Year 4: Column addition
Part of the Year 4 column addition and subtraction chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Column addition
When numbers are big, a written method keeps your working tidy and your answer accurate. In column addition you write one number under the other. Digits with the same value go in the same column: ones under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then you add one column at a time, starting on the right with the ones.
| Th | H | T | O | |
| 3 | 4 | 2 | 5 | |
| + | 2 | 3 | 1 | 4 |
| 5 | 7 | 3 | 9 |
Carrying. Sometimes a column adds up to 10 or more. There is only room for one digit in each column, so we carry. 10 ones are worth 1 ten, so we swap them for a ten and move it to the tens column. We write the carried digit small, under the answer line, so we do not forget it.
Here is 2,468 + 3,375. The ones add up to 8 + 5 = 13. That is 1 ten and 3 ones, so write 3 and carry 1 to the tens column. The same can happen in any column. The carried digit is added in with the next column.
| Th | H | T | O | |
| 2 | 4 | 6 | 8 | |
| + | 3 | 3 | 7 | 5 |
| 5 | 8 | 4 | 3 | |
| 1 | 1 |
The answer can have more digits than the numbers you started with. In 6,785 + 5,436 the thousands column makes 12, so the answer is a five-digit number: 12,221. You can also add numbers with different numbers of digits, like 4,073 + 618. Line the digits up on the right, so that ones are under ones. There is nothing to add in the empty spaces.
Key words. The column method is a written way to add or subtract. Carry means to move the tens (or hundreds...) to the next column when a column adds to 10 or more. Sum and total are the answers to an addition.
Key ideas
- Write the numbers in columns, with ones under ones, tens under tens, hundreds under hundreds and thousands under thousands.
- Add the ones first, then the tens, hundreds and thousands.
- If a column adds up to 10 or more, write the ones digit and carry the tens. Add the carried digit in the next column.
- Line numbers up on the right, not on the left.
- Check with the inverse (opposite) operation: subtract one of the numbers from your answer.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 3 4 2 5 + 2 3 1 4 - Add the ones. Always start with the ones, on the right.5 + 4 = 9
9 is less than 10, so write 9 in the ones column. There is nothing to carry.Th H T O 3 4 2 5 + 2 3 1 4 9 - Add the tens. Now the next column to the left.2 + 1 = 3
3 is less than 10, so write 3 in the tens column. There is nothing to carry.Th H T O 3 4 2 5 + 2 3 1 4 3 9 - Add the hundreds. Now the next column to the left.4 + 3 = 7
7 is less than 10, so write 7 in the hundreds column. There is nothing to carry.Th H T O 3 4 2 5 + 2 3 1 4 7 3 9 - Add the thousands. Now the next column to the left.3 + 2 = 5
5 is less than 10, so write 5 in the thousands column. There is nothing to carry.Th H T O 3 4 2 5 + 2 3 1 4 5 7 3 9 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 3 4 2 5 + 2 3 1 4 5 7 3 9
3,425 + 2,314 = 5,739
Check. Use the opposite (inverse) operation: 5,739 − 2,314 = 3,425. ✓
Estimate: 3,000 + 2,000 = 5,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. Start on the right with the ones, not on the left.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 2 4 6 8 + 3 3 7 5 - Add the ones. Always start with the ones, on the right.8 + 5 = 13
13 is 1 ten and 3 ones. Write 3 in the ones column and carry 1 to the tens column.Th H T O 2 4 6 8 + 3 3 7 5 3 1 - Add the tens. Now the next column to the left. Add the 1 we carried as well.6 + 7 + 1 = 14
14 is 1 hundred and 4 tens. Write 4 in the tens column and carry 1 to the hundreds column.Th H T O 2 4 6 8 + 3 3 7 5 4 3 1 1 - Add the hundreds. Now the next column to the left. Add the 1 we carried as well.4 + 3 + 1 = 8
8 is less than 10, so write 8 in the hundreds column. There is nothing to carry.Th H T O 2 4 6 8 + 3 3 7 5 8 4 3 1 1 - Add the thousands. Now the next column to the left.2 + 3 = 5
