Year 5: Column addition with bigger numbers

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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value.

   	TTh	Th	H	T	O
   	3	4	5	2	6
   +	2	1	3	4	2

2. Add the ones. Always start with the ones, on the right.
   6 + 2 = 8
   8 is less than 10, so write 8 in the ones column. There is nothing to carry.
3. Add the tens. Now the next column to the left.
   2 + 4 = 6
   6 is less than 10, so write 6 in the tens column. There is nothing to carry.
4. Add the hundreds. Now the next column to the left.
   5 + 3 = 8
   8 is less than 10, so write 8 in the hundreds column. There is nothing to carry.
5. Add the thousands. Now the next column to the left.
   4 + 1 = 5
   5 is less than 10, so write 5 in the thousands column. There is nothing to carry.
6. Add the ten thousands. Now the next column to the left.
   3 + 2 = 5
   5 is less than 10, so write 5 in the ten thousands column. There is nothing to carry.
7. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	TTh	Th	H	T	O
   	3	4	5	2	6
   +	2	1	3	4	2
   	5	5	8	6	8

   
   34,526 + 21,342 = 55,868

Check. Use the opposite (inverse) operation: 55,868 − 21,342 = 34,526. ✓
Estimate: 35,000 + 21,000 = 56,000 (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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value.

   	TTh	Th	H	T	O
   	5	2	0	1	3
   +	3	6	2	7	5

2. Add the ones. Always start with the ones, on the right.
   3 + 5 = 8
   8 is less than 10, so write 8 in the ones column. There is nothing to carry.
3. Add the tens. Now the next column to the left.
   1 + 7 = 8
   8 is less than 10, so write 8 in the tens column. There is nothing to carry.
4. Add the hundreds. Now the next column to the left.
   0 + 2 = 2
   2 is less than 10, so write 2 in the hundreds column. There is nothing to carry.
5. Add the thousands. Now the next column to the left.
   2 + 6 = 8
   8 is less than 10, so write 8 in the thousands column. There is nothing to carry.
6. Add the ten thousands. Now the next column to the left.
   5 + 3 = 8
   8 is less than 10, so write 8 in the ten thousands column. There is nothing to carry.
7. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	TTh	Th	H	T	O
   	5	2	0	1	3
   +	3	6	2	7	5
   	8	8	2	8	8

   
   52,013 + 36,275 = 88,288

Check. Use the opposite (inverse) operation: 88,288 − 36,275 = 52,013. ✓
Estimate: 52,000 + 36,000 = 88,000 (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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value.

   	TTh	Th	H	T	O
   	6	0	4	5	2
   +	2	7	1	3	4

2. Add the ones. Always start with the ones, on the right.
   2 + 4 = 6
   6 is less than 10, so write 6 in the ones column. There is nothing to carry.
3. Add the tens. Now the next column to the left.
   5 + 3 = 8
   8 is less than 10, so write 8 in the tens column. There is nothing to carry.
4. 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.
5. Add the thousands. Now the next column to the left.
   0 + 7 = 7
   7 is less than 10, so write 7 in the thousands column. There is nothing to carry.
6. Add the ten thousands. Now the next column to the left.
   6 + 2 = 8
   8 is less than 10, so write 8 in the ten thousands column. There is nothing to carry.
7. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	TTh	Th	H	T	O
   	6	0	4	5	2
   +	2	7	1	3	4
   	8	7	5	8	6

   
   60,452 + 27,134 = 87,586

Check. Use the opposite (inverse) operation: 87,586 − 27,134 = 60,452. ✓
Estimate: 60,000 + 27,000 = 87,000 (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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value.

   	HTh	TTh	Th	H	T	O
   	4	1	3	2	0	5
   +	2	8	5	7	9	4

2. 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.
3. Add the tens. Now the next column to the left.
   0 + 9 = 9
   9 is less than 10, so write 9 in the tens column. There is nothing to carry.
4. Add the hundreds. Now the next column to the left.
   2 + 7 = 9
   9 is less than 10, so write 9 in the hundreds column. There is nothing to carry.
5. Add the thousands. Now the next column to the left.
   3 + 5 = 8
   8 is less than 10, so write 8 in the thousands column. There is nothing to carry.
6. Add the ten thousands. Now the next column to the left.
   1 + 8 = 9
   9 is less than 10, so write 9 in the ten thousands column. There is nothing to carry.
7. Add the hundred thousands. Now the next column to the left.
   4 + 2 = 6
   6 is less than 10, so write 6 in the hundred thousands column. There is nothing to carry.
8. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	HTh	TTh	Th	H	T	O
   	4	1	3	2	0	5
   +	2	8	5	7	9	4
   	6	9	8	9	9	9

   
   413,205 + 285,794 = 698,999

Check. Use the opposite (inverse) operation: 698,999 − 285,794 = 413,205. ✓
Estimate: 410,000 + 290,000 = 700,000 (rounding to the nearest 10,000). 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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value.

   	TTh	Th	H	T	O
   	4	6	2	9	8
   +	3	2	4	5	1

2. Add the ones. Always start with the ones, on the right.
   8 + 1 = 9
   9 is less than 10, so write 9 in the ones column. There is nothing to carry.
3. Add the tens. Now the next column to the left.
   9 + 5 = 14
   14 tens is 1 hundred and 4 tens. Write 4 in the tens column and carry 1 to the hundreds column.
4. Add the hundreds. Now the next column to the left. Add the 1 we carried as well.
   2 + 4 + 1 = 7  (the red digit is the carry)
   7 is less than 10, so write 7 in the hundreds column. There is nothing to carry.
5. Add the thousands. Now the next column to the left.
   6 + 2 = 8
   8 is less than 10, so write 8 in the thousands column. There is nothing to carry.
6. Add the ten thousands. Now the next column to the left.
   4 + 3 = 7
   7 is less than 10, so write 7 in the ten thousands column. There is nothing to carry.
7. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	TTh	Th	H	T	O
   	4	6	2	9	8
   +	3	2	4	5	1
   	7	8	7	4	9
   			1

   
   46,298 + 32,451 = 78,749

Check. Use the opposite (inverse) operation: 78,749 − 32,451 = 46,298. ✓
Estimate: 46,000 + 32,000 = 78,000 (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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value.

