Year 4: Column multiplication: expanded and short

Key words. The expanded method writes each partial product on its own line, so you can see every step. It leads to the short method.

Method. Multiply each digit of the number by the one-digit number, starting with the ones. Write each answer on its own line. Then add the lines.

1. Write the numbers in a column. The number to multiply goes on top. The one-digit number goes underneath, on the right.

   	36
   ×	4
   	24	6 × 4
   	120	30 × 4

2. Multiply the ones. Always start on the right.
   6 × 4 = 24
3. Multiply the tens. The digit 3 is worth 30, so multiply 30 by 4, not just 3.
   30 is 3 tens.  3 × 4 = 12, so 3 tens × 4 = 12 tens = 120
4. Add the lines together. Draw a line and add up the partial products.

   	36
   ×	4
   	24	6 × 4
   	120	30 × 4
   	144

   
   24 + 120 = 144
5. Write the answer.
   36 × 4 = 144

Check. Estimate: 36 is about 40 (to the nearest 10). 40 × 4 = 160. Our answer, 144, is a bit less than 160, which is right because we rounded up. ✓

Watch out. Multiply the whole value of each digit: the 4 in 347 is worth 40, so work out 40 × 6, not 4 × 6.

Key words. The expanded method writes each partial product on its own line, so you can see every step. It leads to the short method.

Method. Multiply each digit of the number by the one-digit number, starting with the ones. Write each answer on its own line. Then add the lines.

1. Write the numbers in a column. The number to multiply goes on top. The one-digit number goes underneath, on the right.

   	52
   ×	7
   	14	2 × 7
   	350	50 × 7

2. Multiply the ones. Always start on the right.
   2 × 7 = 14
3. Multiply the tens. The digit 5 is worth 50, so multiply 50 by 7, not just 5.
   50 is 5 tens.  5 × 7 = 35, so 5 tens × 7 = 35 tens = 350
4. Add the lines together. Draw a line and add up the partial products.

   	52
   ×	7
   	14	2 × 7
   	350	50 × 7
   	364

   
   14 + 350 = 364
5. Write the answer.
   52 × 7 = 364

Check. Estimate: 52 is about 50 (to the nearest 10). 50 × 7 = 350. Our answer, 364, is a bit more than 350, which is right because we rounded down. ✓

Watch out. Multiply the whole value of each digit: the 4 in 347 is worth 40, so work out 40 × 6, not 4 × 6.

Key words. The expanded method writes each partial product on its own line, so you can see every step. It leads to the short method.

Method. Multiply each digit of the number by the one-digit number, starting with the ones. Write each answer on its own line. Then add the lines.

1. Write the numbers in a column. The number to multiply goes on top. The one-digit number goes underneath, on the right.

   	48
   ×	5
   	40	8 × 5
   	200	40 × 5

2. Multiply the ones. Always start on the right.
   8 × 5 = 40
3. Multiply the tens. The digit 4 is worth 40, so multiply 40 by 5, not just 4.
   40 is 4 tens.  4 × 5 = 20, so 4 tens × 5 = 20 tens = 200
4. Add the lines together. Draw a line and add up the partial products.

   	48
   ×	5
   	40	8 × 5
   	200	40 × 5
   	240

   
   40 + 200 = 240
5. Write the answer.
   48 × 5 = 240

Check. Estimate: 48 is about 50 (to the nearest 10). 50 × 5 = 250. Our answer, 240, is a bit less than 250, which is right because we rounded up. ✓

Watch out. Multiply the whole value of each digit: the 4 in 347 is worth 40, so work out 40 × 6, not 4 × 6.

Key words. The expanded method writes each partial product on its own line, so you can see every step. It leads to the short method.

Method. Multiply each digit of the number by the one-digit number, starting with the ones. Write each answer on its own line. Then add the lines.

1. Write the numbers in a column. The number to multiply goes on top. The one-digit number goes underneath, on the right.

   	75
   ×	6
   	30	5 × 6
   	420	70 × 6

2. Multiply the ones. Always start on the right.
   5 × 6 = 30
3. Multiply the tens. The digit 7 is worth 70, so multiply 70 by 6, not just 7.
   70 is 7 tens.  7 × 6 = 42, so 7 tens × 6 = 42 tens = 420
4. Add the lines together. Draw a line and add up the partial products.

   	75
   ×	6
   	30	5 × 6
   	420	70 × 6
   	450

   
   30 + 420 = 450
5. Write the answer.
   75 × 6 = 450

Check. Estimate: 75 is about 80 (to the nearest 10). 80 × 6 = 480. Our answer, 450, is a bit less than 480, which is right because we rounded up. ✓

Watch out. Multiply the whole value of each digit: the 4 in 347 is worth 40, so work out 40 × 6, not 4 × 6.

Key words. The expanded method writes each partial product on its own line, so you can see every step. It leads to the short method.

Method. Multiply each digit of the number by the one-digit number, starting with the ones. Write each answer on its own line. Then add the lines.

1. Write the numbers in a column. The number to multiply goes on top. The one-digit number goes underneath, on the right.

   	123
   ×	4
   	12	3 × 4
   	80	20 × 4
   	400	100 × 4

2. Multiply the ones. Always start on the right.
   3 × 4 = 12
3. Multiply the tens. The digit 2 is worth 20, so multiply 20 by 4, not just 2.
   20 is 2 tens.  2 × 4 = 8, so 2 tens × 4 = 8 tens = 80
4. Multiply the hundreds. The digit 1 is worth 100, so multiply 100 by 4, not just 1.
   100 is 1 hundred.  1 × 4 = 4, so 1 hundred × 4 = 4 hundreds = 400
5. Add the lines together. Draw a line and add up the partial products.

