Step-by-step Maths Level 5: Subtracting in columns, with exchange
Part of the Step-by-step Maths Level 5 adding and subtracting whole numbers to a million chapter. Chapter overview · whole chapter on one page
Subtracting in columns, with exchange
When the digit on top is smaller than the digit below, exchange 1 from the column on the left. That 1 is worth 10 in the column you are working in.
If the column on the left is 0, exchange across it. Each zero becomes a 9 as you pass it, and the next digit that is not zero gives 1.
Key ideas
- Exchange when the top digit is smaller.
- Exchange across zeros: a zero becomes 9 as you pass it.
- Work from the right, one column at a time.
Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.
- Subtract the ones column. 0 is less than 8. The tens and hundreds and thousands and ten thousands are 0, so exchange across them: take 1 hundred thousands and make each zero a 9, which gives 10 ones.10 - 8 = 2
- Subtract the tens column. 9 is at least 6, so subtract directly.9 - 6 = 3
- Subtract the hundreds column. 9 is at least 4, so subtract directly.9 - 4 = 5
- Subtract the thousands column. 9 is at least 3, so subtract directly.9 - 3 = 6
- Subtract the ten thousands column. 9 is at least 7, so subtract directly.9 - 7 = 2
- Subtract the hundred thousands column. 4 is at least 2, so subtract directly.4 - 2 = 2
- Write the answer. Read the digits from the left, and put commas in.226,532
Check. Check: 273,468 + 226,532 = 500,000.
Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.
Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.
- Subtract the ones column. 5 is less than 6. The tens is 0, so exchange across them: take 1 hundreds and make each zero a 9, which gives 10 ones.15 - 6 = 9
- Subtract the tens column. 9 is at least 3, so subtract directly.9 - 3 = 6
- Subtract the hundreds column. 6 is at least 2, so subtract directly.6 - 2 = 4
- Subtract the thousands column. 0 is less than 8. The ten thousands is 0, so exchange across them: take 1 hundred thousands and make each zero a 9, which gives 10 thousands.10 - 8 = 2
- Subtract the ten thousands column. 9 is at least 9, so subtract directly.9 - 9 = 0
- Subtract the hundred thousands column. 3 is at least 0, so subtract directly.3 - 0 = 3
- Write the answer. Read the digits from the left, and put commas in.302,469
Check. Check: 98,236 + 302,469 = 400,705.
Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.
Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.
- Subtract the ones column. 0 is less than 6, so exchange 1 tens for 10 ones.10 - 6 = 4
- Subtract the tens column. 2 is less than 9, so exchange 1 hundreds for 10 tens.12 - 9 = 3
- Subtract the hundreds column. 4 is at least 0, so subtract directly.4 - 0 = 4
- Subtract the thousands column. 2 is less than 8. The ten thousands is 0, so exchange across them: take 1 hundred thousands and make each zero a 9, which gives 10 thousands.12 - 8 = 4
- Subtract the ten thousands column. 9 is at least 1, so subtract directly.9 - 1 = 8
- Subtract the hundred thousands column. 6 is at least 4, so subtract directly.6 - 4 = 2
- Write the answer. Read the digits from the left, and put commas in.284,434
Check. Check: 418,096 + 284,434 = 702,530.
Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.
Watch out
Watch out. In 500,000 - 273,468 the top number has zeros in the middle. Every zero must be exchanged across, one column at a time.
Exam tip
Grown-up tip. Ask: “Is the top digit smaller? Which column do you exchange from?” before the child starts to take away.
Exercise 2C Practice: subtracting with exchange
Non-calculatorMethod. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.
- Subtract the ones column. 9 is at least 9, so subtract directly.9 - 9 = 0
- Subtract the tens column. 2 is less than 8, so exchange 1 hundreds for 10 tens.12 - 8 = 4
- Subtract the hundreds column. 1 is less than 2, so exchange 1 thousands for 10 hundreds.11 - 2 = 9
- Subtract the thousands column. 8 is at least 0, so subtract directly.8 - 0 = 8
- Subtract the ten thousands column. 1 is less than 4, so exchange 1 hundred thousands for 10 ten thousands.11 - 4 = 7
- Subtract the hundred thousands column. 5 is at least 1, so subtract directly.5 - 1 = 4
- Write the answer. Read the digits from the left, and put commas in.478,940
Check. Check: 140,289 + 478,940 = 619,229.
Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.
Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.
- Subtract the ones column. 7 is less than 8, so exchange 1 tens for 10 ones.17 - 8 = 9
- Subtract the tens column. 2 is at least 1, so subtract directly.2 - 1 = 1
- Subtract the hundreds column. 1 is less than 7, so exchange 1 thousands for 10 hundreds.11 - 7 = 4
- Subtract the thousands column. 3 is less than 6. The ten thousands is 0, so exchange across them: take 1 hundred thousands and make each zero a 9, which gives 10 thousands.13 - 6 = 7
- Subtract the ten thousands column. 9 is at least 5, so subtract directly.9 - 5 = 4
- Subtract the hundred thousands column. 3 is at least 3, so subtract directly.3 - 3 = 0
- Write the answer. Read the digits from the left, and put commas in.47,419
Check. Check: 356,718 + 47,419 = 404,137.
Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.
Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.
- Subtract the ones column. 5 is less than 6, so exchange 1 tens for 10 ones.15 - 6 = 9
- Subtract the tens column. 3 is less than 8. The hundreds is 0, so exchange across them: take 1 thousands and make each zero a 9, which gives 10 tens.13 - 8 = 5
- Subtract the hundreds column. 9 is at least 5, so subtract directly.9 - 5 = 4
- Subtract the thousands column. 5 is less than 7, so exchange 1 ten thousands for 10 thousands.15 - 7 = 8
- Subtract the ten thousands column. 7 is less than 9, so exchange 1 hundred thousands for 10 ten thousands.17 - 9 = 8
- Subtract the hundred thousands column. 6 is at least 5, so subtract directly.6 - 5 = 1
- Write the answer. Read the digits from the left, and put commas in.188,459
Check. Check: 597,586 + 188,459 = 786,045.
Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.
Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.
- Subtract the ones column. 1 is less than 8, so exchange 1 tens for 10 ones.11 - 8 = 3
- Subtract the tens column. 2 is at least 1, so subtract directly.2 - 1 = 1
- Subtract the hundreds column. 2 is less than 8, so exchange 1 thousands for 10 hundreds.12 - 8 = 4
- Subtract the thousands column. 2 is less than 9, so exchange 1 ten thousands for 10 thousands.12 - 9 = 3
- Subtract the ten thousands column. 3 is at least 3, so subtract directly.3 - 3 = 0
- Subtract the hundred thousands column. 6 is at least 1, so subtract directly.6 - 1 = 5
- Write the answer. Read the digits from the left, and put commas in.503,413
Check. Check: 139,818 + 503,413 = 643,231.
Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.
Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.
- Subtract the ones column. 6 is at least 6, so subtract directly.6 - 6 = 0
- Subtract the tens column. 0 is less than 2, so exchange 1 hundreds for 10 tens.10 - 2 = 8
- Subtract the hundreds column. 2 is less than 3, so exchange 1 thousands for 10 hundreds.12 - 3 = 9
- Subtract the thousands column. 6 is at least 0, so subtract directly.6 - 0 = 6
- Subtract the ten thousands column. 7 is less than 8, so exchange 1 hundred thousands for 10 ten thousands.17 - 8 = 9
- Subtract the hundred thousands column. 3 is at least 3, so subtract directly.3 - 3 = 0
- Write the answer. Read the digits from the left, and put commas in.96,980
Check. Check: 380,326 + 96,980 = 477,306.
Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.
Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.
- Subtract the ones column. 7 is at least 3, so subtract directly.7 - 3 = 4
- Subtract the tens column. 2 is less than 8, so exchange 1 hundreds for 10 tens.12 - 8 = 4
- Subtract the hundreds column. 4 is at least 2, so subtract directly.4 - 2 = 2
- Subtract the thousands column. 9 is at least 2, so subtract directly.9 - 2 = 7
- Subtract the ten thousands column. 4 is less than 5, so exchange 1 hundred thousands for 10 ten thousands.14 - 5 = 9
- Subtract the hundred thousands column. 8 is at least 0, so subtract directly.8 - 0 = 8
- Write the answer. Read the digits from the left, and put commas in.897,244
Check. Check: 52,283 + 897,244 = 949,527.
Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.
Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.
- Subtract the ones column. 3 is at least 1, so subtract directly.3 - 1 = 2
- Subtract the tens column. 7 is at least 1, so subtract directly.7 - 1 = 6
- Subtract the hundreds column. 5 is less than 6, so exchange 1 thousands for 10 hundreds.15 - 6 = 9
- Subtract the thousands column. 8 is at least 7, so subtract directly.8 - 7 = 1
- Subtract the ten thousands column. 9 is at least 5, so subtract directly.9 - 5 = 4
- Subtract the hundred thousands column. 7 is at least 6, so subtract directly.7 - 6 = 1
- Write the answer. Read the digits from the left, and put commas in.141,962
Check. Check: 657,611 + 141,962 = 799,573.
Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.
Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.
- Subtract the ones column. 9 is at least 4, so subtract directly.9 - 4 = 5
- Subtract the tens column. 7 is at least 6, so subtract directly.7 - 6 = 1
- Subtract the hundreds column. 0 is less than 4, so exchange 1 thousands for 10 hundreds.10 - 4 = 6
- Subtract the thousands column. 7 is at least 5, so subtract directly.7 - 5 = 2
- Subtract the ten thousands column. 5 is less than 6, so exchange 1 hundred thousands for 10 ten thousands.15 - 6 = 9
- Subtract the hundred thousands column. 3 is at least 0, so subtract directly.3 - 0 = 3
- Write the answer. Read the digits from the left, and put commas in.392,615
Check. Check: 65,464 + 392,615 = 458,079.
Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.
Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.
- Subtract the ones column. 7 is at least 4, so subtract directly.7 - 4 = 3
- Subtract the tens column. 9 is at least 7, so subtract directly.9 - 7 = 2
- Subtract the hundreds column. 2 is less than 9. The thousands is 0, so exchange across them: take 1 ten thousands and make each zero a 9, which gives 10 hundreds.12 - 9 = 3
- Subtract the thousands column. 9 is at least 2, so subtract directly.9 - 2 = 7
- Subtract the ten thousands column. 2 is less than 7, so exchange 1 hundred thousands for 10 ten thousands.12 - 7 = 5
- Subtract the hundred thousands column. 6 is at least 0, so subtract directly.6 - 0 = 6
- Write the answer. Read the digits from the left, and put commas in.657,323
Check. Check: 72,974 + 657,323 = 730,297.
Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.
Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.
- Subtract the ones column. 9 is at least 6, so subtract directly.9 - 6 = 3
- Subtract the tens column. 1 is less than 7, so exchange 1 hundreds for 10 tens.11 - 7 = 4
- Subtract the hundreds column. 7 is at least 2, so subtract directly.7 - 2 = 5
- Subtract the thousands column. 3 is less than 5, so exchange 1 ten thousands for 10 thousands.13 - 5 = 8
- Subtract the ten thousands column. 6 is at least 6, so subtract directly.6 - 6 = 0
- Subtract the hundred thousands column. 2 is at least 1, so subtract directly.2 - 1 = 1
- Write the answer. Read the digits from the left, and put commas in.108,543
Check. Check: 165,276 + 108,543 = 273,819.
Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.
Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.
- Subtract the ones column. 4 is at least 3, so subtract directly.4 - 3 = 1
- Subtract the tens column. 7 is at least 7, so subtract directly.7 - 7 = 0
- Subtract the hundreds column. 5 is at least 0, so subtract directly.5 - 0 = 5
- Subtract the thousands column. 5 is less than 6, so exchange 1 ten thousands for 10 thousands.15 - 6 = 9
- Subtract the ten thousands column. 0 is less than 1, so exchange 1 hundred thousands for 10 ten thousands.10 - 1 = 9
- Subtract the hundred thousands column. 5 is at least 5, so subtract directly.5 - 5 = 0
- Write the answer. Read the digits from the left, and put commas in.99,501
Check. Check: 516,073 + 99,501 = 615,574.
Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.
Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.
- Subtract the ones column. 7 is at least 0, so subtract directly.7 - 0 = 7
- Subtract the tens column. 4 is less than 6, so exchange 1 hundreds for 10 tens.14 - 6 = 8
- Subtract the hundreds column. 3 is less than 8, so exchange 1 thousands for 10 hundreds.13 - 8 = 5
- Subtract the thousands column. 5 is less than 8, so exchange 1 ten thousands for 10 thousands.15 - 8 = 7
- Subtract the ten thousands column. 7 is at least 6, so subtract directly.7 - 6 = 1
- Subtract the hundred thousands column. 6 is at least 2, so subtract directly.6 - 2 = 4
- Write the answer. Read the digits from the left, and put commas in.417,587
Check. Check: 268,860 + 417,587 = 686,447.
Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.
Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.
- Subtract the ones column. 1 is less than 2, so exchange 1 tens for 10 ones.11 - 2 = 9
- Subtract the tens column. 3 is at least 3, so subtract directly.3 - 3 = 0
- Subtract the hundreds column. 8 is at least 8, so subtract directly.8 - 8 = 0
- Subtract the thousands column. 6 is at least 6, so subtract directly.6 - 6 = 0
- Subtract the ten thousands column. 4 is at least 4, so subtract directly.4 - 4 = 0
- Subtract the hundred thousands column. 7 is at least 6, so subtract directly.7 - 6 = 1
- Write the answer. Read the digits from the left, and put commas in.100,009
Check. Check: 646,832 + 100,009 = 746,841.
Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.
Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.
- Subtract the ones column. 3 is less than 6, so exchange 1 tens for 10 ones.13 - 6 = 7
- Subtract the tens column. 3 is less than 5, so exchange 1 hundreds for 10 tens.13 - 5 = 8
- Subtract the hundreds column. 8 is at least 2, so subtract directly.8 - 2 = 6
- Subtract the thousands column. 5 is less than 9, so exchange 1 ten thousands for 10 thousands.15 - 9 = 6
- Subtract the ten thousands column. 4 is less than 5, so exchange 1 hundred thousands for 10 ten thousands.14 - 5 = 9
- Subtract the hundred thousands column. 7 is at least 4, so subtract directly.7 - 4 = 3
- Write the answer. Read the digits from the left, and put commas in.396,687
Check. Check: 459,256 + 396,687 = 855,943.
Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.
Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.
- Subtract the ones column. 0 is less than 8, so exchange 1 tens for 10 ones.10 - 8 = 2
- Subtract the tens column. 6 is less than 8, so exchange 1 hundreds for 10 tens.16 - 8 = 8
- Subtract the hundreds column. 0 is less than 6, so exchange 1 thousands for 10 hundreds.10 - 6 = 4
- Subtract the thousands column. 5 is at least 2, so subtract directly.5 - 2 = 3
- Subtract the ten thousands column. 5 is at least 4, so subtract directly.5 - 4 = 1
- Subtract the hundred thousands column. 9 is at least 7, so subtract directly.9 - 7 = 2
- Write the answer. Read the digits from the left, and put commas in.213,482
Check. Check: 742,688 + 213,482 = 956,170.
Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.
Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.
- Subtract the ones column. 1 is less than 9, so exchange 1 tens for 10 ones.11 - 9 = 2
- Subtract the tens column. 1 is less than 2, so exchange 1 hundreds for 10 tens.11 - 2 = 9
- Subtract the hundreds column. 4 is less than 9, so exchange 1 thousands for 10 hundreds.14 - 9 = 5
- Subtract the thousands column. 4 is less than 9, so exchange 1 ten thousands for 10 thousands.14 - 9 = 5
- Subtract the ten thousands column. 3 is less than 9, so exchange 1 hundred thousands for 10 ten thousands.13 - 9 = 4
- Subtract the hundred thousands column. 4 is at least 4, so subtract directly.4 - 4 = 0
- Write the answer. Read the digits from the left, and put commas in.45,592
Check. Check: 499,929 + 45,592 = 545,521.
Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.