   	TTh	Th	H	T	O
   	2	7	3	1	5
   +	4	1	2	6	8

2. Add the ones. Always start with the ones, on the right.
   5 + 8 = 13
   13 ones is 1 ten and 3 ones. Write 3 in the ones column and carry 1 to the tens column.
3. Add the tens. Now the next column to the left. Add the 1 we carried as well.
   1 + 6 + 1 = 8  (the red digit is the carry)
   8 is less than 10, so write 8 in the tens column. There is nothing to carry.
4. 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.
5. Add the thousands. Now the next column to the left.
   7 + 1 = 8
   8 is less than 10, so write 8 in the thousands column. There is nothing to carry.
6. Add the ten thousands. Now the next column to the left.
   2 + 4 = 6
   6 is less than 10, so write 6 in the ten thousands column. There is nothing to carry.
7. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	TTh	Th	H	T	O
   	2	7	3	1	5
   +	4	1	2	6	8
   	6	8	5	8	3
   				1

   
   27,315 + 41,268 = 68,583

Check. Use the opposite (inverse) operation: 68,583 − 41,268 = 27,315. ✓
Estimate: 27,000 + 41,000 = 68,000 (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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value.

   	HTh	TTh	Th	H	T	O
   	5	3	4	1	6	2
   +	2	1	4	7	8	6

2. Add the ones. Always start with the ones, on the right.
   2 + 6 = 8
   8 is less than 10, so write 8 in the ones column. There is nothing to carry.
3. Add the tens. Now the next column to the left.
   6 + 8 = 14
   14 tens is 1 hundred and 4 tens. Write 4 in the tens column and carry 1 to the hundreds column.
4. Add the hundreds. Now the next column to the left. Add the 1 we carried as well.
   1 + 7 + 1 = 9  (the red digit is the carry)
   9 is less than 10, so write 9 in the hundreds column. There is nothing to carry.
5. Add the thousands. Now the next column to the left.
   4 + 4 = 8
   8 is less than 10, so write 8 in the thousands column. There is nothing to carry.
6. Add the ten thousands. Now the next column to the left.
   3 + 1 = 4
   4 is less than 10, so write 4 in the ten thousands column. There is nothing to carry.
7. Add the hundred thousands. Now the next column to the left.
   5 + 2 = 7
   7 is less than 10, so write 7 in the hundred thousands column. There is nothing to carry.
8. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	HTh	TTh	Th	H	T	O
   	5	3	4	1	6	2
   +	2	1	4	7	8	6
   	7	4	8	9	4	8
   				1

   
   534,162 + 214,786 = 748,948

Check. Use the opposite (inverse) operation: 748,948 − 214,786 = 534,162. ✓
Estimate: 530,000 + 210,000 = 740,000 (rounding to the nearest 10,000). 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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value.

   	HTh	TTh	Th	H	T	O
   	3	0	5	8	1	1
   +	1	9	2	4	3	7

2. Add the ones. Always start with the ones, on the right.
   1 + 7 = 8
   8 is less than 10, so write 8 in the ones column. There is nothing to carry.
3. Add the tens. Now the next column to the left.
   1 + 3 = 4
   4 is less than 10, so write 4 in the tens column. There is nothing to carry.
4. Add the hundreds. Now the next column to the left.
   8 + 4 = 12
   12 hundreds is 1 thousand and 2 hundreds. Write 2 in the hundreds column and carry 1 to the thousands column.
5. Add the thousands. Now the next column to the left. Add the 1 we carried as well.
   5 + 2 + 1 = 8  (the red digit is the carry)
   8 is less than 10, so write 8 in the thousands column. There is nothing to carry.
6. Add the ten thousands. Now the next column to the left.
   0 + 9 = 9
   9 is less than 10, so write 9 in the ten thousands column. There is nothing to carry.
7. Add the hundred thousands. Now the next column to the left.
   3 + 1 = 4
   4 is less than 10, so write 4 in the hundred thousands column. There is nothing to carry.
8. 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	8	1	1
   +	1	9	2	4	3	7
   	4	9	8	2	4	8
   			1

   
   305,811 + 192,437 = 498,248

Check. Use the opposite (inverse) operation: 498,248 − 192,437 = 305,811. ✓
Estimate: 310,000 + 190,000 = 500,000 (rounding to the nearest 10,000). 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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value.

   	TTh	Th	H	T	O
   	3	7	4	8	6
   +	2	5	7	5	8

2. Add the ones. Always start with the ones, on the right.
   6 + 8 = 14
   14 ones is 1 ten and 4 ones. Write 4 in the ones column and carry 1 to the tens column.
3. Add the tens. Now the next column to the left. Add the 1 we carried as well.
   8 + 5 + 1 = 14  (the red digit is the carry)
   14 tens is 1 hundred and 4 tens. Write 4 in the tens column and carry 1 to the hundreds column.
4. Add the hundreds. Now the next column to the left. Add the 1 we carried as well.
   4 + 7 + 1 = 12  (the red digit is the carry)
   12 hundreds is 1 thousand and 2 hundreds. Write 2 in the hundreds column and carry 1 to the thousands column.
5. Add the thousands. Now the next column to the left. Add the 1 we carried as well.
   7 + 5 + 1 = 13  (the red digit is the carry)
   13 thousands is 1 ten thousand and 3 thousands. Write 3 in the thousands column and carry 1 to the ten thousands column.
6. Add the ten thousands. Now the next column to the left. Add the 1 we carried as well.
   3 + 2 + 1 = 6  (the red digit is the carry)
   6 is less than 10, so write 6 in the ten thousands column. There is nothing to carry.
7. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	TTh	Th	H	T	O
   	3	7	4	8	6
   +	2	5	7	5	8
   	6	3	2	4	4
   	1	1	1	1

   
   37,486 + 25,758 = 63,244

Check. Use the opposite (inverse) operation: 63,244 − 25,758 = 37,486. ✓
Estimate: 37,000 + 26,000 = 63,000 (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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value.