   	123
   ×	4
   	12	3 × 4
   	80	20 × 4
   	400	100 × 4
   	492

   
   12 + 80 = 92
   92 + 400 = 492
6. Write the answer.
   123 × 4 = 492

Check. Estimate: 123 is about 100 (to the nearest 100). 100 × 4 = 400. Our answer, 492, is a bit more than 400, which is right because we rounded down. ✓

Watch out. Multiply the whole value of each digit: the 4 in 347 is worth 40, so work out 40 × 6, not 4 × 6.

Key words. The expanded method writes each partial product on its own line, so you can see every step. It leads to the short method.

Method. Multiply each digit of the number by the one-digit number, starting with the ones. Write each answer on its own line. Then add the lines.

1. Write the numbers in a column. The number to multiply goes on top. The one-digit number goes underneath, on the right.

   	254
   ×	3
   	12	4 × 3
   	150	50 × 3
   	600	200 × 3

2. Multiply the ones. Always start on the right.
   4 × 3 = 12
3. Multiply the tens. The digit 5 is worth 50, so multiply 50 by 3, not just 5.
   50 is 5 tens.  5 × 3 = 15, so 5 tens × 3 = 15 tens = 150
4. Multiply the hundreds. The digit 2 is worth 200, so multiply 200 by 3, not just 2.
   200 is 2 hundreds.  2 × 3 = 6, so 2 hundreds × 3 = 6 hundreds = 600
5. Add the lines together. Draw a line and add up the partial products.

   	254
   ×	3
   	12	4 × 3
   	150	50 × 3
   	600	200 × 3
   	762

   
   12 + 150 = 162
   162 + 600 = 762
6. Write the answer.
   254 × 3 = 762

Check. Estimate: 254 is about 300 (to the nearest 100). 300 × 3 = 900. Our answer, 762, is a bit less than 900, which is right because we rounded up. ✓

Watch out. Multiply the whole value of each digit: the 4 in 347 is worth 40, so work out 40 × 6, not 4 × 6.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	T	O
   	2	1
   ×		4

2. Multiply the ones. Always start with the ones, on the right.
   1 × 4 = 4
   4 is less than 10, so write 4 in the ones column. There is nothing to carry.
3. Multiply the tens. Now the next column to the left.
   2 × 4 = 8
   8 is less than 10, so write 8 in the tens column. There is nothing to carry.
4. Read the answer. Check that the answer has about the right number of digits, then write it.

   	T	O
   	2	1
   ×		4
   	8	4

   
   21 × 4 = 84

Check. Estimate: 21 is about 20 (to the nearest 10). 20 × 4 = 80. Our answer, 84, is a bit more than 80, which is right because we rounded down. ✓

Watch out. Start on the right with the ones. Multiply every digit by the one-digit number.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	T	O
   	3	2
   ×		3

2. Multiply the ones. Always start with the ones, on the right.
   2 × 3 = 6
   6 is less than 10, so write 6 in the ones column. There is nothing to carry.
3. Multiply the tens. Now the next column to the left.
   3 × 3 = 9
   9 is less than 10, so write 9 in the tens column. There is nothing to carry.
4. Read the answer. Check that the answer has about the right number of digits, then write it.

   	T	O
   	3	2
   ×		3
   	9	6

   
   32 × 3 = 96

Check. Estimate: 32 is about 30 (to the nearest 10). 30 × 3 = 90. Our answer, 96, is a bit more than 90, which is right because we rounded down. ✓

Watch out. Start on the right with the ones. Multiply every digit by the one-digit number.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	T	O
   	4	2
   ×		2

2. Multiply the ones. Always start with the ones, on the right.
   2 × 2 = 4
   4 is less than 10, so write 4 in the ones column. There is nothing to carry.
3. Multiply the tens. Now the next column to the left.
   4 × 2 = 8
   8 is less than 10, so write 8 in the tens column. There is nothing to carry.
4. Read the answer. Check that the answer has about the right number of digits, then write it.

   	T	O
   	4	2
   ×		2
   	8	4

   
   42 × 2 = 84

Check. Estimate: 42 is about 40 (to the nearest 10). 40 × 2 = 80. Our answer, 84, is a bit more than 80, which is right because we rounded down. ✓

Watch out. Start on the right with the ones. Multiply every digit by the one-digit number.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	T	O
   	3	3
   ×		3

2. Multiply the ones. Always start with the ones, on the right.
   3 × 3 = 9
   9 is less than 10, so write 9 in the ones column. There is nothing to carry.
3. Multiply the tens. Now the next column to the left.
   3 × 3 = 9
   9 is less than 10, so write 9 in the tens column. There is nothing to carry.
4. Read the answer. Check that the answer has about the right number of digits, then write it.

   	T	O
   	3	3
   ×		3
   	9	9

   
   33 × 3 = 99

Check. Estimate: 33 is about 30 (to the nearest 10). 30 × 3 = 90. Our answer, 99, is a bit more than 90, which is right because we rounded down. ✓

Watch out. Start on the right with the ones. Multiply every digit by the one-digit number.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	T	O
   	2	4
   ×		2

2. Multiply the ones. Always start with the ones, on the right.
   4 × 2 = 8
   8 is less than 10, so write 8 in the ones column. There is nothing to carry.
3. Multiply the tens. Now the next column to the left.
   2 × 2 = 4
   4 is less than 10, so write 4 in the tens column. There is nothing to carry.
4. Read the answer. Check that the answer has about the right number of digits, then write it.

