Year 4: Multiplying and dividing by 10 and 100

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To multiply by 10, move every digit 1 place to the left and put a zero in the empty place on the right. Do not just “add a zero”: it is the digits that move.

1. Say what each digit is worth. The digits have different values because of their columns.
   8 ones
2. Make every digit 10 times bigger. Multiplying by 10 makes each digit 10 times bigger. That moves it 1 place to the left.
   8 ones become 8 tens
3. Show it in a place-value table. The 1 gap on the right is empty, so we put a zero there.

   	Th	H	T	O
   8				8
   × 10	← 1 place left
   80			8	0

4. Write the answer. The zero place holders keep every digit in the right column.
   8 × 10 = 80

Check. Divide back: 80 ÷ 10 = 8. ✓

Watch out. Move the digits, then fill the empty place with a zero. Check the answer is 10 times bigger.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To multiply by 10, move every digit 1 place to the left and put a zero in the empty place on the right. Do not just “add a zero”: it is the digits that move.

1. Say what each digit is worth. The digits have different values because of their columns.
   2 tens
   3 ones
2. Make every digit 10 times bigger. Multiplying by 10 makes each digit 10 times bigger. That moves it 1 place to the left.
   2 tens become 2 hundreds
   3 ones become 3 tens
3. Show it in a place-value table. The 1 gap on the right is empty, so we put a zero there.

   	Th	H	T	O
   23			2	3
   × 10	← 1 place left
   230		2	3	0

4. Write the answer. The zero place holders keep every digit in the right column.
   23 × 10 = 230

Check. Divide back: 230 ÷ 10 = 23. ✓

Watch out. Move the digits, then fill the empty place with a zero. Check the answer is 10 times bigger.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To multiply by 10, move every digit 1 place to the left and put a zero in the empty place on the right. Do not just “add a zero”: it is the digits that move.

1. Say what each digit is worth. The digits have different values because of their columns.
   6 tens
   5 ones
2. Make every digit 10 times bigger. Multiplying by 10 makes each digit 10 times bigger. That moves it 1 place to the left.
   6 tens become 6 hundreds
   5 ones become 5 tens
3. Show it in a place-value table. The 1 gap on the right is empty, so we put a zero there.

   	Th	H	T	O
   65			6	5
   × 10	← 1 place left
   650		6	5	0

4. Write the answer. The zero place holders keep every digit in the right column.
   65 × 10 = 650

Check. Divide back: 650 ÷ 10 = 65. ✓

Watch out. Move the digits, then fill the empty place with a zero. Check the answer is 10 times bigger.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To multiply by 10, move every digit 1 place to the left and put a zero in the empty place on the right. Do not just “add a zero”: it is the digits that move.

1. Say what each digit is worth. The digits have different values because of their columns.
   9 tens
2. Make every digit 10 times bigger. Multiplying by 10 makes each digit 10 times bigger. That moves it 1 place to the left.
   9 tens become 9 hundreds
3. Show it in a place-value table. The 1 gap on the right is empty, so we put a zero there.

   	Th	H	T	O
   90			9	0
   × 10	← 1 place left
   900		9	0	0

4. Write the answer. The zero place holders keep every digit in the right column.
   90 × 10 = 900

Check. Divide back: 900 ÷ 10 = 90. ✓

Watch out. The zeros are place holders. Count them: 90 × 10 must end with 1 zero more than the zeros 90 already ends with.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To multiply by 10, move every digit 1 place to the left and put a zero in the empty place on the right. Do not just “add a zero”: it is the digits that move.

1. Say what each digit is worth. The digits have different values because of their columns.
   1 hundred
   4 tens
   7 ones
2. Make every digit 10 times bigger. Multiplying by 10 makes each digit 10 times bigger. That moves it 1 place to the left.
   1 hundred becomes 1 thousand
   4 tens become 4 hundreds
   7 ones become 7 tens
3. Show it in a place-value table. The 1 gap on the right is empty, so we put a zero there.

   	Th	H	T	O
   147		1	4	7
   × 10	← 1 place left
   1,470	1	4	7	0

4. Write the answer. The zero place holders keep every digit in the right column.
   147 × 10 = 1,470

Check. Divide back: 1,470 ÷ 10 = 147. ✓

Watch out. Move the digits, then fill the empty place with a zero. Check the answer is 10 times bigger.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To multiply by 10, move every digit 1 place to the left and put a zero in the empty place on the right. Do not just “add a zero”: it is the digits that move.

1. Say what each digit is worth. The digits have different values because of their columns.
   3 hundreds
   8 tens
2. Make every digit 10 times bigger. Multiplying by 10 makes each digit 10 times bigger. That moves it 1 place to the left.
   3 hundreds become 3 thousands
   8 tens become 8 hundreds
3. Show it in a place-value table. The 1 gap on the right is empty, so we put a zero there.