   	TTh	Th	H	T	O
   	6	8	9	2	5
   +	1	4	6	9	7

2. Add the ones. Always start with the ones, on the right.
   5 + 7 = 12
   12 ones is 1 ten and 2 ones. Write 2 in the ones column and carry 1 to the tens column.
3. Add the tens. Now the next column to the left. Add the 1 we carried as well.
   2 + 9 + 1 = 12  (the red digit is the carry)
   12 tens is 1 hundred and 2 tens. Write 2 in the tens column and carry 1 to the hundreds column.
4. Add the hundreds. Now the next column to the left. Add the 1 we carried as well.
   9 + 6 + 1 = 16  (the red digit is the carry)
   16 hundreds is 1 thousand and 6 hundreds. Write 6 in the hundreds column and carry 1 to the thousands column.
5. Add the thousands. Now the next column to the left. Add the 1 we carried as well.
   8 + 4 + 1 = 13  (the red digit is the carry)
   13 thousands is 1 ten thousand and 3 thousands. Write 3 in the thousands column and carry 1 to the ten thousands column.
6. Add the ten thousands. Now the next column to the left. Add the 1 we carried as well.
   6 + 1 + 1 = 8  (the red digit is the carry)
   8 is less than 10, so write 8 in the ten thousands column. There is nothing to carry.
7. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	TTh	Th	H	T	O
   	6	8	9	2	5
   +	1	4	6	9	7
   	8	3	6	2	2
   	1	1	1	1

   
   68,925 + 14,697 = 83,622

Check. Use the opposite (inverse) operation: 83,622 − 14,697 = 68,925. ✓
Estimate: 69,000 + 15,000 = 84,000 (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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value.

   	HTh	TTh	Th	H	T	O
   	4	7	2	8	6	5
   +	3	5	9	4	7	8

2. Add the ones. Always start with the ones, on the right.
   5 + 8 = 13
   13 ones is 1 ten and 3 ones. Write 3 in the ones column and carry 1 to the tens column.
3. Add the tens. Now the next column to the left. Add the 1 we carried as well.
   6 + 7 + 1 = 14  (the red digit is the carry)
   14 tens is 1 hundred and 4 tens. Write 4 in the tens column and carry 1 to the hundreds column.
4. Add the hundreds. Now the next column to the left. Add the 1 we carried as well.
   8 + 4 + 1 = 13  (the red digit is the carry)
   13 hundreds is 1 thousand and 3 hundreds. Write 3 in the hundreds column and carry 1 to the thousands column.
5. Add the thousands. Now the next column to the left. Add the 1 we carried as well.
   2 + 9 + 1 = 12  (the red digit is the carry)
   12 thousands is 1 ten thousand and 2 thousands. Write 2 in the thousands column and carry 1 to the ten thousands column.
6. Add the ten thousands. Now the next column to the left. Add the 1 we carried as well.
   7 + 5 + 1 = 13  (the red digit is the carry)
   13 ten thousands is 1 hundred thousand and 3 ten thousands. Write 3 in the ten thousands column and carry 1 to the hundred thousands column.
7. Add the hundred thousands. Now the next column to the left. Add the 1 we carried as well.
   4 + 3 + 1 = 8  (the red digit is the carry)
   8 is less than 10, so write 8 in the hundred thousands column. There is nothing to carry.
8. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	HTh	TTh	Th	H	T	O
   	4	7	2	8	6	5
   +	3	5	9	4	7	8
   	8	3	2	3	4	3
   	1	1	1	1	1

   
   472,865 + 359,478 = 832,343

Check. Use the opposite (inverse) operation: 832,343 − 359,478 = 472,865. ✓
Estimate: 470,000 + 360,000 = 830,000 (rounding to the nearest 10,000). 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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value.

   	HTh	TTh	Th	H	T	O
   	2	8	6	7	4	9
   +	1	9	5	8	7	6

2. Add the ones. Always start with the ones, on the right.
   9 + 6 = 15
   15 ones is 1 ten and 5 ones. Write 5 in the ones column and carry 1 to the tens column.
3. Add the tens. Now the next column to the left. Add the 1 we carried as well.
   4 + 7 + 1 = 12  (the red digit is the carry)
   12 tens is 1 hundred and 2 tens. Write 2 in the tens column and carry 1 to the hundreds column.
4. Add the hundreds. Now the next column to the left. Add the 1 we carried as well.
   7 + 8 + 1 = 16  (the red digit is the carry)
   16 hundreds is 1 thousand and 6 hundreds. Write 6 in the hundreds column and carry 1 to the thousands column.
5. Add the thousands. Now the next column to the left. Add the 1 we carried as well.
   6 + 5 + 1 = 12  (the red digit is the carry)
   12 thousands is 1 ten thousand and 2 thousands. Write 2 in the thousands column and carry 1 to the ten thousands column.
6. Add the ten thousands. Now the next column to the left. Add the 1 we carried as well.
   8 + 9 + 1 = 18  (the red digit is the carry)
   18 ten thousands is 1 hundred thousand and 8 ten thousands. Write 8 in the ten thousands column and carry 1 to the hundred thousands column.
7. Add the hundred thousands. Now the next column to the left. Add the 1 we carried as well.
   2 + 1 + 1 = 4  (the red digit is the carry)
   4 is less than 10, so write 4 in the hundred thousands column. There is nothing to carry.
8. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	HTh	TTh	Th	H	T	O
   	2	8	6	7	4	9
   +	1	9	5	8	7	6
   	4	8	2	6	2	5
   	1	1	1	1	1

   
   286,749 + 195,876 = 482,625

Check. Use the opposite (inverse) operation: 482,625 − 195,876 = 286,749. ✓
Estimate: 290,000 + 200,000 = 490,000 (rounding to the nearest 10,000). 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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value. The numbers have different lengths, so line them up on the right.