5 is less than 10, so write 5 in the thousands column. There is nothing to carry.Th H T O 2 4 6 8 + 3 3 7 5 5 8 4 3 1 1 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 2 4 6 8 + 3 3 7 5 5 8 4 3 1 1
2,468 + 3,375 = 5,843
Check. Use the opposite (inverse) operation: 5,843 − 3,375 = 2,468. ✓
Estimate: 2,000 + 3,000 = 5,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 3 8 4 6 + 2 7 5 9 - Add the ones. Always start with the ones, on the right.6 + 9 = 15
15 is 1 ten and 5 ones. Write 5 in the ones column and carry 1 to the tens column.Th H T O 3 8 4 6 + 2 7 5 9 5 1 - Add the tens. Now the next column to the left. Add the 1 we carried as well.4 + 5 + 1 = 10
10 is 1 hundred and 0 tens. Write 0 in the tens column and carry 1 to the hundreds column.Th H T O 3 8 4 6 + 2 7 5 9 0 5 1 1 - Add the hundreds. Now the next column to the left. Add the 1 we carried as well.8 + 7 + 1 = 16
16 is 1 thousand and 6 hundreds. Write 6 in the hundreds column and carry 1 to the thousands column.Th H T O 3 8 4 6 + 2 7 5 9 6 0 5 1 1 1 - Add the thousands. Now the next column to the left. Add the 1 we carried as well.3 + 2 + 1 = 6
6 is less than 10, so write 6 in the thousands column. There is nothing to carry.Th H T O 3 8 4 6 + 2 7 5 9 6 6 0 5 1 1 1 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 3 8 4 6 + 2 7 5 9 6 6 0 5 1 1 1
3,846 + 2,759 = 6,605
Check. Use the opposite (inverse) operation: 6,605 − 2,759 = 3,846. ✓
Estimate: 4,000 + 3,000 = 7,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 4 0 7 3 + 6 1 8 - Add the ones. Always start with the ones, on the right.3 + 8 = 11
11 is 1 ten and 1 one. Write 1 in the ones column and carry 1 to the tens column.Th H T O 4 0 7 3 + 6 1 8 1 1 - Add the tens. Now the next column to the left. Add the 1 we carried as well.7 + 1 + 1 = 9
9 is less than 10, so write 9 in the tens column. There is nothing to carry.Th H T O 4 0 7 3 + 6 1 8 9 1 1 - Add the hundreds. Now the next column to the left.0 + 6 = 6
6 is less than 10, so write 6 in the hundreds column. There is nothing to carry.Th H T O 4 0 7 3 + 6 1 8 6 9 1 1 - Bring down the thousands digit. The other number has no digit in this column, so there is nothing to add.There is only one digit here, so write 4 in the thousands column.
Th H T O 4 0 7 3 + 6 1 8 4 6 9 1 1 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 4 0 7 3 + 6 1 8 4 6 9 1 1
4,073 + 618 = 4,691
Check. Use the opposite (inverse) operation: 4,691 − 618 = 4,073. ✓
Estimate: 4,100 + 600 = 4,700 (rounding to the nearest 100). It is close to the exact answer. ✓
Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
TTh Th H T O 6 7 8 5 + 5 4 3 6 - Add the ones. Always start with the ones, on the right.5 + 6 = 11
11 is 1 ten and 1 one. Write 1 in the ones column and carry 1 to the tens column.TTh Th H T O 6 7 8 5 + 5 4 3 6 1 1 - Add the tens. Now the next column to the left. Add the 1 we carried as well.8 + 3 + 1 = 12
12 is 1 hundred and 2 tens. Write 2 in the tens column and carry 1 to the hundreds column.TTh Th H T O 6 7 8 5 + 5 4 3 6 2 1 1 1 - Add the hundreds. Now the next column to the left. Add the 1 we carried as well.7 + 4 + 1 = 12
12 is 1 thousand and 2 hundreds. Write 2 in the hundreds column and carry 1 to the thousands column.TTh Th H T O 6 7 8 5 + 5 4 3 6 2 2 1 1 1 1 - Add the thousands. Now the next column to the left. Add the 1 we carried as well.6 + 5 + 1 = 12
12 is 1 ten thousand and 2 thousands. Write 2 in the thousands column and carry 1 to the ten thousands column.TTh Th H T O 6 7 8 5 + 5 4 3 6 2 2 2 1 1 1 1 1 - Write the carried digit. There are no digits left in the ten thousands column, but we carried 1 into it.Nothing to add except the carried digit. Write 1.
TTh Th H T O 6 7 8 5 + 5 4 3 6 1 2 2 2 1 1 1 1 1 - Read the answer. Check the answer has the right number of digits, then write it.
TTh Th H T O 6 7 8 5 + 5 4 3 6 1 2 2 2 1 1 1 1 1
6,785 + 5,436 = 12,221
Check. Use the opposite (inverse) operation: 12,221 − 5,436 = 6,785. ✓
Estimate: 7,000 + 5,000 = 12,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.
