12 thousands.
12 − 8 = 4 - Exchange, then subtract the ten thousands. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.0 ten thousands is not enough to take away 6. We need to exchange.
(There were 1 ten thousands to start with, but we gave one away in an earlier exchange.)
Exchange 1 hundred thousand for 10 ten thousands: 9 hundred thousands become 8 hundred thousands, and 0 ten thousands become 10 ten thousands.
10 − 6 = 4 - Subtract the hundred 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 that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 8 910 112 313 411 217 7− 5 6 8 7 3 9 3 4 4 6 8 8
913,427 − 568,739 = 344,688
Check. Use the opposite (inverse) operation: 344,688 + 568,739 = 913,427. ✓
Estimate: 910,000 − 570,000 = 340,000 (rounding to the nearest 10,000). 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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
TTh Th H T O 3 0 2 0 5 − 1 4 7 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 7. We need to exchange.
(There were 2 hundreds to start with, but we gave one away in an earlier exchange.)
The thousands has 0, so there is nothing to exchange from there. We start further to the left, at the ten thousands.
Exchange 1 ten thousand for 10 thousands: 3 ten thousands become 2 ten thousands, and 0 thousands become 10 thousands.
Exchange 1 thousand for 10 hundreds: 10 thousands become 9 thousands, and 1 hundred become 11 hundreds.
11 − 7 = 4 - Subtract the thousands. 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 ten 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 that the answer has a sensible number of digits, then write it.
TTh Th H T O 2 39 011 29 015 5− 1 4 7 6 8 1 5 4 3 7
30,205 − 14,768 = 15,437
Check. Use the opposite (inverse) operation: 15,437 + 14,768 = 30,205. ✓
Estimate: 30,000 − 15,000 = 15,000 (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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
TTh Th H T O 8 0 0 0 3 − 2 4 5 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.3 ones is not enough to take away 7. We need to exchange.
The tens, hundreds and thousands have 0, so there is nothing to exchange from there. We start further to the left, at the ten thousands.
Exchange 1 ten thousand for 10 thousands: 8 ten thousands become 7 ten thousands, and 0 thousands become 10 thousands.
Exchange 1 thousand for 10 hundreds: 10 thousands become 9 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 = 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 − 5 = 4 - Subtract the thousands. 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 ten thousands. Now the next column to the left.(This digit is 7 now, not 8, because we exchanged from this column.)
7 − 2 = 5 - Read the answer. Check that the answer has a sensible number of digits, then write it.
TTh Th H T O 7 89 09 09 013 3− 2 4 5 6 7 5 5 4 3 6
80,003 − 24,567 = 55,436
Check. Use the opposite (inverse) operation: 55,436 + 24,567 = 80,003. ✓
Estimate: 80,000 − 25,000 = 55,000 (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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
HTh TTh Th H T O 6 0 4 0 3 0 − 2 5 8 9 4 1 - 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 1. We need to exchange.
Exchange 1 ten for 10 ones: 3 tens become 2 tens, and 0 ones become 10 ones.
10 − 1 = 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.2 tens is not enough to take away 4. We need to exchange.
(There were 3 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: 4 thousands become 3 thousands, and 0 hundreds become 10 hundreds.
Exchange 1 hundred for 10 tens: 10 hundreds become 9 hundreds, and 2 tens become 12 tens.
12 − 4 = 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 − 9 = 0 - Exchange, then subtract the thousands. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.3 thousands is not enough to take away 8. We need to exchange.
(There were 4 thousands to start with, but we gave one away in an earlier exchange.)
The ten thousands has 0, so there is nothing to exchange from there. We start further to the left, at the hundred thousands.
Exchange 1 hundred thousand for 10 ten thousands: 6 hundred thousands become 5 hundred thousands, and 0 ten thousands become 10 ten thousands.
Exchange 1 ten thousand for 10 thousands: 10 ten thousands become 9 ten thousands, and 3 thousands become 13 thousands.