   	T	O
   	2	4
   ×		2
   	4	8

   
   24 × 2 = 48

Check. Estimate: 24 is about 20 (to the nearest 10). 20 × 2 = 40. Our answer, 48, is a bit more than 40, which is right because we rounded down. ✓

Watch out. Start on the right with the ones. Multiply every digit by the one-digit number.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	H	T	O
   		4	1
   ×			6

2. Multiply the ones. Always start with the ones, on the right.
   1 × 6 = 6
   6 is less than 10, so write 6 in the ones column. There is nothing to carry.
3. Multiply the tens. Now the next column to the left.
   4 × 6 = 24
   24 is 2 hundreds and 4 tens. Write 4 in the tens column and carry 2 to the hundreds column.
4. Write the carried digit. There are no digits left to multiply in the hundreds column, but we carried 2 into it.
   Nothing to multiply. Write 2 in the hundreds column.
5. Read the answer. Check that the answer has about the right number of digits, then write it.

   	H	T	O
   		4	1
   ×			6
   	2	4	6
   	2

   
   41 × 6 = 246

Check. Estimate: 41 is about 40 (to the nearest 10). 40 × 6 = 240. Our answer, 246, is a bit more than 240, which is right because we rounded down. ✓

Watch out. Do not forget the carried digits. Write each one small, then add it in the next column AFTER you have multiplied.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	H	T	O
   		3	6
   ×			4

2. Multiply the ones. Always start with the ones, on the right.
   6 × 4 = 24
   24 is 2 tens and 4 ones. Write 4 in the ones column and carry 2 to the tens column.
3. Multiply the tens. Now the next column to the left. Multiply, then add the 2 we carried.
   3 × 4 = 12, and 12 + 2 (carried) = 14
   14 is 1 hundred and 4 tens. Write 4 in the tens column and carry 1 to the hundreds column.
4. Write the carried digit. There are no digits left to multiply in the hundreds column, but we carried 1 into it.
   Nothing to multiply. Write 1 in the hundreds column.
5. Read the answer. Check that the answer has about the right number of digits, then write it.

   	H	T	O
   		3	6
   ×			4
   	1	4	4
   	1	2

   
   36 × 4 = 144

Check. Estimate: 36 is about 40 (to the nearest 10). 40 × 4 = 160. Our answer, 144, is a bit less than 160, which is right because we rounded up. ✓

Watch out. Do not forget the carried digits. Write each one small, then add it in the next column AFTER you have multiplied.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	H	T	O
   		4	7
   ×			3

2. Multiply the ones. Always start with the ones, on the right.
   7 × 3 = 21
   21 is 2 tens and 1 one. Write 1 in the ones column and carry 2 to the tens column.
3. Multiply the tens. Now the next column to the left. Multiply, then add the 2 we carried.
   4 × 3 = 12, and 12 + 2 (carried) = 14
   14 is 1 hundred and 4 tens. Write 4 in the tens column and carry 1 to the hundreds column.
4. Write the carried digit. There are no digits left to multiply in the hundreds column, but we carried 1 into it.
   Nothing to multiply. Write 1 in the hundreds column.
5. Read the answer. Check that the answer has about the right number of digits, then write it.

   	H	T	O
   		4	7
   ×			3
   	1	4	1
   	1	2

   
   47 × 3 = 141

Check. Estimate: 47 is about 50 (to the nearest 10). 50 × 3 = 150. Our answer, 141, is a bit less than 150, which is right because we rounded up. ✓

Watch out. Do not forget the carried digits. Write each one small, then add it in the next column AFTER you have multiplied.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	H	T	O
   		5	8
   ×			6

2. Multiply the ones. Always start with the ones, on the right.
   8 × 6 = 48
   48 is 4 tens and 8 ones. Write 8 in the ones column and carry 4 to the tens column.
3. Multiply the tens. Now the next column to the left. Multiply, then add the 4 we carried.
   5 × 6 = 30, and 30 + 4 (carried) = 34
   34 is 3 hundreds and 4 tens. Write 4 in the tens column and carry 3 to the hundreds column.
4. Write the carried digit. There are no digits left to multiply in the hundreds column, but we carried 3 into it.
   Nothing to multiply. Write 3 in the hundreds column.
5. Read the answer. Check that the answer has about the right number of digits, then write it.

   	H	T	O
   		5	8
   ×			6
   	3	4	8
   	3	4

   
   58 × 6 = 348

Check. Estimate: 58 is about 60 (to the nearest 10). 60 × 6 = 360. Our answer, 348, is a bit less than 360, which is right because we rounded up. ✓

Watch out. Do not forget the carried digits. Write each one small, then add it in the next column AFTER you have multiplied.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	H	T	O
   		6	5
   ×			7

2. Multiply the ones. Always start with the ones, on the right.
   5 × 7 = 35
   35 is 3 tens and 5 ones. Write 5 in the ones column and carry 3 to the tens column.
3. Multiply the tens. Now the next column to the left. Multiply, then add the 3 we carried.
   6 × 7 = 42, and 42 + 3 (carried) = 45
   45 is 4 hundreds and 5 tens. Write 5 in the tens column and carry 4 to the hundreds column.
4. Write the carried digit. There are no digits left to multiply in the hundreds column, but we carried 4 into it.
   Nothing to multiply. Write 4 in the hundreds column.
5. Read the answer. Check that the answer has about the right number of digits, then write it.

   	H	T	O
   		6	5
   ×			7
   	4	5	5
   	4	3

   
   65 × 7 = 455

Check. Estimate: 65 is about 70 (to the nearest 10). 70 × 7 = 490. Our answer, 455, is a bit less than 490, which is right because we rounded up. ✓

Watch out. Do not forget the carried digits. Write each one small, then add it in the next column AFTER you have multiplied.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	H	T	O
   		8	3
   ×			9

2. Multiply the ones. Always start with the ones, on the right.
   3 × 9 = 27
   27 is 2 tens and 7 ones. Write 7 in the ones column and carry 2 to the tens column.
3. Multiply the tens. Now the next column to the left. Multiply, then add the 2 we carried.
   8 × 9 = 72, and 72 + 2 (carried) = 74
   74 is 7 hundreds and 4 tens. Write 4 in the tens column and carry 7 to the hundreds column.
4. Write the carried digit. There are no digits left to multiply in the hundreds column, but we carried 7 into it.
   Nothing to multiply. Write 7 in the hundreds column.
5. Read the answer. Check that the answer has about the right number of digits, then write it.