Watch out
Do not forget the carried digit! It is easy to write the carry and then not add it in the next column. Also line the numbers up on the right: if you add 4,073 + 618, the 8 goes under the 3 (ones under ones), not under the 4.Exercise 2A Column addition
Non-calculatorKey words. Base-ten blocks show numbers: a big cube is 1,000, a flat is 100, a rod is 10 and a small cube is 1.
Method. Read each number from the blocks first. Then add the two numbers with the column method.
- Read the first set of blocks. A big cube is 1,000, a flat is 100, a rod is 10 and a small cube is 1.1 big cube, 2 flats, 3 rods, 5 small cubes
1,000 + 200 + 30 + 5 = 1,235 - Read the second set of blocks. Count each kind of block again.2 big cubes, 1 flat, 4 rods, 2 small cubes
2,000 + 100 + 40 + 2 = 2,142 - Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 1 2 3 5 + 2 1 4 2 - Add the ones. Always start with the ones, on the right.5 + 2 = 7
7 is less than 10, so write 7 in the ones column. There is nothing to carry. - Add the tens. Now the next column to the left.3 + 4 = 7
7 is less than 10, so write 7 in the tens column. There is nothing to carry. - Add the hundreds. Now the next column to the left.2 + 1 = 3
3 is less than 10, so write 3 in the hundreds column. There is nothing to carry. - Add the thousands. Now the next column to the left.1 + 2 = 3
3 is less than 10, so write 3 in the thousands column. There is nothing to carry. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 1 2 3 5 + 2 1 4 2 3 3 7 7
1,235 + 2,142 = 3,377
Check. Use the opposite operation: 3,377 − 2,142 = 1,235. ✓
Watch out. Count the blocks of each kind carefully before you add. A flat is 100, not 10.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 2 1 3 4 + 4 5 2 1 - Add the ones. Always start with the ones, on the right.4 + 1 = 5
5 is less than 10, so write 5 in the ones column. There is nothing to carry. - Add the tens. Now the next column to the left.3 + 2 = 5
5 is less than 10, so write 5 in the tens column. There is nothing to carry. - Add the hundreds. Now the next column to the left.1 + 5 = 6
6 is less than 10, so write 6 in the hundreds column. There is nothing to carry. - Add the thousands. Now the next column to the left.2 + 4 = 6
6 is less than 10, so write 6 in the thousands column. There is nothing to carry. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 2 1 3 4 + 4 5 2 1 6 6 5 5
2,134 + 4,521 = 6,655
Check. Use the opposite (inverse) operation: 6,655 − 4,521 = 2,134. ✓
Estimate: 2,000 + 5,000 = 7,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. Start on the right with the ones, not on the left.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 1 3 0 5 + 3 2 7 4 - Add the ones. Always start with the ones, on the right.5 + 4 = 9
9 is less than 10, so write 9 in the ones column. There is nothing to carry. - Add the tens. Now the next column to the left.0 + 7 = 7
7 is less than 10, so write 7 in the tens column. There is nothing to carry. - Add the hundreds. Now the next column to the left.3 + 2 = 5
5 is less than 10, so write 5 in the hundreds column. There is nothing to carry. - Add the thousands. Now the next column to the left.1 + 3 = 4
4 is less than 10, so write 4 in the thousands column. There is nothing to carry. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 1 3 0 5 + 3 2 7 4 4 5 7 9
1,305 + 3,274 = 4,579
Check. Use the opposite (inverse) operation: 4,579 − 3,274 = 1,305. ✓
Estimate: 1,000 + 3,000 = 4,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. Start on the right with the ones, not on the left.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 5 2 1 2 + 4 3 6 7 - Add the ones. Always start with the ones, on the right.2 + 7 = 9
9 is less than 10, so write 9 in the ones column. There is nothing to carry. - Add the tens. Now the next column to the left.1 + 6 = 7
7 is less than 10, so write 7 in the tens column. There is nothing to carry. - Add the hundreds. Now the next column to the left.2 + 3 = 5
5 is less than 10, so write 5 in the hundreds column. There is nothing to carry. - Add the thousands. Now the next column to the left.5 + 4 = 9
9 is less than 10, so write 9 in the thousands column. There is nothing to carry. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 5 2 1 2 + 4 3 6 7 9 5 7 9
5,212 + 4,367 = 9,579
Check. Use the opposite (inverse) operation: 9,579 − 4,367 = 5,212. ✓