   	Th	H	T	O
   380		3	8	0
   × 10	← 1 place left
   3,800	3	8	0	0

4. Write the answer. The zero place holders keep every digit in the right column.
   380 × 10 = 3,800

Check. Divide back: 3,800 ÷ 10 = 380. ✓

Watch out. The zeros are place holders. Count them: 380 × 10 must end with 1 zero more than the zeros 380 already ends with.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To multiply by 100, move every digit 2 places to the left and put 2 zeros in the empty places on the right. Do not just “add a zero”: it is the digits that move.

1. Say what each digit is worth. The digits have different values because of their columns.
   4 ones
2. Make every digit 100 times bigger. Multiplying by 100 makes each digit 100 times bigger. That moves it 2 places to the left.
   4 ones become 4 hundreds
3. Show it in a place-value table. The 2 gaps on the right are empty, so we put zeros there.

   	Th	H	T	O
   4				4
   × 100	← 2 places left
   400		4	0	0

4. Write the answer. The zero place holders keep every digit in the right column.
   4 × 100 = 400

Check. Divide back: 400 ÷ 100 = 4. ✓

Watch out. Move the digits, then fill the empty places with zeros. Check the answer is 100 times bigger.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To multiply by 100, move every digit 2 places to the left and put 2 zeros in the empty places on the right. Do not just “add a zero”: it is the digits that move.

1. Say what each digit is worth. The digits have different values because of their columns.
   1 ten
   7 ones
2. Make every digit 100 times bigger. Multiplying by 100 makes each digit 100 times bigger. That moves it 2 places to the left.
   1 ten becomes 1 thousand
   7 ones become 7 hundreds
3. Show it in a place-value table. The 2 gaps on the right are empty, so we put zeros there.

   	Th	H	T	O
   17			1	7
   × 100	← 2 places left
   1,700	1	7	0	0

4. Write the answer. The zero place holders keep every digit in the right column.
   17 × 100 = 1,700

Check. Divide back: 1,700 ÷ 100 = 17. ✓

Watch out. Move the digits, then fill the empty places with zeros. Check the answer is 100 times bigger.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To multiply by 100, move every digit 2 places to the left and put 2 zeros in the empty places on the right. Do not just “add a zero”: it is the digits that move.

1. Say what each digit is worth. The digits have different values because of their columns.
   6 tens
2. Make every digit 100 times bigger. Multiplying by 100 makes each digit 100 times bigger. That moves it 2 places to the left.
   6 tens become 6 thousands
3. Show it in a place-value table. The 2 gaps on the right are empty, so we put zeros there.

   	Th	H	T	O
   60			6	0
   × 100	← 2 places left
   6,000	6	0	0	0

4. Write the answer. The zero place holders keep every digit in the right column.
   60 × 100 = 6,000

Check. Divide back: 6,000 ÷ 100 = 60. ✓

Watch out. The zeros are place holders. Count them: 60 × 100 must end with 2 zeros more than the zeros 60 already ends with.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To multiply by 100, move every digit 2 places to the left and put 2 zeros in the empty places on the right. Do not just “add a zero”: it is the digits that move.

1. Say what each digit is worth. The digits have different values because of their columns.
   2 hundreds
   5 ones
2. Make every digit 100 times bigger. Multiplying by 100 makes each digit 100 times bigger. That moves it 2 places to the left.
   2 hundreds become 2 ten thousands
   5 ones become 5 hundreds
3. Show it in a place-value table. The 2 gaps on the right are empty, so we put zeros there.

   	TTh	Th	H	T	O
   205			2	0	5
   × 100	← 2 places left
   20,500	2	0	5	0	0

4. Write the answer. The zero place holders keep every digit in the right column.
   205 × 100 = 20,500

Check. Divide back: 20,500 ÷ 100 = 205. ✓

Watch out. Move the digits, then fill the empty places with zeros. Check the answer is 100 times bigger.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To multiply by 100, move every digit 2 places to the left and put 2 zeros in the empty places on the right. Do not just “add a zero”: it is the digits that move.

1. Say what each digit is worth. The digits have different values because of their columns.
   3 hundreds
   8 ones
2. Make every digit 100 times bigger. Multiplying by 100 makes each digit 100 times bigger. That moves it 2 places to the left.
   3 hundreds become 3 ten thousands
   8 ones become 8 hundreds
3. Show it in a place-value table. The 2 gaps on the right are empty, so we put zeros there.

   	TTh	Th	H	T	O
   308			3	0	8
   × 100	← 2 places left
   30,800	3	0	8	0	0

4. Write the answer. The zero place holders keep every digit in the right column.
   308 × 100 = 30,800

Check. Divide back: 30,800 ÷ 100 = 308. ✓

Watch out. Move the digits, then fill the empty places with zeros. Check the answer is 100 times bigger.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To multiply by 100, move every digit 2 places to the left and put 2 zeros in the empty places on the right. Do not just “add a zero”: it is the digits that move.