   	H	T	O
   		8	3
   ×			9
   	7	4	7
   	7	2

   
   83 × 9 = 747

Check. Estimate: 83 is about 80 (to the nearest 10). 80 × 9 = 720. Our answer, 747, is a bit more than 720, which is right because we rounded down. ✓

Watch out. Do not forget the carried digits. Write each one small, then add it in the next column AFTER you have multiplied.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	H	T	O
   		9	4
   ×			8

2. Multiply the ones. Always start with the ones, on the right.
   4 × 8 = 32
   32 is 3 tens and 2 ones. Write 2 in the ones column and carry 3 to the tens column.
3. Multiply the tens. Now the next column to the left. Multiply, then add the 3 we carried.
   9 × 8 = 72, and 72 + 3 (carried) = 75
   75 is 7 hundreds and 5 tens. Write 5 in the tens column and carry 7 to the hundreds column.
4. Write the carried digit. There are no digits left to multiply in the hundreds column, but we carried 7 into it.
   Nothing to multiply. Write 7 in the hundreds column.
5. Read the answer. Check that the answer has about the right number of digits, then write it.

   	H	T	O
   		9	4
   ×			8
   	7	5	2
   	7	3

   
   94 × 8 = 752

Check. Estimate: 94 is about 90 (to the nearest 10). 90 × 8 = 720. Our answer, 752, is a bit more than 720, which is right because we rounded down. ✓

Watch out. Do not forget the carried digits. Write each one small, then add it in the next column AFTER you have multiplied.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	H	T	O
   	3	2	1
   ×			2

2. Multiply the ones. Always start with the ones, on the right.
   1 × 2 = 2
   2 is less than 10, so write 2 in the ones column. There is nothing to carry.
3. Multiply the tens. Now the next column to the left.
   2 × 2 = 4
   4 is less than 10, so write 4 in the tens column. There is nothing to carry.
4. Multiply the hundreds. Now the next column to the left.
   3 × 2 = 6
   6 is less than 10, so write 6 in the hundreds column. There is nothing to carry.
5. Read the answer. Check that the answer has about the right number of digits, then write it.

   	H	T	O
   	3	2	1
   ×			2
   	6	4	2

   
   321 × 2 = 642

Check. Estimate: 321 is about 300 (to the nearest 100). 300 × 2 = 600. Our answer, 642, is a bit more than 600, which is right because we rounded down. ✓

Watch out. Start on the right with the ones. Multiply every digit by the one-digit number.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	H	T	O
   	2	1	2
   ×			4

2. Multiply the ones. Always start with the ones, on the right.
   2 × 4 = 8
   8 is less than 10, so write 8 in the ones column. There is nothing to carry.
3. Multiply the tens. Now the next column to the left.
   1 × 4 = 4
   4 is less than 10, so write 4 in the tens column. There is nothing to carry.
4. Multiply the hundreds. Now the next column to the left.
   2 × 4 = 8
   8 is less than 10, so write 8 in the hundreds column. There is nothing to carry.
5. Read the answer. Check that the answer has about the right number of digits, then write it.

   	H	T	O
   	2	1	2
   ×			4
   	8	4	8

   
   212 × 4 = 848

Check. Estimate: 212 is about 200 (to the nearest 100). 200 × 4 = 800. Our answer, 848, is a bit more than 800, which is right because we rounded down. ✓

Watch out. Start on the right with the ones. Multiply every digit by the one-digit number.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	H	T	O
   	1	3	3
   ×			3

2. Multiply the ones. Always start with the ones, on the right.
   3 × 3 = 9
   9 is less than 10, so write 9 in the ones column. There is nothing to carry.
3. Multiply the tens. Now the next column to the left.
   3 × 3 = 9
   9 is less than 10, so write 9 in the tens column. There is nothing to carry.
4. Multiply the hundreds. Now the next column to the left.
   1 × 3 = 3
   3 is less than 10, so write 3 in the hundreds column. There is nothing to carry.
5. Read the answer. Check that the answer has about the right number of digits, then write it.

   	H	T	O
   	1	3	3
   ×			3
   	3	9	9

   
   133 × 3 = 399

Check. Estimate: 133 is about 100 (to the nearest 100). 100 × 3 = 300. Our answer, 399, is a bit more than 300, which is right because we rounded down. ✓

Watch out. Start on the right with the ones. Multiply every digit by the one-digit number.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	H	T	O
   	2	3	1
   ×			3

2. Multiply the ones. Always start with the ones, on the right.
   1 × 3 = 3
   3 is less than 10, so write 3 in the ones column. There is nothing to carry.
3. Multiply the tens. Now the next column to the left.
   3 × 3 = 9
   9 is less than 10, so write 9 in the tens column. There is nothing to carry.
4. Multiply the hundreds. Now the next column to the left.
   2 × 3 = 6
   6 is less than 10, so write 6 in the hundreds column. There is nothing to carry.
5. Read the answer. Check that the answer has about the right number of digits, then write it.

   	H	T	O
   	2	3	1
   ×			3
   	6	9	3

   
   231 × 3 = 693

Check. Estimate: 231 is about 200 (to the nearest 100). 200 × 3 = 600. Our answer, 693, is a bit more than 600, which is right because we rounded down. ✓

Watch out. Start on the right with the ones. Multiply every digit by the one-digit number.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	H	T	O
   	1	1	0
   ×			5

2. Multiply the ones. Always start with the ones, on the right.
   0 × 5 = 0
   0 is less than 10, so write 0 in the ones column. There is nothing to carry.
3. Multiply the tens. Now the next column to the left.
   1 × 5 = 5
   5 is less than 10, so write 5 in the tens column. There is nothing to carry.
4. Multiply the hundreds. Now the next column to the left.
   1 × 5 = 5
   5 is less than 10, so write 5 in the hundreds column. There is nothing to carry.
5. Read the answer. Check that the answer has about the right number of digits, then write it.