Estimate: 5,000 + 4,000 = 9,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. Start on the right with the ones, not on the left.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 3 4 5 0 + 2 5 0 9 - Add the ones. Always start with the ones, on the right.0 + 9 = 9
9 is less than 10, so write 9 in the ones column. There is nothing to carry. - Add the tens. Now the next column to the left.5 + 0 = 5
5 is less than 10, so write 5 in the tens column. There is nothing to carry. - Add the hundreds. Now the next column to the left.4 + 5 = 9
9 is less than 10, so write 9 in the hundreds column. There is nothing to carry. - Add the thousands. Now the next column to the left.3 + 2 = 5
5 is less than 10, so write 5 in the thousands column. There is nothing to carry. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 3 4 5 0 + 2 5 0 9 5 9 5 9
3,450 + 2,509 = 5,959
Check. Use the opposite (inverse) operation: 5,959 − 2,509 = 3,450. ✓
Estimate: 3,000 + 3,000 = 6,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. Start on the right with the ones, not on the left.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 2 4 3 6 + 3 1 5 8 - Add the ones. Always start with the ones, on the right.6 + 8 = 14
14 is 1 ten and 4 ones. Write 4 in the ones column and carry 1 to the tens column. - Add the tens. Now the next column to the left. Add the 1 we carried as well.3 + 5 + 1 = 9
9 is less than 10, so write 9 in the tens column. There is nothing to carry. - Add the hundreds. Now the next column to the left.4 + 1 = 5
5 is less than 10, so write 5 in the hundreds column. There is nothing to carry. - Add the thousands. Now the next column to the left.2 + 3 = 5
5 is less than 10, so write 5 in the thousands column. There is nothing to carry. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 2 4 3 6 + 3 1 5 8 5 5 9 4 1
2,436 + 3,158 = 5,594
Check. Use the opposite (inverse) operation: 5,594 − 3,158 = 2,436. ✓
Estimate: 2,000 + 3,000 = 5,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 1 2 7 5 + 4 3 1 8 - Add the ones. Always start with the ones, on the right.5 + 8 = 13
13 is 1 ten and 3 ones. Write 3 in the ones column and carry 1 to the tens column. - Add the tens. Now the next column to the left. Add the 1 we carried as well.7 + 1 + 1 = 9
9 is less than 10, so write 9 in the tens column. There is nothing to carry. - Add the hundreds. Now the next column to the left.2 + 3 = 5
5 is less than 10, so write 5 in the hundreds column. There is nothing to carry. - Add the thousands. Now the next column to the left.1 + 4 = 5
5 is less than 10, so write 5 in the thousands column. There is nothing to carry. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 1 2 7 5 + 4 3 1 8 5 5 9 3 1
1,275 + 4,318 = 5,593
Check. Use the opposite (inverse) operation: 5,593 − 4,318 = 1,275. ✓
Estimate: 1,000 + 4,000 = 5,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 3 6 2 9 + 2 1 4 5 - Add the ones. Always start with the ones, on the right.9 + 5 = 14
14 is 1 ten and 4 ones. Write 4 in the ones column and carry 1 to the tens column. - Add the tens. Now the next column to the left. Add the 1 we carried as well.2 + 4 + 1 = 7
7 is less than 10, so write 7 in the tens column. There is nothing to carry. - Add the hundreds. Now the next column to the left.6 + 1 = 7
7 is less than 10, so write 7 in the hundreds column. There is nothing to carry. - Add the thousands. Now the next column to the left.3 + 2 = 5
5 is less than 10, so write 5 in the thousands column. There is nothing to carry. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 3 6 2 9 + 2 1 4 5 5 7 7 4 1
3,629 + 2,145 = 5,774
Check. Use the opposite (inverse) operation: 5,774 − 2,145 = 3,629. ✓
Estimate: 4,000 + 2,000 = 6,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 5 7 0 3 + 1 2 8 9 - Add the ones. Always start with the ones, on the right.3 + 9 = 12
12 is 1 ten and 2 ones. Write 2 in the ones column and carry 1 to the tens column. - Add the tens. Now the next column to the left. Add the 1 we carried as well.0 + 8 + 1 = 9
9 is less than 10, so write 9 in the tens column. There is nothing to carry. - Add the hundreds. Now the next column to the left.7 + 2 = 9
9 is less than 10, so write 9 in the hundreds column. There is nothing to carry. - Add the thousands. Now the next column to the left.5 + 1 = 6
6 is less than 10, so write 6 in the thousands column. There is nothing to carry. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 5 7 0 3 + 1 2 8 9 6 9 9 2 1
5,703 + 1,289 = 6,992
Check. Use the opposite (inverse) operation: 6,992 − 1,289 = 5,703. ✓