   	TTh	Th	H	T	O
   	4	5	2	0	8
   +		3	7	9	6

2. Add the ones. Always start with the ones, on the right.
   8 + 6 = 14
   14 ones is 1 ten and 4 ones. Write 4 in the ones column and carry 1 to the tens column.
3. Add the tens. Now the next column to the left. Add the 1 we carried as well.
   0 + 9 + 1 = 10  (the red digit is the carry)
   10 tens is 1 hundred and 0 tens. Write 0 in the tens column and carry 1 to the hundreds column.
4. Add the hundreds. Now the next column to the left. Add the 1 we carried as well.
   2 + 7 + 1 = 10  (the red digit is the carry)
   10 hundreds is 1 thousand and 0 hundreds. Write 0 in the hundreds column and carry 1 to the thousands column.
5. Add the thousands. Now the next column to the left. Add the 1 we carried as well.
   5 + 3 + 1 = 9  (the red digit is the carry)
   9 is less than 10, so write 9 in the thousands column. There is nothing to carry.
6. Bring down the ten thousands digit. The other numbers have no digit in this column, so there is nothing to add.
   There is only one digit here, so write 4 in the ten thousands column.
7. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	TTh	Th	H	T	O
   	4	5	2	0	8
   +		3	7	9	6
   	4	9	0	0	4
   		1	1	1

   
   45,208 + 3,796 = 49,004

Check. Use the opposite (inverse) operation: 49,004 − 3,796 = 45,208. ✓
Estimate: 45,200 + 3,800 = 49,000 (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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value. The numbers have different lengths, so line them up on the right.

   	TTh	Th	H	T	O
   		7	4	5	9
   +	6	2	3	8	5

2. Add the ones. Always start with the ones, on the right.
   9 + 5 = 14
   14 ones is 1 ten and 4 ones. Write 4 in the ones column and carry 1 to the tens column.
3. Add the tens. Now the next column to the left. Add the 1 we carried as well.
   5 + 8 + 1 = 14  (the red digit is the carry)
   14 tens is 1 hundred and 4 tens. Write 4 in the tens column and carry 1 to the hundreds column.
4. Add the hundreds. Now the next column to the left. Add the 1 we carried as well.
   4 + 3 + 1 = 8  (the red digit is the carry)
   8 is less than 10, so write 8 in the hundreds column. There is nothing to carry.
5. Add the thousands. Now the next column to the left.
   7 + 2 = 9
   9 is less than 10, so write 9 in the thousands column. There is nothing to carry.
6. Bring down the ten thousands digit. The other numbers have no digit in this column, so there is nothing to add.
   There is only one digit here, so write 6 in the ten thousands column.
7. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	TTh	Th	H	T	O
   		7	4	5	9
   +	6	2	3	8	5
   	6	9	8	4	4
   			1	1

   
   7,459 + 62,385 = 69,844

Check. Use the opposite (inverse) operation: 69,844 − 62,385 = 7,459. ✓
Estimate: 7,500 + 62,400 = 69,900 (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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value. The numbers have different lengths, so line them up on the right.

   	HTh	TTh	Th	H	T	O
   	2	3	1	6	8	4
   +			8	9	7	5

2. Add the ones. Always start with the ones, on the right.
   4 + 5 = 9
   9 is less than 10, so write 9 in the ones column. There is nothing to carry.
3. Add the tens. Now the next column to the left.
   8 + 7 = 15
   15 tens is 1 hundred and 5 tens. Write 5 in the tens column and carry 1 to the hundreds column.
4. Add the hundreds. Now the next column to the left. Add the 1 we carried as well.
   6 + 9 + 1 = 16  (the red digit is the carry)
   16 hundreds is 1 thousand and 6 hundreds. Write 6 in the hundreds column and carry 1 to the thousands column.
5. Add the thousands. Now the next column to the left. Add the 1 we carried as well.
   1 + 8 + 1 = 10  (the red digit is the carry)
   10 thousands is 1 ten thousand and 0 thousands. Write 0 in the thousands column and carry 1 to the ten thousands column.
6. Add the ten thousands. Now the next column to the left. Add the 1 we carried as well.
   3 + 1 = 4  (the red digit is the carry)
   4 is less than 10, so write 4 in the ten thousands column. There is nothing to carry.
7. Bring down the hundred thousands digit. The other numbers have no digit in this column, so there is nothing to add.
   There is only one digit here, so write 2 in the hundred thousands column.
8. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	HTh	TTh	Th	H	T	O
   	2	3	1	6	8	4
   +			8	9	7	5
   	2	4	0	6	5	9
   		1	1	1

   
   231,684 + 8,975 = 240,659

Check. Use the opposite (inverse) operation: 240,659 − 8,975 = 231,684. ✓
Estimate: 231,700 + 9,000 = 240,700 (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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value. The numbers have different lengths, so line them up on the right.