   	H	T	O
   	1	1	0
   ×			5
   	5	5	0

   
   110 × 5 = 550

Check. Estimate: 110 is about 100 (to the nearest 100). 100 × 5 = 500. Our answer, 550, is a bit more than 500, which is right because we rounded down. ✓

Watch out. Start on the right with the ones. Multiply every digit by the one-digit number.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	H	T	O
   	1	2	2
   ×			4

2. Multiply the ones. Always start with the ones, on the right.
   2 × 4 = 8
   8 is less than 10, so write 8 in the ones column. There is nothing to carry.
3. Multiply the tens. Now the next column to the left.
   2 × 4 = 8
   8 is less than 10, so write 8 in the tens column. There is nothing to carry.
4. Multiply the hundreds. Now the next column to the left.
   1 × 4 = 4
   4 is less than 10, so write 4 in the hundreds column. There is nothing to carry.
5. Read the answer. Check that the answer has about the right number of digits, then write it.

   	H	T	O
   	1	2	2
   ×			4
   	4	8	8

   
   122 × 4 = 488

Check. Estimate: 122 is about 100 (to the nearest 100). 100 × 4 = 400. Our answer, 488, is a bit more than 400, which is right because we rounded down. ✓

Watch out. Start on the right with the ones. Multiply every digit by the one-digit number.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	H	T	O
   	2	5	6
   ×			3

2. Multiply the ones. Always start with the ones, on the right.
   6 × 3 = 18
   18 is 1 ten and 8 ones. Write 8 in the ones column and carry 1 to the tens column.
3. Multiply the tens. Now the next column to the left. Multiply, then add the 1 we carried.
   5 × 3 = 15, and 15 + 1 (carried) = 16
   16 is 1 hundred and 6 tens. Write 6 in the tens column and carry 1 to the hundreds column.
4. Multiply the hundreds. Now the next column to the left. Multiply, then add the 1 we carried.
   2 × 3 = 6, and 6 + 1 (carried) = 7
   7 is less than 10, so write 7 in the hundreds column. There is nothing to carry.
5. Read the answer. Check that the answer has about the right number of digits, then write it.

   	H	T	O
   	2	5	6
   ×			3
   	7	6	8
   	1	1

   
   256 × 3 = 768

Check. Estimate: 256 is about 300 (to the nearest 100). 300 × 3 = 900. Our answer, 768, is a bit less than 900, which is right because we rounded up. ✓

Watch out. Do not forget the carried digits. Write each one small, then add it in the next column AFTER you have multiplied.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	Th	H	T	O
   		3	4	7
   ×				5

2. Multiply the ones. Always start with the ones, on the right.
   7 × 5 = 35
   35 is 3 tens and 5 ones. Write 5 in the ones column and carry 3 to the tens column.
3. Multiply the tens. Now the next column to the left. Multiply, then add the 3 we carried.
   4 × 5 = 20, and 20 + 3 (carried) = 23
   23 is 2 hundreds and 3 tens. Write 3 in the tens column and carry 2 to the hundreds column.
4. Multiply the hundreds. Now the next column to the left. Multiply, then add the 2 we carried.
   3 × 5 = 15, and 15 + 2 (carried) = 17
   17 is 1 thousand and 7 hundreds. Write 7 in the hundreds column and carry 1 to the thousands column.
5. Write the carried digit. There are no digits left to multiply in the thousands column, but we carried 1 into it.
   Nothing to multiply. Write 1 in the thousands column.
6. Read the answer. Check that the answer has about the right number of digits, then write it.

   	Th	H	T	O
   		3	4	7
   ×				5
   	1	7	3	5
   	1	2	3

   
   347 × 5 = 1,735

Check. Estimate: 347 is about 300 (to the nearest 100). 300 × 5 = 1,500. Our answer, 1,735, is a bit more than 1,500, which is right because we rounded down. ✓

Watch out. Do not forget the carried digits. Write each one small, then add it in the next column AFTER you have multiplied.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	Th	H	T	O
   		4	1	8
   ×				6

2. Multiply the ones. Always start with the ones, on the right.
   8 × 6 = 48
   48 is 4 tens and 8 ones. Write 8 in the ones column and carry 4 to the tens column.
3. Multiply the tens. Now the next column to the left. Multiply, then add the 4 we carried.
   1 × 6 = 6, and 6 + 4 (carried) = 10
   10 is 1 hundred and 0 tens. Write 0 in the tens column and carry 1 to the hundreds column.
4. Multiply the hundreds. Now the next column to the left. Multiply, then add the 1 we carried.
   4 × 6 = 24, and 24 + 1 (carried) = 25
   25 is 2 thousands and 5 hundreds. Write 5 in the hundreds column and carry 2 to the thousands column.
5. Write the carried digit. There are no digits left to multiply in the thousands column, but we carried 2 into it.
   Nothing to multiply. Write 2 in the thousands column.
6. Read the answer. Check that the answer has about the right number of digits, then write it.