13 − 8 = 5 - Subtract the ten thousands. 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 hundred 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 that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 5 69 013 49 012 310 0− 2 5 8 9 4 1 3 4 5 0 8 9
604,030 − 258,941 = 345,089
Check. Use the opposite (inverse) operation: 345,089 + 258,941 = 604,030. ✓
Estimate: 600,000 − 260,000 = 340,000 (rounding to the nearest 10,000). 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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
HTh TTh Th H T O 9 0 0 0 0 7 − 1 2 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.7 ones is not enough to take away 8. We need to exchange.
The tens, hundreds, thousands and ten thousands have 0, so there is nothing to exchange from there. We start further to the left, at the hundred thousands.
Exchange 1 hundred thousand for 10 ten thousands: 9 hundred thousands become 8 hundred thousands, and 0 ten thousands become 10 ten thousands.
Exchange 1 ten thousand for 10 thousands: 10 ten thousands become 9 ten thousands, and 0 thousands become 10 thousands.
Exchange 1 thousand for 10 hundreds: 10 thousands become 9 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 − 8 = 9 - 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 9 now, not 0, because we exchanged from this column.)
9 − 3 = 6 - Subtract the ten thousands. 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 hundred thousands. Now the next column to the left.(This digit is 8 now, not 9, because we exchanged from this column.)
8 − 1 = 7 - Read the answer. Check that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 8 99 09 09 09 017 7− 1 2 3 4 5 8 7 7 6 5 4 9
900,007 − 123,458 = 776,549
Check. Use the opposite (inverse) operation: 776,549 + 123,458 = 900,007. ✓
Estimate: 900,000 − 120,000 = 780,000 (rounding to the nearest 10,000). 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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
TTh Th H T O 5 0 0 0 0 − 2 3 7 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, hundreds and thousands have 0, so there is nothing to exchange from there. We start further to the left, at the ten thousands.
Exchange 1 ten thousand for 10 thousands: 5 ten thousands become 4 ten thousands, and 0 thousands become 10 thousands.
Exchange 1 thousand for 10 hundreds: 10 thousands become 9 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 − 7 = 2 - Subtract the thousands. 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 ten 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 that the answer has a sensible number of digits, then write it.
TTh Th H T O 4 59 09 09 010 0− 2 3 7 6 4 2 6 2 3 6
50,000 − 23,764 = 26,236
Check. Use the opposite (inverse) operation: 26,236 + 23,764 = 50,000. ✓
Estimate: 50,000 − 24,000 = 26,000 (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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
HTh TTh Th H T O 3 0 0 0 0 0 − 1 2 4 5 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, hundreds, thousands and ten thousands have 0, so there is nothing to exchange from there. We start further to the left, at the hundred thousands.
Exchange 1 hundred thousand for 10 ten thousands: 3 hundred thousands become 2 hundred thousands, and 0 ten thousands become 10 ten thousands.
Exchange 1 ten thousand for 10 thousands: 10 ten thousands become 9 ten thousands, and 0 thousands become 10 thousands.
Exchange 1 thousand for 10 hundreds: 10 thousands become 9 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 − 5 = 4 - Subtract the thousands. 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 ten thousands. 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 hundred 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 that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 2 39 09 09 09 010 0− 1 2 4 5 6 8 1 7 5 4 3 2
300,000 − 124,568 = 175,432
Check. Use the opposite (inverse) operation: 175,432 + 124,568 = 300,000. ✓
Estimate: 300,000 − 120,000 = 180,000 (rounding to the nearest 10,000). 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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
HTh TTh Th H T O 7 0 0 0 0 0 − 3 6 5 8 2 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, hundreds, thousands and ten thousands have 0, so there is nothing to exchange from there. We start further to the left, at the hundred thousands.