   	HTh	TTh	Th	H	T	O
   				9	0	6
   +	4	8	1	2	5	7

2. Add the ones. Always start with the ones, on the right.
   6 + 7 = 13
   13 ones is 1 ten and 3 ones. Write 3 in the ones column and carry 1 to the tens column.
3. Add the tens. Now the next column to the left. Add the 1 we carried as well.
   0 + 5 + 1 = 6  (the red digit is the carry)
   6 is less than 10, so write 6 in the tens column. There is nothing to carry.
4. Add the hundreds. Now the next column to the left.
   9 + 2 = 11
   11 hundreds is 1 thousand and 1 hundred. Write 1 in the hundreds column and carry 1 to the thousands column.
5. Add the thousands. Now the next column to the left. Add the 1 we carried as well.
   1 + 1 = 2  (the red digit is the carry)
   2 is less than 10, so write 2 in the thousands column. There is nothing to carry.
6. Bring down the ten thousands digit. The other numbers have no digit in this column, so there is nothing to add.
   There is only one digit here, so write 8 in the ten thousands column.
7. Bring down the hundred thousands digit. The other numbers have no digit in this column, so there is nothing to add.
   There is only one digit here, so write 4 in the hundred thousands column.
8. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	HTh	TTh	Th	H	T	O
   				9	0	6
   +	4	8	1	2	5	7
   	4	8	2	1	6	3
   			1		1

   
   906 + 481,257 = 482,163

Check. Use the opposite (inverse) operation: 482,163 − 481,257 = 906. ✓
Estimate: 910 + 481,260 = 482,170 (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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value. The numbers have different lengths, so line them up on the right.

   	HTh	TTh	Th	H	T	O
   	3	0	6	0	4	0
   +		9	5	9	6	0

2. 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.
3. Add the tens. Now the next column to the left.
   4 + 6 = 10
   10 tens is 1 hundred and 0 tens. Write 0 in the tens column and carry 1 to the hundreds column.
4. Add the hundreds. Now the next column to the left. Add the 1 we carried as well.
   0 + 9 + 1 = 10  (the red digit is the carry)
   10 hundreds is 1 thousand and 0 hundreds. Write 0 in the hundreds column and carry 1 to the thousands column.
5. Add the thousands. Now the next column to the left. Add the 1 we carried as well.
   6 + 5 + 1 = 12  (the red digit is the carry)
   12 thousands is 1 ten thousand and 2 thousands. Write 2 in the thousands column and carry 1 to the ten thousands column.
6. Add the ten thousands. Now the next column to the left. Add the 1 we carried as well.
   0 + 9 + 1 = 10  (the red digit is the carry)
   10 ten thousands is 1 hundred thousand and 0 ten thousands. Write 0 in the ten thousands column and carry 1 to the hundred thousands column.
7. Add the hundred thousands. Now the next column to the left. Add the 1 we carried as well.
   3 + 1 = 4  (the red digit is the carry)
   4 is less than 10, so write 4 in the hundred thousands column. There is nothing to carry.
8. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	HTh	TTh	Th	H	T	O
   	3	0	6	0	4	0
   +		9	5	9	6	0
   	4	0	2	0	0	0
   	1	1	1	1

   
   306,040 + 95,960 = 402,000

Check. Use the opposite (inverse) operation: 402,000 − 95,960 = 306,040. ✓
Estimate: 306,000 + 96,000 = 402,000 (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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value. The numbers have different lengths, so line them up on the right.

   	HTh	TTh	Th	H	T	O
   	4	0	0	9	0	8
   +		9	9	0	9	2

2. Add the ones. Always start with the ones, on the right.
   8 + 2 = 10
   10 ones is 1 ten and 0 ones. Write 0 in the ones column and carry 1 to the tens column.
3. Add the tens. Now the next column to the left. Add the 1 we carried as well.
   0 + 9 + 1 = 10  (the red digit is the carry)
   10 tens is 1 hundred and 0 tens. Write 0 in the tens column and carry 1 to the hundreds column.
4. Add the hundreds. Now the next column to the left. Add the 1 we carried as well.
   9 + 0 + 1 = 10  (the red digit is the carry)
   10 hundreds is 1 thousand and 0 hundreds. Write 0 in the hundreds column and carry 1 to the thousands column.
5. Add the thousands. Now the next column to the left. Add the 1 we carried as well.
   0 + 9 + 1 = 10  (the red digit is the carry)
   10 thousands is 1 ten thousand and 0 thousands. Write 0 in the thousands column and carry 1 to the ten thousands column.
6. Add the ten thousands. Now the next column to the left. Add the 1 we carried as well.
   0 + 9 + 1 = 10  (the red digit is the carry)
   10 ten thousands is 1 hundred thousand and 0 ten thousands. Write 0 in the ten thousands column and carry 1 to the hundred thousands column.
7. Add the hundred thousands. Now the next column to the left. Add the 1 we carried as well.
   4 + 1 = 5  (the red digit is the carry)
   5 is less than 10, so write 5 in the hundred thousands column. There is nothing to carry.
8. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	HTh	TTh	Th	H	T	O
   	4	0	0	9	0	8
   +		9	9	0	9	2
   	5	0	0	0	0	0
   	1	1	1	1	1

   
   400,908 + 99,092 = 500,000

Check. Use the opposite (inverse) operation: 500,000 − 99,092 = 400,908. ✓
Estimate: 401,000 + 99,000 = 500,000 (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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value. The numbers have different lengths, so line them up on the right.