   	Th	H	T	O
   		4	1	8
   ×				6
   	2	5	0	8
   	2	1	4

   
   418 × 6 = 2,508

Check. Estimate: 418 is about 400 (to the nearest 100). 400 × 6 = 2,400. Our answer, 2,508, is a bit more than 2,400, which is right because we rounded down. ✓

Watch out. Do not forget the carried digits. Write each one small, then add it in the next column AFTER you have multiplied.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	Th	H	T	O
   		5	2	9
   ×				4

2. Multiply the ones. Always start with the ones, on the right.
   9 × 4 = 36
   36 is 3 tens and 6 ones. Write 6 in the ones column and carry 3 to the tens column.
3. Multiply the tens. Now the next column to the left. Multiply, then add the 3 we carried.
   2 × 4 = 8, and 8 + 3 (carried) = 11
   11 is 1 hundred and 1 ten. Write 1 in the tens column and carry 1 to the hundreds column.
4. Multiply the hundreds. Now the next column to the left. Multiply, then add the 1 we carried.
   5 × 4 = 20, and 20 + 1 (carried) = 21
   21 is 2 thousands and 1 hundred. Write 1 in the hundreds column and carry 2 to the thousands column.
5. Write the carried digit. There are no digits left to multiply in the thousands column, but we carried 2 into it.
   Nothing to multiply. Write 2 in the thousands column.
6. Read the answer. Check that the answer has about the right number of digits, then write it.

   	Th	H	T	O
   		5	2	9
   ×				4
   	2	1	1	6
   	2	1	3

   
   529 × 4 = 2,116

Check. Estimate: 529 is about 500 (to the nearest 100). 500 × 4 = 2,000. Our answer, 2,116, is a bit more than 2,000, which is right because we rounded down. ✓

Watch out. Do not forget the carried digits. Write each one small, then add it in the next column AFTER you have multiplied.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	Th	H	T	O
   		6	7	8
   ×				7

2. Multiply the ones. Always start with the ones, on the right.
   8 × 7 = 56
   56 is 5 tens and 6 ones. Write 6 in the ones column and carry 5 to the tens column.
3. Multiply the tens. Now the next column to the left. Multiply, then add the 5 we carried.
   7 × 7 = 49, and 49 + 5 (carried) = 54
   54 is 5 hundreds and 4 tens. Write 4 in the tens column and carry 5 to the hundreds column.
4. Multiply the hundreds. Now the next column to the left. Multiply, then add the 5 we carried.
   6 × 7 = 42, and 42 + 5 (carried) = 47
   47 is 4 thousands and 7 hundreds. Write 7 in the hundreds column and carry 4 to the thousands column.
5. Write the carried digit. There are no digits left to multiply in the thousands column, but we carried 4 into it.
   Nothing to multiply. Write 4 in the thousands column.
6. Read the answer. Check that the answer has about the right number of digits, then write it.

   	Th	H	T	O
   		6	7	8
   ×				7
   	4	7	4	6
   	4	5	5

   
   678 × 7 = 4,746

Check. Estimate: 678 is about 700 (to the nearest 100). 700 × 7 = 4,900. Our answer, 4,746, is a bit less than 4,900, which is right because we rounded up. ✓

Watch out. Do not forget the carried digits. Write each one small, then add it in the next column AFTER you have multiplied.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	Th	H	T	O
   		8	4	5
   ×				9

2. Multiply the ones. Always start with the ones, on the right.
   5 × 9 = 45
   45 is 4 tens and 5 ones. Write 5 in the ones column and carry 4 to the tens column.
3. Multiply the tens. Now the next column to the left. Multiply, then add the 4 we carried.
   4 × 9 = 36, and 36 + 4 (carried) = 40
   40 is 4 hundreds and 0 tens. Write 0 in the tens column and carry 4 to the hundreds column.
4. Multiply the hundreds. Now the next column to the left. Multiply, then add the 4 we carried.
   8 × 9 = 72, and 72 + 4 (carried) = 76
   76 is 7 thousands and 6 hundreds. Write 6 in the hundreds column and carry 7 to the thousands column.
5. Write the carried digit. There are no digits left to multiply in the thousands column, but we carried 7 into it.
   Nothing to multiply. Write 7 in the thousands column.
6. Read the answer. Check that the answer has about the right number of digits, then write it.

   	Th	H	T	O
   		8	4	5
   ×				9
   	7	6	0	5
   	7	4	4

   
   845 × 9 = 7,605

Check. Estimate: 845 is about 800 (to the nearest 100). 800 × 9 = 7,200. Our answer, 7,605, is a bit more than 7,200, which is right because we rounded down. ✓

Watch out. Do not forget the carried digits. Write each one small, then add it in the next column AFTER you have multiplied.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	Th	H	T	O
   		3	0	6
   ×				4

2. Multiply the ones. Always start with the ones, on the right.
   6 × 4 = 24
   24 is 2 tens and 4 ones. Write 4 in the ones column and carry 2 to the tens column.
3. Multiply the tens. Now the next column to the left. Multiply, then add the 2 we carried.
   0 × 4 = 0, and 0 + 2 (carried) = 2
   2 is less than 10, so write 2 in the tens column. There is nothing to carry.
4. Multiply the hundreds. Now the next column to the left.
   3 × 4 = 12
   12 is 1 thousand and 2 hundreds. Write 2 in the hundreds column and carry 1 to the thousands column.
5. Write the carried digit. There are no digits left to multiply in the thousands column, but we carried 1 into it.
   Nothing to multiply. Write 1 in the thousands column.
6. Read the answer. Check that the answer has about the right number of digits, then write it.