Estimate: 6,000 + 1,000 = 7,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 2 7 5 8 + 3 4 9 6 - Add the ones. Always start with the ones, on the right.8 + 6 = 14
14 is 1 ten and 4 ones. Write 4 in the ones column and carry 1 to the tens column. - Add the tens. Now the next column to the left. Add the 1 we carried as well.5 + 9 + 1 = 15
15 is 1 hundred and 5 tens. Write 5 in the tens column and carry 1 to the hundreds column. - Add the hundreds. Now the next column to the left. Add the 1 we carried as well.7 + 4 + 1 = 12
12 is 1 thousand and 2 hundreds. Write 2 in the hundreds column and carry 1 to the thousands column. - Add the thousands. Now the next column to the left. Add the 1 we carried as well.2 + 3 + 1 = 6
6 is less than 10, so write 6 in the thousands column. There is nothing to carry. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 2 7 5 8 + 3 4 9 6 6 2 5 4 1 1 1
2,758 + 3,496 = 6,254
Check. Use the opposite (inverse) operation: 6,254 − 3,496 = 2,758. ✓
Estimate: 3,000 + 3,000 = 6,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 4 6 8 5 + 2 5 4 7 - Add the ones. Always start with the ones, on the right.5 + 7 = 12
12 is 1 ten and 2 ones. Write 2 in the ones column and carry 1 to the tens column. - Add the tens. Now the next column to the left. Add the 1 we carried as well.8 + 4 + 1 = 13
13 is 1 hundred and 3 tens. Write 3 in the tens column and carry 1 to the hundreds column. - Add the hundreds. Now the next column to the left. Add the 1 we carried as well.6 + 5 + 1 = 12
12 is 1 thousand and 2 hundreds. Write 2 in the hundreds column and carry 1 to the thousands column. - Add the thousands. Now the next column to the left. Add the 1 we carried as well.4 + 2 + 1 = 7
7 is less than 10, so write 7 in the thousands column. There is nothing to carry. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 4 6 8 5 + 2 5 4 7 7 2 3 2 1 1 1
4,685 + 2,547 = 7,232
Check. Use the opposite (inverse) operation: 7,232 − 2,547 = 4,685. ✓
Estimate: 5,000 + 3,000 = 8,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 3 8 7 9 + 4 3 6 3 - Add the ones. Always start with the ones, on the right.9 + 3 = 12
12 is 1 ten and 2 ones. Write 2 in the ones column and carry 1 to the tens column. - Add the tens. Now the next column to the left. Add the 1 we carried as well.7 + 6 + 1 = 14
14 is 1 hundred and 4 tens. Write 4 in the tens column and carry 1 to the hundreds column. - Add the hundreds. Now the next column to the left. Add the 1 we carried as well.8 + 3 + 1 = 12
12 is 1 thousand and 2 hundreds. Write 2 in the hundreds column and carry 1 to the thousands column. - Add the thousands. Now the next column to the left. Add the 1 we carried as well.3 + 4 + 1 = 8
8 is less than 10, so write 8 in the thousands column. There is nothing to carry. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 3 8 7 9 + 4 3 6 3 8 2 4 2 1 1 1
3,879 + 4,363 = 8,242
Check. Use the opposite (inverse) operation: 8,242 − 4,363 = 3,879. ✓
Estimate: 4,000 + 4,000 = 8,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 1 9 9 9 + 5 5 5 5 - Add the ones. Always start with the ones, on the right.9 + 5 = 14
14 is 1 ten and 4 ones. Write 4 in the ones column and carry 1 to the tens column. - Add the tens. Now the next column to the left. Add the 1 we carried as well.9 + 5 + 1 = 15
15 is 1 hundred and 5 tens. Write 5 in the tens column and carry 1 to the hundreds column. - Add the hundreds. Now the next column to the left. Add the 1 we carried as well.9 + 5 + 1 = 15
15 is 1 thousand and 5 hundreds. Write 5 in the hundreds column and carry 1 to the thousands column. - Add the thousands. Now the next column to the left. Add the 1 we carried as well.1 + 5 + 1 = 7
7 is less than 10, so write 7 in the thousands column. There is nothing to carry. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 1 9 9 9 + 5 5 5 5 7 5 5 4 1 1 1
1,999 + 5,555 = 7,554
Check. Use the opposite (inverse) operation: 7,554 − 5,555 = 1,999. ✓
Estimate: 2,000 + 6,000 = 8,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 2 8 4 5 + 3 7 6 - Add the ones. Always start with the ones, on the right.5 + 6 = 11
11 is 1 ten and 1 one. Write 1 in the ones column and carry 1 to the tens column. - Add the tens. Now the next column to the left. Add the 1 we carried as well.4 + 7 + 1 = 12
12 is 1 hundred and 2 tens. Write 2 in the tens column and carry 1 to the hundreds column. - Add the hundreds. Now the next column to the left. Add the 1 we carried as well.8 + 3 + 1 = 12