   	HTh	TTh	Th	H	T	O
   	1	9	9	9	9	9
   +						1

2. Add the ones. Always start with the ones, on the right.
   9 + 1 = 10
   10 ones is 1 ten and 0 ones. Write 0 in the ones column and carry 1 to the tens column.
3. Add the tens. Now the next column to the left. Add the 1 we carried as well.
   9 + 1 = 10  (the red digit is the carry)
   10 tens is 1 hundred and 0 tens. Write 0 in the tens column and carry 1 to the hundreds column.
4. Add the hundreds. Now the next column to the left. Add the 1 we carried as well.
   9 + 1 = 10  (the red digit is the carry)
   10 hundreds is 1 thousand and 0 hundreds. Write 0 in the hundreds column and carry 1 to the thousands column.
5. Add the thousands. Now the next column to the left. Add the 1 we carried as well.
   9 + 1 = 10  (the red digit is the carry)
   10 thousands is 1 ten thousand and 0 thousands. Write 0 in the thousands column and carry 1 to the ten thousands column.
6. Add the ten thousands. Now the next column to the left. Add the 1 we carried as well.
   9 + 1 = 10  (the red digit is the carry)
   10 ten thousands is 1 hundred thousand and 0 ten thousands. Write 0 in the ten thousands column and carry 1 to the hundred thousands column.
7. Add the hundred thousands. Now the next column to the left. Add the 1 we carried as well.
   1 + 1 = 2  (the red digit is the carry)
   2 is less than 10, so write 2 in the hundred thousands column. There is nothing to carry.
8. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	HTh	TTh	Th	H	T	O
   	1	9	9	9	9	9
   +						1
   	2	0	0	0	0	0
   	1	1	1	1	1

   
   199,999 + 1 = 200,000

Check. Use the opposite (inverse) operation: 200,000 − 1 = 199,999. ✓
Estimate: 200,000 + 0 = 200,000 (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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value.

   	M	HTh	TTh	Th	H	T	O
   		2	5	0	0	5	0
   +		7	4	9	9	5	0

2. 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.
3. Add the tens. Now the next column to the left.
   5 + 5 = 10
   10 tens is 1 hundred and 0 tens. Write 0 in the tens column and carry 1 to the hundreds column.
4. Add the hundreds. Now the next column to the left. Add the 1 we carried as well.
   0 + 9 + 1 = 10  (the red digit is the carry)
   10 hundreds is 1 thousand and 0 hundreds. Write 0 in the hundreds column and carry 1 to the thousands column.
5. Add the thousands. Now the next column to the left. Add the 1 we carried as well.
   0 + 9 + 1 = 10  (the red digit is the carry)
   10 thousands is 1 ten thousand and 0 thousands. Write 0 in the thousands column and carry 1 to the ten thousands column.
6. Add the ten thousands. Now the next column to the left. Add the 1 we carried as well.
   5 + 4 + 1 = 10  (the red digit is the carry)
   10 ten thousands is 1 hundred thousand and 0 ten thousands. Write 0 in the ten thousands column and carry 1 to the hundred thousands column.
7. Add the hundred thousands. Now the next column to the left. Add the 1 we carried as well.
   2 + 7 + 1 = 10  (the red digit is the carry)
   10 hundred thousands is 1 million and 0 hundred thousands. Write 0 in the hundred thousands column and carry 1 to the millions column.
8. Write the carried digit. There are no digits left in the millions column, but we carried 1 into it.
   There is only one digit here, so write 1 in the millions column.
9. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	M	HTh	TTh	Th	H	T	O
   		2	5	0	0	5	0
   +		7	4	9	9	5	0
   	1	0	0	0	0	0	0
   	1	1	1	1	1

   
   250,050 + 749,950 = 1,000,000

Check. Use the opposite (inverse) operation: 1,000,000 − 749,950 = 250,050. ✓
Estimate: 250,000 + 750,000 = 1,000,000 (rounding to the nearest 10,000). 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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value. The numbers have different lengths, so line them up on the right.

   	TTh	Th	H	T	O
   		4	3	2	5
   +	1	8	7	6	0
   +			3	5	7

2. Add the ones. Always start with the ones, on the right.
   5 + 0 + 7 = 12
   12 ones is 1 ten and 2 ones. Write 2 in the ones column and carry 1 to the tens column.
3. Add the tens. Now the next column to the left. Add the 1 we carried as well.
   2 + 6 + 5 + 1 = 14  (the red digit is the carry)
   14 tens is 1 hundred and 4 tens. Write 4 in the tens column and carry 1 to the hundreds column.
4. Add the hundreds. Now the next column to the left. Add the 1 we carried as well.
   3 + 7 + 3 + 1 = 14  (the red digit is the carry)
   14 hundreds is 1 thousand and 4 hundreds. Write 4 in the hundreds column and carry 1 to the thousands column.
5. Add the thousands. Now the next column to the left. Add the 1 we carried as well.
   4 + 8 + 1 = 13  (the red digit is the carry)
   13 thousands is 1 ten thousand and 3 thousands. Write 3 in the thousands column and carry 1 to the ten thousands column.
6. Add the ten thousands. Now the next column to the left. Add the 1 we carried as well.
   1 + 1 = 2  (the red digit is the carry)
   2 is less than 10, so write 2 in the ten thousands column. There is nothing to carry.
7. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	TTh	Th	H	T	O
   		4	3	2	5
   +	1	8	7	6	0
   +			3	5	7
   	2	3	4	4	2
   	1	1	1	1

   
   4,325 + 18,760 + 357 = 23,442

Check. Use the opposite (inverse) operation: 23,442 − 18,760 − 357 = 4,325. ✓
Estimate: 4,330 + 18,760 + 360 = 23,450 (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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value. The numbers have different lengths, so line them up on the right.