Exchange 1 hundred thousand for 10 ten thousands: 7 hundred thousands become 6 hundred thousands, and 0 ten thousands become 10 ten thousands.
Exchange 1 ten thousand for 10 thousands: 10 ten thousands become 9 ten thousands, and 0 thousands become 10 thousands.
Exchange 1 thousand for 10 hundreds: 10 thousands become 9 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 − 2 = 7 - 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 = 1 - Subtract the thousands. 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 ten thousands. 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 hundred 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 that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 6 79 09 09 09 010 0− 3 6 5 8 2 9 3 3 4 1 7 1
700,000 − 365,829 = 334,171
Check. Use the opposite (inverse) operation: 334,171 + 365,829 = 700,000. ✓
Estimate: 700,000 − 370,000 = 330,000 (rounding to the nearest 10,000). 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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on. The numbers have different lengths, so line them up on the right.
M HTh TTh Th H T O 1 0 0 0 0 0 0 − 2 4 5 6 1 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, hundreds, thousands, ten thousands and hundred thousands have 0, so there is nothing to exchange from there. We start further to the left, at the millions.
Exchange 1 million for 10 hundred thousands: 1 million become 0 millions, and 0 hundred thousands become 10 hundred thousands.
Exchange 1 hundred thousand for 10 ten thousands: 10 hundred thousands become 9 hundred thousands, and 0 ten thousands become 10 ten thousands.
Exchange 1 ten thousand for 10 thousands: 10 ten thousands become 9 ten thousands, and 0 thousands become 10 thousands.
Exchange 1 thousand for 10 hundreds: 10 thousands become 9 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 - 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 - Subtract the hundreds. 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 thousands. 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 ten thousands. 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 hundred thousands. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 2 = 7 - Bring down the millions digit. The bottom number has no digit in this column, so there is nothing to take away.(This digit is 0 now, not 1, because we exchanged from this column.)
Nothing to take away in this column, so the digit stays: 0.
We do not write a 0 at the front of an answer, so leave this space empty. - Read the answer. Check that the answer has a sensible number of digits, then write it.
M HTh TTh Th H T O 0 19 09 09 09 09 010 0− 2 4 5 6 1 7 7 5 4 3 8 3
1,000,000 − 245,617 = 754,383
Check. Use the opposite (inverse) operation: 754,383 + 245,617 = 1,000,000. ✓
Estimate: 1,000,000 − 250,000 = 750,000 (rounding to the nearest 10,000). 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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on. The numbers have different lengths, so line them up on the right.
TTh Th H T O 4 6 2 3 1 − 5 8 7 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.1 one is not enough to take away 4. We need to exchange.
Exchange 1 ten for 10 ones: 3 tens become 2 tens, and 1 one become 11 ones.
11 − 4 = 7 - 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 7. 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 − 7 = 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 − 5 = 0 - Bring down the ten thousands digit. The bottom number has no digit in this column, so there is nothing to take away.Nothing to take away in this column, so the digit stays: 4.
- Read the answer. Check that the answer has a sensible number of digits, then write it.
TTh Th H T O 4 5 611 212 311 1− 5 8 7 4 4 0 3 5 7
46,231 − 5,874 = 40,357
Check. Use the opposite (inverse) operation: 40,357 + 5,874 = 46,231. ✓
Estimate: 46,200 − 5,900 = 40,300 (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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on. The numbers have different lengths, so line them up on the right.
HTh TTh Th H T O 4 6 2 3 1 0 − 5 8 7 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.
Exchange 1 ten for 10 ones: 1 ten become 0 tens, and 0 ones become 10 ones.
10 − 4 = 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.0 tens is not enough to take away 7. 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: 3 hundreds become 2 hundreds, and 0 tens become 10 tens.
10 − 7 = 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.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: 2 thousands become 1 thousand, and 2 hundreds become 12 hundreds.
12 − 8 = 4 - Exchange, then subtract the thousands. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.1 thousand is not enough to take away 5. We need to exchange.