12 is 1 thousand and 2 hundreds. Write 2 in the hundreds column and carry 1 to the thousands column. - Add the thousands. Now the next column to the left. Add the 1 we carried as well.2 + 1 = 3
3 is less than 10, so write 3 in the thousands column. There is nothing to carry. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 2 8 4 5 + 3 7 6 3 2 2 1 1 1 1
2,845 + 376 = 3,221
Check. Use the opposite (inverse) operation: 3,221 − 376 = 2,845. ✓
Estimate: 2,800 + 400 = 3,200 (rounding to the nearest 100). It is close to the exact answer. ✓
Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 4 0 0 8 + 6 9 5 - Add the ones. Always start with the ones, on the right.8 + 5 = 13
13 is 1 ten and 3 ones. Write 3 in the ones column and carry 1 to the tens column. - Add the tens. Now the next column to the left. Add the 1 we carried as well.0 + 9 + 1 = 10
10 is 1 hundred and 0 tens. Write 0 in the tens column and carry 1 to the hundreds column. - Add the hundreds. Now the next column to the left. Add the 1 we carried as well.0 + 6 + 1 = 7
7 is less than 10, so write 7 in the hundreds column. There is nothing to carry. - Bring down the thousands digit. The other number has no digit in this column, so there is nothing to add.There is only one digit here, so write 4 in the thousands column.
- Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 4 0 0 8 + 6 9 5 4 7 0 3 1 1
4,008 + 695 = 4,703
Check. Use the opposite (inverse) operation: 4,703 − 695 = 4,008. ✓
Estimate: 4,000 + 700 = 4,700 (rounding to the nearest 100). It is close to the exact answer. ✓
Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 5 3 7 + 4 2 6 0 - Add the ones. Always start with the ones, on the right.7 + 0 = 7
7 is less than 10, so write 7 in the ones column. There is nothing to carry. - Add the tens. Now the next column to the left.3 + 6 = 9
9 is less than 10, so write 9 in the tens column. There is nothing to carry. - Add the hundreds. Now the next column to the left.5 + 2 = 7
7 is less than 10, so write 7 in the hundreds column. There is nothing to carry. - Bring down the thousands digit. The other number has no digit in this column, so there is nothing to add.There is only one digit here, so write 4 in the thousands column.
- Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 5 3 7 + 4 2 6 0 4 7 9 7
537 + 4,260 = 4,797
Check. Use the opposite (inverse) operation: 4,797 − 4,260 = 537. ✓
Estimate: 500 + 4,300 = 4,800 (rounding to the nearest 100). It is close to the exact answer. ✓
Watch out. Line up the digits on the RIGHT, so ones are under ones. Do not line up the numbers on the left.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 6 + 3 9 9 4 - Add the ones. Always start with the ones, on the right.6 + 4 = 10
10 is 1 ten and 0 ones. Write 0 in the ones column and carry 1 to the tens column. - Add the tens. Now the next column to the left. Add the 1 we carried as well.9 + 1 = 10
10 is 1 hundred and 0 tens. Write 0 in the tens column and carry 1 to the hundreds column. - Add the hundreds. Now the next column to the left. Add the 1 we carried as well.9 + 1 = 10
10 is 1 thousand and 0 hundreds. Write 0 in the hundreds column and carry 1 to the thousands column. - Add the thousands. Now the next column to the left. Add the 1 we carried as well.3 + 1 = 4
4 is less than 10, so write 4 in the thousands column. There is nothing to carry. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 6 + 3 9 9 4 4 0 0 0 1 1 1
6 + 3,994 = 4,000
Check. Use the opposite (inverse) operation: 4,000 − 3,994 = 6. ✓
Estimate: 10 + 3,990 = 4,000 (rounding to the nearest 10). It is close to the exact answer. ✓
Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
TTh Th H T O 7 8 4 6 + 5 3 7 9 - Add the ones. Always start with the ones, on the right.6 + 9 = 15
15 is 1 ten and 5 ones. Write 5 in the ones column and carry 1 to the tens column. - Add the tens. Now the next column to the left. Add the 1 we carried as well.4 + 7 + 1 = 12
12 is 1 hundred and 2 tens. Write 2 in the tens column and carry 1 to the hundreds column. - Add the hundreds. Now the next column to the left. Add the 1 we carried as well.8 + 3 + 1 = 12
12 is 1 thousand and 2 hundreds. Write 2 in the hundreds column and carry 1 to the thousands column. - Add the thousands. Now the next column to the left. Add the 1 we carried as well.7 + 5 + 1 = 13
13 is 1 ten thousand and 3 thousands. Write 3 in the thousands column and carry 1 to the ten thousands column. - Write the carried digit. There are no digits left in the ten thousands column, but we carried 1 into it.Nothing to add except the carried digit. Write 1.