   	HTh	TTh	Th	H	T	O
   		6	2	4	5	0
   +			8	7	9	5
   +		3	1	2	0	6

2. Add the ones. Always start with the ones, on the right.
   0 + 5 + 6 = 11
   11 ones is 1 ten and 1 one. Write 1 in the ones column and carry 1 to the tens column.
3. Add the tens. Now the next column to the left. Add the 1 we carried as well.
   5 + 9 + 0 + 1 = 15  (the red digit is the carry)
   15 tens is 1 hundred and 5 tens. Write 5 in the tens column and carry 1 to the hundreds column.
4. Add the hundreds. Now the next column to the left. Add the 1 we carried as well.
   4 + 7 + 2 + 1 = 14  (the red digit is the carry)
   14 hundreds is 1 thousand and 4 hundreds. Write 4 in the hundreds column and carry 1 to the thousands column.
5. Add the thousands. Now the next column to the left. Add the 1 we carried as well.
   2 + 8 + 1 + 1 = 12  (the red digit is the carry)
   12 thousands is 1 ten thousand and 2 thousands. Write 2 in the thousands column and carry 1 to the ten thousands column.
6. Add the ten thousands. Now the next column to the left. Add the 1 we carried as well.
   6 + 3 + 1 = 10  (the red digit is the carry)
   10 ten thousands is 1 hundred thousand and 0 ten thousands. Write 0 in the ten thousands column and carry 1 to the hundred thousands column.
7. Write the carried digit. There are no digits left in the hundred thousands column, but we carried 1 into it.
   There is only one digit here, so write 1 in the hundred thousands column.
8. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	HTh	TTh	Th	H	T	O
   		6	2	4	5	0
   +			8	7	9	5
   +		3	1	2	0	6
   	1	0	2	4	5	1
   	1	1	1	1	1

   
   62,450 + 8,795 + 31,206 = 102,451

Check. Use the opposite (inverse) operation: 102,451 − 8,795 − 31,206 = 62,450. ✓
Estimate: 62,500 + 8,800 + 31,200 = 102,500 (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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value. The numbers have different lengths, so line them up on the right.

   	HTh	TTh	Th	H	T	O
   	1	2	5	6	0	0
   +		7	4	3	5	0
   +		9	8	4	2	5

2. Add the ones. Always start with the ones, on the right.
   0 + 0 + 5 = 5
   5 is less than 10, so write 5 in the ones column. There is nothing to carry.
3. Add the tens. Now the next column to the left.
   0 + 5 + 2 = 7
   7 is less than 10, so write 7 in the tens column. There is nothing to carry.
4. Add the hundreds. Now the next column to the left.
   6 + 3 + 4 = 13
   13 hundreds is 1 thousand and 3 hundreds. Write 3 in the hundreds column and carry 1 to the thousands column.
5. Add the thousands. Now the next column to the left. Add the 1 we carried as well.
   5 + 4 + 8 + 1 = 18  (the red digit is the carry)
   18 thousands is 1 ten thousand and 8 thousands. Write 8 in the thousands column and carry 1 to the ten thousands column.
6. Add the ten thousands. Now the next column to the left. Add the 1 we carried as well.
   2 + 7 + 9 + 1 = 19  (the red digit is the carry)
   19 ten thousands is 1 hundred thousand and 9 ten thousands. Write 9 in the ten thousands column and carry 1 to the hundred thousands column.
7. Add the hundred thousands. Now the next column to the left. Add the 1 we carried as well.
   1 + 1 = 2  (the red digit is the carry)
   2 is less than 10, so write 2 in the hundred thousands column. There is nothing to carry.
8. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	HTh	TTh	Th	H	T	O
   	1	2	5	6	0	0
   +		7	4	3	5	0
   +		9	8	4	2	5
   	2	9	8	3	7	5
   	1	1	1

   
   125,600 + 74,350 + 98,425 = 298,375

Check. Use the opposite (inverse) operation: 298,375 − 74,350 − 98,425 = 125,600. ✓
Estimate: 126,000 + 74,000 + 98,000 = 298,000 (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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value.

   	M	HTh	TTh	Th	H	T	O
   		6	7	4	5	9	2
   +		5	3	8	7	1	6

2. Add the ones. Always start with the ones, on the right.
   2 + 6 = 8
   8 is less than 10, so write 8 in the ones column. There is nothing to carry.
3. Add the tens. Now the next column to the left.
   9 + 1 = 10
   10 tens is 1 hundred and 0 tens. Write 0 in the tens column and carry 1 to the hundreds column.
4. Add the hundreds. Now the next column to the left. Add the 1 we carried as well.
   5 + 7 + 1 = 13  (the red digit is the carry)
   13 hundreds is 1 thousand and 3 hundreds. Write 3 in the hundreds column and carry 1 to the thousands column.
5. Add the thousands. Now the next column to the left. Add the 1 we carried as well.
   4 + 8 + 1 = 13  (the red digit is the carry)
   13 thousands is 1 ten thousand and 3 thousands. Write 3 in the thousands column and carry 1 to the ten thousands column.
6. Add the ten thousands. Now the next column to the left. Add the 1 we carried as well.
   7 + 3 + 1 = 11  (the red digit is the carry)
   11 ten thousands is 1 hundred thousand and 1 ten thousand. Write 1 in the ten thousands column and carry 1 to the hundred thousands column.
7. Add the hundred thousands. Now the next column to the left. Add the 1 we carried as well.
   6 + 5 + 1 = 12  (the red digit is the carry)
   12 hundred thousands is 1 million and 2 hundred thousands. Write 2 in the hundred thousands column and carry 1 to the millions column.
8. Write the carried digit. There are no digits left in the millions column, but we carried 1 into it.
   There is only one digit here, so write 1 in the millions column.
9. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	M	HTh	TTh	Th	H	T	O
   		6	7	4	5	9	2
   +		5	3	8	7	1	6
   	1	2	1	3	3	0	8
   	1	1	1	1	1

   
   674,592 + 538,716 = 1,213,308

Check. Use the opposite (inverse) operation: 1,213,308 − 538,716 = 674,592. ✓
Estimate: 670,000 + 540,000 = 1,210,000 (rounding to the nearest 10,000). 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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value.