(There were 2 thousands to start with, but we gave one away in an earlier exchange.)
Exchange 1 ten thousand for 10 thousands: 6 ten thousands become 5 ten thousands, and 1 thousand become 11 thousands.
11 − 5 = 6 - Bring down the ten 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. - Bring down the hundred thousands digit. The bottom number has no digit in this column, so there is nothing to take away.Nothing to take away in this column, so the digit stays: 4.
- Read the answer. Check that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 4 5 611 212 310 110 0− 5 8 7 4 4 5 6 4 3 6
462,310 − 5,874 = 456,436
Check. Use the opposite (inverse) operation: 456,436 + 5,874 = 462,310. ✓
Estimate: 462,300 − 5,900 = 456,400 (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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on. The numbers have different lengths, so line them up on the right.
HTh TTh Th H T O 3 0 5 2 0 0 − 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 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 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 - Bring down the hundreds digit. The bottom number has no digit in this column, so there is nothing to take away.(This digit is 1 now, not 2, because we exchanged from this column.)
Nothing to take away in this column, so the digit stays: 1. - Bring down the thousands digit. The bottom number has no digit in this column, so there is nothing to take away.Nothing to take away in this column, so the digit stays: 5.
- Bring down the ten thousands digit. The bottom number has no digit in this column, so there is nothing to take away.Nothing to take away in this column, so the digit stays: 0.
- Bring down the hundred thousands digit. The bottom number has no digit in this column, so there is nothing to take away.Nothing to take away in this column, so the digit stays: 3.
- Read the answer. Check that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 3 0 5 1 29 010 0− 6 8 3 0 5 1 3 2
305,200 − 68 = 305,132
Check. Use the opposite (inverse) operation: 305,132 + 68 = 305,200. ✓
Estimate: 305,200 − 70 = 305,130 (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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on. The numbers have different lengths, so line them up on the right.
HTh TTh Th H T O 8 0 0 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, hundreds, thousands and ten thousands have 0, so there is nothing to exchange from there. We start further to the left, at the hundred thousands.
Exchange 1 hundred thousand for 10 ten thousands: 8 hundred thousands become 7 hundred thousands, and 0 ten thousands become 10 ten thousands.
Exchange 1 ten thousand for 10 thousands: 10 ten thousands become 9 ten thousands, and 0 thousands become 10 thousands.
Exchange 1 thousand for 10 hundreds: 10 thousands become 9 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 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 ten thousands 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 hundred thousands digit. The bottom number has no digit in this column, so there is nothing to take away.(This digit is 7 now, not 8, because we exchanged from this column.)
Nothing to take away in this column, so the digit stays: 7. - Read the answer. Check that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 7 89 09 09 09 010 0− 7 7 9 9 9 9 3
800,000 − 7 = 799,993
Check. Use the opposite (inverse) operation: 799,993 + 7 = 800,000. ✓
Estimate: 800,000 − 10 = 799,990 (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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
TTh Th H T O 6 2 1 4 0 − 3 8 9 7 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 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 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: 2 thousands become 1 thousand, and 0 hundreds become 10 hundreds.
10 − 9 = 1 - Exchange, then subtract the thousands. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.1 thousand is not enough to take away 8. We need to exchange.
(There were 2 thousands to start with, but we gave one away in an earlier exchange.)
Exchange 1 ten thousand for 10 thousands: 6 ten thousands become 5 ten thousands, and 1 thousand become 11 thousands.
11 − 8 = 3 - Subtract the ten 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 that the answer has a sensible number of digits, then write it.