   	Th	H	T	O
   		3	0	6
   ×				4
   	1	2	2	4
   	1		2

   
   306 × 4 = 1,224

Check. Estimate: 306 is about 300 (to the nearest 100). 300 × 4 = 1,200. Our answer, 1,224, is a bit more than 1,200, which is right because we rounded down. ✓

Watch out. A zero digit still needs a step: 0 × the number is 0, but do not forget to add the carried digit.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	Th	H	T	O
   		4	5	0
   ×				6

2. Multiply the ones. Always start with the ones, on the right.
   0 × 6 = 0
   0 is less than 10, so write 0 in the ones column. There is nothing to carry.
3. Multiply the tens. Now the next column to the left.
   5 × 6 = 30
   30 is 3 hundreds and 0 tens. Write 0 in the tens column and carry 3 to the hundreds column.
4. Multiply the hundreds. Now the next column to the left. Multiply, then add the 3 we carried.
   4 × 6 = 24, and 24 + 3 (carried) = 27
   27 is 2 thousands and 7 hundreds. Write 7 in the hundreds column and carry 2 to the thousands column.
5. Write the carried digit. There are no digits left to multiply in the thousands column, but we carried 2 into it.
   Nothing to multiply. Write 2 in the thousands column.
6. Read the answer. Check that the answer has about the right number of digits, then write it.

   	Th	H	T	O
   		4	5	0
   ×				6
   	2	7	0	0
   	2	3

   
   450 × 6 = 2,700

Check. Estimate: 450 is about 500 (to the nearest 100). 500 × 6 = 3,000. Our answer, 2,700, is a bit less than 3,000, which is right because we rounded up. ✓

Watch out. A zero digit still needs a step: 0 × the number is 0, but do not forget to add the carried digit.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	Th	H	T	O
   		7	0	9
   ×				5

2. Multiply the ones. Always start with the ones, on the right.
   9 × 5 = 45
   45 is 4 tens and 5 ones. Write 5 in the ones column and carry 4 to the tens column.
3. Multiply the tens. Now the next column to the left. Multiply, then add the 4 we carried.
   0 × 5 = 0, and 0 + 4 (carried) = 4
   4 is less than 10, so write 4 in the tens column. There is nothing to carry.
4. Multiply the hundreds. Now the next column to the left.
   7 × 5 = 35
   35 is 3 thousands and 5 hundreds. Write 5 in the hundreds column and carry 3 to the thousands column.
5. Write the carried digit. There are no digits left to multiply in the thousands column, but we carried 3 into it.
   Nothing to multiply. Write 3 in the thousands column.
6. Read the answer. Check that the answer has about the right number of digits, then write it.

   	Th	H	T	O
   		7	0	9
   ×				5
   	3	5	4	5
   	3		4

   
   709 × 5 = 3,545

Check. Estimate: 709 is about 700 (to the nearest 100). 700 × 5 = 3,500. Our answer, 3,545, is a bit more than 3,500, which is right because we rounded down. ✓

Watch out. A zero digit still needs a step: 0 × the number is 0, but do not forget to add the carried digit.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	Th	H	T	O
   		9	2	0
   ×				7

2. Multiply the ones. Always start with the ones, on the right.
   0 × 7 = 0
   0 is less than 10, so write 0 in the ones column. There is nothing to carry.
3. Multiply the tens. Now the next column to the left.
   2 × 7 = 14
   14 is 1 hundred and 4 tens. Write 4 in the tens column and carry 1 to the hundreds column.
4. Multiply the hundreds. Now the next column to the left. Multiply, then add the 1 we carried.
   9 × 7 = 63, and 63 + 1 (carried) = 64
   64 is 6 thousands and 4 hundreds. Write 4 in the hundreds column and carry 6 to the thousands column.
5. Write the carried digit. There are no digits left to multiply in the thousands column, but we carried 6 into it.
   Nothing to multiply. Write 6 in the thousands column.
6. Read the answer. Check that the answer has about the right number of digits, then write it.

   	Th	H	T	O
   		9	2	0
   ×				7
   	6	4	4	0
   	6	1

   
   920 × 7 = 6,440

Check. Estimate: 920 is about 900 (to the nearest 100). 900 × 7 = 6,300. Our answer, 6,440, is a bit more than 6,300, which is right because we rounded down. ✓

Watch out. A zero digit still needs a step: 0 × the number is 0, but do not forget to add the carried digit.

Key words. To estimate is to find an answer that is close, usually by rounding first. ≈ means “is about equal to”.

Method. Round the big number and multiply to get an estimate. Then work out the exact answer with short multiplication and check that it is close to the estimate.

1. Round 48 to the nearest 10. Rounded numbers are easy to multiply.
   48 ≈ 50  (the ones digit is 8, so round up)
2. Work out the estimate. Multiply the rounded number by the one-digit number.
   50 × 6 = 300
3. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	H	T	O
   		4	8
   ×			6

4. Multiply the ones. Always start with the ones, on the right.
   8 × 6 = 48
   48 is 4 tens and 8 ones. Write 8 in the ones column and carry 4 to the tens column.
5. Multiply the tens. Now the next column to the left. Multiply, then add the 4 we carried.
   4 × 6 = 24, and 24 + 4 (carried) = 28
   28 is 2 hundreds and 8 tens. Write 8 in the tens column and carry 2 to the hundreds column.
6. Write the carried digit. There are no digits left to multiply in the hundreds column, but we carried 2 into it.
   Nothing to multiply. Write 2 in the hundreds column.
7. Compare the exact answer with the estimate. They should be close.

   	H	T	O
   		4	8
   ×			6
   	2	8	8
   	2	4

   
   Exact: 288. Estimate: 300. They are close. ✓

Check. Estimate: 48 is about 50 (to the nearest 10). 50 × 6 = 300. Our answer, 288, is a bit less than 300, which is right because we rounded up. ✓

Watch out. An estimate is not the exact answer. It is a quick way to catch big mistakes.

Key words. To estimate is to find an answer that is close, usually by rounding first. ≈ means “is about equal to”.

Method. Round the big number and multiply to get an estimate. Then work out the exact answer with short multiplication and check that it is close to the estimate.