   	M	HTh	TTh	Th	H	T	O
   		8	5	0	0	0	0
   +		2	7	5	4	0	0

2. 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.
3. 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.
4. Add the hundreds. Now the next column to the left.
   0 + 4 = 4
   4 is less than 10, so write 4 in the hundreds column. There is nothing to carry.
5. Add the thousands. Now the next column to the left.
   0 + 5 = 5
   5 is less than 10, so write 5 in the thousands column. There is nothing to carry.
6. Add the ten thousands. Now the next column to the left.
   5 + 7 = 12
   12 ten thousands is 1 hundred thousand and 2 ten thousands. Write 2 in the ten thousands column and carry 1 to the hundred thousands column.
7. Add the hundred thousands. Now the next column to the left. Add the 1 we carried as well.
   8 + 2 + 1 = 11  (the red digit is the carry)
   11 hundred thousands is 1 million and 1 hundred thousand. Write 1 in the hundred thousands column and carry 1 to the millions column.
8. Write the carried digit. There are no digits left in the millions column, but we carried 1 into it.
   There is only one digit here, so write 1 in the millions column.
9. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	M	HTh	TTh	Th	H	T	O
   		8	5	0	0	0	0
   +		2	7	5	4	0	0
   	1	1	2	5	4	0	0
   	1	1

   
   850,000 + 275,400 = 1,125,400

Check. Use the opposite (inverse) operation: 1,125,400 − 275,400 = 850,000. ✓
Estimate: 850,000 + 280,000 = 1,130,000 (rounding to the nearest 10,000). 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 to the next column. The sum or total is the answer to an addition.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. If a column makes 10 or more, carry to the next column.

1. Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and so on, so every digit is added to digits of the same value.

   	M	HTh	TTh	Th	H	T	O
   		9	9	9	9	9	9
   +		9	9	9	9	9	9

2. Add the ones. Always start with the ones, on the right.
   9 + 9 = 18
   18 ones is 1 ten and 8 ones. Write 8 in the ones column and carry 1 to the tens column.
3. Add the tens. Now the next column to the left. Add the 1 we carried as well.
   9 + 9 + 1 = 19  (the red digit is the carry)
   19 tens is 1 hundred and 9 tens. Write 9 in the tens column and carry 1 to the hundreds column.
4. Add the hundreds. Now the next column to the left. Add the 1 we carried as well.
   9 + 9 + 1 = 19  (the red digit is the carry)
   19 hundreds is 1 thousand and 9 hundreds. Write 9 in the hundreds column and carry 1 to the thousands column.
5. Add the thousands. Now the next column to the left. Add the 1 we carried as well.
   9 + 9 + 1 = 19  (the red digit is the carry)
   19 thousands is 1 ten thousand and 9 thousands. Write 9 in the thousands column and carry 1 to the ten thousands column.
6. Add the ten thousands. Now the next column to the left. Add the 1 we carried as well.
   9 + 9 + 1 = 19  (the red digit is the carry)
   19 ten thousands is 1 hundred thousand and 9 ten thousands. Write 9 in the ten thousands column and carry 1 to the hundred thousands column.
7. Add the hundred thousands. Now the next column to the left. Add the 1 we carried as well.
   9 + 9 + 1 = 19  (the red digit is the carry)
   19 hundred thousands is 1 million and 9 hundred thousands. Write 9 in the hundred thousands column and carry 1 to the millions column.
8. Write the carried digit. There are no digits left in the millions column, but we carried 1 into it.
   There is only one digit here, so write 1 in the millions column.
9. Read the answer. Check that the answer has a sensible number of digits, then write it.

   	M	HTh	TTh	Th	H	T	O
   		9	9	9	9	9	9
   +		9	9	9	9	9	9
   	1	9	9	9	9	9	8
   	1	1	1	1	1	1

   
   999,999 + 999,999 = 1,999,998

Check. Use the opposite (inverse) operation: 1,999,998 − 999,999 = 999,999. ✓
Estimate: 1,000,000 + 1,000,000 = 2,000,000 (rounding to the nearest 10,000). 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.

Method. To make the total as big as possible, put the biggest digits in the biggest columns. Think about how much each column is worth.

1. Look at the columns. Only the five-digit number has a ten thousands digit, so that column has just one digit. The thousands, hundreds, tens and ones columns each have two digits (one from each number).
   TTh: 1 digit   Th, H, T, O: 2 digits each
2. Put the biggest digit in the ten thousands. A ten thousand is worth much more than any other column, so it gets the 9.
   9 _ _ _ _  +  _ _ _ _
3. Fill the other columns in order. The next two biggest digits go in the thousands, then the hundreds, the tens and the ones.
   8 and 7 in the thousands
   6 and 5 in the hundreds
   4 and 3 in the tens
   2 and 1 in the ones
4. Make the two numbers and add. Any split of each pair between the two numbers gives the same total.
   98,642 + 7,531
   

   	HTh	TTh	Th	H	T	O
   		9	8	6	4	2
   +			7	5	3	1
   	1	0	6	1	7	3
   	1	1	1

Check. Column by column: 90,000 + 15,000 + 1,100 + 70 + 3 = 106,173. ✓

Watch out. Check that you used every digit from 1 to 9 exactly once.

Method. To make the total as small as possible, put the smallest digits in the biggest columns.

1. Start with the biggest column. The ten thousands digit is worth the most, so it gets the smallest digit. It cannot be 0, and we have no 0, so it gets the 1.
   1 _ _ _ _  +  _ _ _ _
2. Fill the other columns in order. The next smallest digits go in the thousands, then the hundreds, the tens and the ones.
   2 and 3 in the thousands
   4 and 5 in the hundreds
   6 and 7 in the tens
   8 and 9 in the ones
3. Make the two numbers and add. Any split of each pair gives the same total.
   12,468 + 3,579
   

   	TTh	Th	H	T	O
   	1	2	4	6	8
   +		3	5	7	9
   	1	6	0	4	7
   		1	1	1

Check. Column by column: 10,000 + 5,000 + 900 + 130 + 17 = 16,047. ✓

Watch out. Check that you used every digit from 1 to 9 exactly once.