TTh Th H T O 5 611 210 113 410 0− 3 8 9 7 5 2 3 1 6 5
62,140 − 38,975 = 23,165
Check. Use the opposite (inverse) operation: 23,165 + 38,975 = 62,140. ✓
Estimate: 62,000 − 39,000 = 23,000 (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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
HTh TTh Th H T O 6 0 0 0 0 0 − 2 4 5 0 0 0 - Subtract the ones. Always start with the ones, on the right.0 − 0 = 0
- Subtract the tens. Now the next column to the left.0 − 0 = 0
- Subtract the hundreds. Now the next column to the left.0 − 0 = 0
- Exchange, then subtract the thousands. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.0 thousands is not enough to take away 5. We need to exchange.
The ten thousands has 0, so there is nothing to exchange from there. We start further to the left, at the hundred thousands.
Exchange 1 hundred thousand for 10 ten thousands: 6 hundred thousands become 5 hundred thousands, and 0 ten thousands become 10 ten thousands.
Exchange 1 ten thousand for 10 thousands: 10 ten thousands become 9 ten thousands, and 0 thousands become 10 thousands.
10 − 5 = 5 - Subtract the ten thousands. 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 hundred 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 that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 5 69 010 00 0 0 − 2 4 5 0 0 0 3 5 5 0 0 0
600,000 − 245,000 = 355,000
Check. Use the opposite (inverse) operation: 355,000 + 245,000 = 600,000. ✓
Estimate: 600,000 − 250,000 = 350,000 (rounding to the nearest 10,000). 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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on. The numbers have different lengths, so line them up on the right.
HTh TTh Th H T O 1 5 0 3 0 0 − 7 8 6 5 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 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 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 − 5 = 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.2 hundreds is not enough to take away 6. We need to exchange.
(There were 3 hundreds to start with, but we gave one away in an earlier exchange.)
The thousands has 0, so there is nothing to exchange from there. We start further to the left, at the ten thousands.
Exchange 1 ten thousand for 10 thousands: 5 ten thousands become 4 ten thousands, and 0 thousands become 10 thousands.
Exchange 1 thousand for 10 hundreds: 10 thousands become 9 thousands, and 2 hundreds become 12 hundreds.
12 − 6 = 6 - Subtract the thousands. 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 ten thousands. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.4 ten thousands is not enough to take away 7. We need to exchange.
(There were 5 ten thousands to start with, but we gave one away in an earlier exchange.)
Exchange 1 hundred thousand for 10 ten thousands: 1 hundred thousand become 0 hundred thousands, and 4 ten thousands become 14 ten thousands.
14 − 7 = 7 - Bring down the hundred thousands digit. The bottom number has no digit in this column, so there is nothing to take away.(This digit is 0 now, not 1, because we exchanged from this column.)
Nothing to take away in this column, so the digit stays: 0.
We do not write a 0 at the front of an answer, so leave this space empty. - Read the answer. Check that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 0 114 59 012 39 010 0− 7 8 6 5 4 7 1 6 4 6
150,300 − 78,654 = 71,646
Check. Use the opposite (inverse) operation: 71,646 + 78,654 = 150,300. ✓
Estimate: 150,000 − 79,000 = 71,000 (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. A comparison bar model shows two amounts side by side. The difference is how much longer one bar is than the other.
Method. Draw a comparison bar model. The longer bar is the bigger amount. The dashed part is the difference. Then decide whether to add or subtract.
- Draw a comparison bar model. The two bars let us see which amount is bigger and what the difference is.
- Choose the operation. We want the difference between the two amounts, so we take the smaller from the bigger.87,450 − 59,230
- Work it out. Use the column method because the numbers are big.87,450 − 59,230 = 28,220
TTh Th H T O 7 817 74 5 0 − 5 9 2 3 0 2 8 2 2 0 - Write the answer. 28,220 people
Check. Use the opposite operation: 59,230 + 28,220 = 87,450. ✓
Watch out. “More than” does not always mean add. Draw the bars first, then think about which bar you are finding.