- Read the answer. Check the answer has the right number of digits, then write it.
TTh Th H T O 7 8 4 6 + 5 3 7 9 1 3 2 2 5 1 1 1 1
7,846 + 5,379 = 13,225
Check. Use the opposite (inverse) operation: 13,225 − 5,379 = 7,846. ✓
Estimate: 8,000 + 5,000 = 13,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
TTh Th H T O 6 5 0 0 + 5 7 0 0 - Add the ones. Always start with the ones, on the right.0 + 0 = 0
0 is less than 10, so write 0 in the ones column. There is nothing to carry. - Add the tens. Now the next column to the left.0 + 0 = 0
0 is less than 10, so write 0 in the tens column. There is nothing to carry. - Add the hundreds. Now the next column to the left.5 + 7 = 12
12 is 1 thousand and 2 hundreds. Write 2 in the hundreds column and carry 1 to the thousands column. - Add the thousands. Now the next column to the left. Add the 1 we carried as well.6 + 5 + 1 = 12
12 is 1 ten thousand and 2 thousands. Write 2 in the thousands column and carry 1 to the ten thousands column. - Write the carried digit. There are no digits left in the ten thousands column, but we carried 1 into it.Nothing to add except the carried digit. Write 1.
- Read the answer. Check the answer has the right number of digits, then write it.
TTh Th H T O 6 5 0 0 + 5 7 0 0 1 2 2 0 0 1 1
6,500 + 5,700 = 12,200
Check. Use the opposite (inverse) operation: 12,200 − 5,700 = 6,500. ✓
Estimate: 7,000 + 6,000 = 13,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
TTh Th H T O 9 9 9 9 + 1 - Add the ones. Always start with the ones, on the right.9 + 1 = 10
10 is 1 ten and 0 ones. Write 0 in the ones column and carry 1 to the tens column. - Add the tens. Now the next column to the left. Add the 1 we carried as well.9 + 1 = 10
10 is 1 hundred and 0 tens. Write 0 in the tens column and carry 1 to the hundreds column. - Add the hundreds. Now the next column to the left. Add the 1 we carried as well.9 + 1 = 10
10 is 1 thousand and 0 hundreds. Write 0 in the hundreds column and carry 1 to the thousands column. - Add the thousands. Now the next column to the left. Add the 1 we carried as well.9 + 1 = 10
10 is 1 ten thousand and 0 thousands. Write 0 in the thousands column and carry 1 to the ten thousands column. - Write the carried digit. There are no digits left in the ten thousands column, but we carried 1 into it.Nothing to add except the carried digit. Write 1.
- Read the answer. Check the answer has the right number of digits, then write it.
TTh Th H T O 9 9 9 9 + 1 1 0 0 0 0 1 1 1 1
9,999 + 1 = 10,000
Check. Use the opposite (inverse) operation: 10,000 − 1 = 9,999. ✓
Estimate: 10,000 + 0 = 10,000 (rounding to the nearest 10). It is close to the exact answer. ✓
Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.
Method. Draw a bar model to see what is happening. Decide whether to add or subtract, then use a written method.
- Draw a bar model. A picture shows what we know and what we need to find.
- Choose the operation. We are putting two amounts together, so we add.£1,285 + £478
- Work it out. Use the column method if the numbers are big.£1,285 + £478 = £1,763
Th H T O 1 2 8 5 + 4 7 8 1 7 6 3 1 1 - Write the answer. £1,763
Check. Use the opposite operation: £1,763 − £478 = £1,285. ✓
Watch out. Read the question again at the end. Does your answer make sense, and does it answer what was asked?