1. Round 287 to the nearest 100. Rounded numbers are easy to multiply.
   287 ≈ 300  (the tens digit is 8, so round up)
2. Work out the estimate. Multiply the rounded number by the one-digit number.
   300 × 4 = 1,200
3. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	Th	H	T	O
   		2	8	7
   ×				4

4. Multiply the ones. Always start with the ones, on the right.
   7 × 4 = 28
   28 is 2 tens and 8 ones. Write 8 in the ones column and carry 2 to the tens column.
5. Multiply the tens. Now the next column to the left. Multiply, then add the 2 we carried.
   8 × 4 = 32, and 32 + 2 (carried) = 34
   34 is 3 hundreds and 4 tens. Write 4 in the tens column and carry 3 to the hundreds column.
6. Multiply the hundreds. Now the next column to the left. Multiply, then add the 3 we carried.
   2 × 4 = 8, and 8 + 3 (carried) = 11
   11 is 1 thousand and 1 hundred. Write 1 in the hundreds column and carry 1 to the thousands column.
7. Write the carried digit. There are no digits left to multiply in the thousands column, but we carried 1 into it.
   Nothing to multiply. Write 1 in the thousands column.
8. Compare the exact answer with the estimate. They should be close.

   	Th	H	T	O
   		2	8	7
   ×				4
   	1	1	4	8
   	1	3	2

   
   Exact: 1,148. Estimate: 1,200. They are close. ✓

Check. Estimate: 287 is about 300 (to the nearest 100). 300 × 4 = 1,200. Our answer, 1,148, is a bit less than 1,200, which is right because we rounded up. ✓

Watch out. An estimate is not the exact answer. It is a quick way to catch big mistakes.

Key words. To estimate is to find an answer that is close, usually by rounding first. ≈ means “is about equal to”.

Method. Round the big number and multiply to get an estimate. Then work out the exact answer with short multiplication and check that it is close to the estimate.

1. Round 513 to the nearest 100. Rounded numbers are easy to multiply.
   513 ≈ 500  (the tens digit is 1, so round down)
2. Work out the estimate. Multiply the rounded number by the one-digit number.
   500 × 8 = 4,000
3. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	Th	H	T	O
   		5	1	3
   ×				8

4. Multiply the ones. Always start with the ones, on the right.
   3 × 8 = 24
   24 is 2 tens and 4 ones. Write 4 in the ones column and carry 2 to the tens column.
5. Multiply the tens. Now the next column to the left. Multiply, then add the 2 we carried.
   1 × 8 = 8, and 8 + 2 (carried) = 10
   10 is 1 hundred and 0 tens. Write 0 in the tens column and carry 1 to the hundreds column.
6. Multiply the hundreds. Now the next column to the left. Multiply, then add the 1 we carried.
   5 × 8 = 40, and 40 + 1 (carried) = 41
   41 is 4 thousands and 1 hundred. Write 1 in the hundreds column and carry 4 to the thousands column.
7. Write the carried digit. There are no digits left to multiply in the thousands column, but we carried 4 into it.
   Nothing to multiply. Write 4 in the thousands column.
8. Compare the exact answer with the estimate. They should be close.

   	Th	H	T	O
   		5	1	3
   ×				8
   	4	1	0	4
   	4	1	2

   
   Exact: 4,104. Estimate: 4,000. They are close. ✓

Check. Estimate: 513 is about 500 (to the nearest 100). 500 × 8 = 4,000. Our answer, 4,104, is a bit more than 4,000, which is right because we rounded down. ✓

Watch out. An estimate is not the exact answer. It is a quick way to catch big mistakes.

Method. Do the multiplication again with short multiplication and compare it with Jack’s answer.

1. Work out the correct answer. Multiply each column. Add the carried digit in the next column.

   	H	T	O
   		3	6
   ×			4
   	1	4	4
   	1	2

   
   36 × 4 = 144
2. Compare with Jack’s answer. Jack wrote 124.
   144 is not 124, so Jack made a mistake.
3. Find the mistake. Jack forgot to add the carried digits.
   The carry from the ones column should have been added in the tens column.

Check. Estimate: 36 is about 40 (to the nearest 10). 40 × 4 = 160. Our answer, 144, is a bit less than 160, which is right because we rounded up. ✓

Watch out. Write each carried digit small, and add it in the next column after you have multiplied that column.

Method. Do the multiplication again with short multiplication and compare it with Amira’s answer.

1. Work out the correct answer. Multiply each column. Add the carried digit in the next column.

   	Th	H	T	O
   		3	4	7
   ×				6
   	2	0	8	2
   	2	2	4

   
   347 × 6 = 2,082
2. Compare with Amira’s answer. Amira wrote 1,842.
   2,082 is not 1,842, so Amira made a mistake.
3. Find the mistake. Amira forgot to add the carried digits.
   The carry from the ones column should have been added in the tens column.

Check. Estimate: 347 is about 300 (to the nearest 100). 300 × 6 = 1,800. Our answer, 2,082, is a bit more than 1,800, which is right because we rounded down. ✓

Watch out. Write each carried digit small, and add it in the next column after you have multiplied that column.

Method. Do the multiplication again with short multiplication and compare it with Noah’s answer.

1. Work out the correct answer. Multiply each column. Add the carried digit in the next column.

   	Th	H	T	O
   		5	2	8
   ×				3
   	1	5	8	4
   	1		2

   
   528 × 3 = 1,584
2. Compare with Noah’s answer. Noah wrote 1,564.
   1,584 is not 1,564, so Noah made a mistake.
3. Find the mistake. Noah forgot to add the carried digits.
   The carry from the ones column should have been added in the tens column.

Check. Estimate: 528 is about 500 (to the nearest 100). 500 × 3 = 1,500. Our answer, 1,584, is a bit more than 1,500, which is right because we rounded down. ✓

Watch out. Write each carried digit small, and add it in the next column after you have multiplied that column.