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 know the whole distance and one part, and want the other part, so we subtract.250,000 km − 138,475 km
- Work it out. Use the column method because the numbers are big.250,000 km − 138,475 km = 111,525 km
HTh TTh Th H T O 2 4 59 09 09 010 0− 1 3 8 4 7 5 1 1 1 5 2 5 - Write the answer. 111,525 km
Check. Use the opposite operation: 111,525 km + 138,475 km = 250,000 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 know the whole (all the tickets) and one part (the tickets sold), so we subtract.120,000 − 47,685
- Work it out. Use the column method because the numbers are big.120,000 − 47,685 = 72,315
HTh TTh Th H T O 0 111 29 09 09 010 0− 4 7 6 8 5 7 2 3 1 5 - Write the answer. 72,315 tickets
Check. Use the opposite operation: 72,315 + 47,685 = 120,000. ✓
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.
TTh Th H T O 5 69 013 49 012 2− 2 8 9 7 5 3 1 4 2 7
60,402 − 28,975 = 31,427 - Compare with Leo’s answer. Leo wrote 48,573.31,427 is not 48,573, 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 and hundreds columns should have used an exchange.
Check. Use the opposite operation: 31,427 + 28,975 = 60,402. ✓
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. Work out both subtractions. Look for 9s in each answer.
- Work out 500,000 − 1. The ones column needs an exchange, and the exchange passes through every zero.
HTh TTh Th H T O 4 59 09 09 09 010 0− 1 4 9 9 9 9 9
499,999: the 9s are the zeros we passed. - Work out 500,000 − 100,000. Here the bottom digit is only in the hundred thousands column, which is 5 − 1. There is nothing to exchange.
HTh TTh Th H T O 5 0 0 0 0 0 − 1 0 0 0 0 0 4 0 0 0 0 0
400,000: no 9s. - Answer Dev. The 9s only appear when we have to exchange across the zeros. They do not always appear.No. 499,999 has 9s but 400,000 does not.
Check. 499,999 + 1 = 500,000 ✓ and 400,000 + 100,000 = 500,000. ✓
Watch out. One example that does not fit is enough to show that “always” is wrong. It is called a counter-example.
Method. Try some examples. Look for one where the answer has five digits and one where it does not.
- Try 900,000 − 10,000. The six-digit number is big and the five-digit number is small.
HTh TTh Th H T O 8 910 00 0 0 0 − 1 0 0 0 0 8 9 0 0 0 0
890,000 has 6 digits. - Try 100,000 − 99,995. The six-digit number is the smallest possible and the five-digit number is nearly as big.
HTh TTh Th H T O 0 19 09 09 09 010 0− 9 9 9 9 5 5
5 has 1 digit. - Decide. The answer can have six digits or fewer.Sometimes (it could also be exactly 5 digits, such as 130,000 − 50,000 = 80,000)
Check. 130,000 − 50,000 = 80,000, which has 5 digits, so the answer really can be 5 digits. ✓
Watch out. “Never” and “always” need a rule that works for every example. Look for ones that break the rule.
Method. Work out each subtraction with the column method and look for a pattern in the three answers.
- Reverse each number and subtract. Take the reversed number (the smaller one) away from the number we started with.852 − 258 = 594
H T O 7 814 512 2− 2 5 8 5 9 4
731 − 137 = 594H T O 6 712 311 1− 1 3 7 5 9 4
964 − 469 = 495H T O 8 915 614 4− 4 6 9 4 9 5 - Look at the answers. The answers are 594, 594 and 495.852 − 258 = 594
731 − 137 = 594
964 − 469 = 495 - Say what you notice. Each middle digit is 9. In 594, 5 + 4 = 9. In 495, 4 + 5 = 9.The middle digit is always 9, and the first and last digits add up to 9.
Check. All the answers are in the 99 times table: 594 = 6 × 99 and 495 = 5 × 99. A computer check of every number that fits the rules finds the same pattern every time. ✓
Watch out. Check the rule works with another number of your own, such as 641 − 146 = 495 (4 + 5 = 9).