Method. Draw a bar model to see what is happening. Decide whether to add or subtract, then use a written method.
- Draw a bar model. A picture shows what we know and what we need to find.
- Choose the operation. We are putting two amounts together, so we add.3,478 km + 2,596 km
- Work it out. Use the column method if the numbers are big.3,478 km + 2,596 km = 6,074 km
Th H T O 3 4 7 8 + 2 5 9 6 6 0 7 4 1 1 1 - Write the answer. 6,074 km
Check. Use the opposite operation: 6,074 km − 2,596 km = 3,478 km. ✓
Watch out. Read the question again at the end. Does your answer make sense, and does it answer what was asked?
Method. Draw a bar model to see what is happening. Decide whether to add or subtract, then use a written method.
- Draw a bar model. A picture shows what we know and what we need to find.
- Choose the operation. We are putting two amounts together, so we add.3,846 + 4,975
- Work it out. Use the column method if the numbers are big.3,846 + 4,975 = 8,821
Th H T O 3 8 4 6 + 4 9 7 5 8 8 2 1 1 1 1 - Write the answer. 8,821 fans
Check. Use the opposite operation: 8,821 − 4,975 = 3,846. ✓
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 Jack’s answer.
- Work out the correct answer. Use the column method carefully.
Th H T O 3 4 7 8 + 2 8 4 5 6 3 2 3 1 1 1
3,478 + 2,845 = 6,323 - Compare with Jack’s answer. Jack wrote 5,213.6,323 is not 5,213, so Jack made a mistake.
- Find the mistake. In the columns that make 10 or more, the tens must be carried. He just wrote the ones digit and lost the carried 1s.The carries from the ones, tens and hundreds columns were missing.
Check. Use the opposite operation: 6,323 − 2,845 = 3,478. ✓
Watch out. A carried digit is part of the sum for the next column. Write it small, under the line, so you do not forget it.
Method. Do the column addition and count the carries.
- Add the columns, starting with the ones. We look for every column that makes 10 or more.ones: 8 + 5 = 13 → carry 1
tens: 6 + 4 + 1 = 11 → carry 1
hundreds: 5 + 7 + 1 = 13 → carry 1
thousands: 4 + 2 + 1 = 7 → nothing to carry - Show it in columns. The carries are the small red digits.4,568 + 2,745 = 7,313
Th H T O 4 5 6 8 + 2 7 4 5 7 3 1 3 1 1 1 - Count the carries and answer Zainab. There are 3 carries, not 4. Zainab is wrong.
Check. 4,568 + 2,745 = 7,313. The sum is a four-digit number, so there is no carry out of the thousands column. ✓
Watch out. A carry only happens when a column adds up to 10 or more. 7 is less than 10, so the thousands column does not carry.
Method. Try some examples. If you can find one with a four-digit answer and one with a five-digit answer, the answer is “sometimes”.
- Try two small four-digit numbers. Small numbers are less likely to make a five-digit answer.2,134 + 3,251 = 5,385
Th H T O 2 1 3 4 + 3 2 5 1 5 3 8 5
5,385 has 4 digits. - Try two big four-digit numbers. Big numbers might make 10,000 or more.6,500 + 5,700 = 12,200
TTh Th H T O 6 5 0 0 + 5 7 0 0 1 2 2 0 0 1 1
12,200 has 5 digits. - Decide. We found an example of each.Sometimes
Check. The biggest answer is 9,999 + 9,999 = 19,998 (five digits), and the smallest is 1,000 + 1,000 = 2,000 (four digits). ✓
Watch out. To show “sometimes”, you need one example where it is true AND one where it is false.
Method. To make the total as big as possible, put the biggest digits in the biggest columns.
- Think about the thousands column. A thousand is worth much more than a hundred. So the two biggest digits, 8 and 7, go in the thousands column (one in each number).8 _ _ _ and 7 _ _ _
- Fill the other columns in the same way. The next two biggest digits go in the hundreds, then the tens, then the ones.6 and 5 in the hundreds
4 and 3 in the tens
2 and 1 in the ones - Make two numbers and add them. Any way of splitting each pair between the two numbers gives the same total.8,642 + 7,531
8,642 + 7,531 = 16,173TTh Th H T O 8 6 4 2 + 7 5 3 1 1 6 1 7 3 1 1
Check. The columns add to: 15 thousands + 11 hundreds + 7 tens + 3 ones = 15,000 + 1,100 + 70 + 3 = 16,173. ✓
Watch out. Check that you used every digit once: 8, 6, 4, 2, 7, 5, 3, 1.