1. Say what each digit is worth. The digits have different values because of their columns.
   9 tens
   9 ones
2. Make every digit 100 times bigger. Multiplying by 100 makes each digit 100 times bigger. That moves it 2 places to the left.
   9 tens become 9 thousands
   9 ones become 9 hundreds
3. Show it in a place-value table. The 2 gaps on the right are empty, so we put zeros there.

   	Th	H	T	O
   99			9	9
   × 100	← 2 places left
   9,900	9	9	0	0

4. Write the answer. The zero place holders keep every digit in the right column.
   99 × 100 = 9,900

Check. Divide back: 9,900 ÷ 100 = 99. ✓

Watch out. Move the digits, then fill the empty places with zeros. Check the answer is 100 times bigger.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To divide by 10, move every digit 1 place to the right. A number that ends in 1 zero will divide exactly.

1. Look at the end of the number. Are there at least 1 zero? Every digit moves 1 place to the right, so the ones column must be able to hold the moved digits. A number that ends in 1 zero divides exactly.
   70 ends in 1 zero. ✓
2. Make every digit 10 times smaller. Dividing by 10 makes each digit 10 times smaller. That moves it 1 place to the right.
   7 tens become 7 ones
3. Show it in a place-value table. The last 1 zero falls off the end.

   	Th	H	T	O
   70			7	0
   ÷ 10	→ 1 place right
   7				7

4. Write the answer.
   70 ÷ 10 = 7

Check. Multiply back: 7 × 10 = 70. ✓

Watch out. Move the digits 1 place to the right. Check the answer is 10 times smaller.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To divide by 10, move every digit 1 place to the right. A number that ends in 1 zero will divide exactly.

1. Look at the end of the number. Are there at least 1 zero? Every digit moves 1 place to the right, so the ones column must be able to hold the moved digits. A number that ends in 1 zero divides exactly.
   340 ends in 1 zero. ✓
2. Make every digit 10 times smaller. Dividing by 10 makes each digit 10 times smaller. That moves it 1 place to the right.
   3 hundreds become 3 tens
   4 tens become 4 ones
3. Show it in a place-value table. The last 1 zero falls off the end.

   	Th	H	T	O
   340		3	4	0
   ÷ 10	→ 1 place right
   34			3	4

4. Write the answer.
   340 ÷ 10 = 34

Check. Multiply back: 34 × 10 = 340. ✓

Watch out. Move the digits 1 place to the right. Check the answer is 10 times smaller.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To divide by 10, move every digit 1 place to the right. A number that ends in 1 zero will divide exactly.

1. Look at the end of the number. Are there at least 1 zero? Every digit moves 1 place to the right, so the ones column must be able to hold the moved digits. A number that ends in 1 zero divides exactly.
   800 ends in 2 zeros. ✓
2. Make every digit 10 times smaller. Dividing by 10 makes each digit 10 times smaller. That moves it 1 place to the right.
   8 hundreds become 8 tens
3. Show it in a place-value table. The last 1 zero falls off the end.

   	Th	H	T	O
   800		8	0	0
   ÷ 10	→ 1 place right
   80			8	0

4. Write the answer.
   800 ÷ 10 = 80

Check. Multiply back: 80 × 10 = 800. ✓

Watch out. Take away 1 zero from the end. Do not take away every zero: 600 ÷ 10 is 60, not 6.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To divide by 10, move every digit 1 place to the right. A number that ends in 1 zero will divide exactly.

1. Look at the end of the number. Are there at least 1 zero? Every digit moves 1 place to the right, so the ones column must be able to hold the moved digits. A number that ends in 1 zero divides exactly.
   1,250 ends in 1 zero. ✓
2. Make every digit 10 times smaller. Dividing by 10 makes each digit 10 times smaller. That moves it 1 place to the right.
   1 thousand becomes 1 hundred
   2 hundreds become 2 tens
   5 tens become 5 ones
3. Show it in a place-value table. The last 1 zero falls off the end.

   	Th	H	T	O
   1,250	1	2	5	0
   ÷ 10	→ 1 place right
   125		1	2	5

4. Write the answer.
   1,250 ÷ 10 = 125

Check. Multiply back: 125 × 10 = 1,250. ✓

Watch out. Move the digits 1 place to the right. Check the answer is 10 times smaller.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To divide by 10, move every digit 1 place to the right. A number that ends in 1 zero will divide exactly.

1. Look at the end of the number. Are there at least 1 zero? Every digit moves 1 place to the right, so the ones column must be able to hold the moved digits. A number that ends in 1 zero divides exactly.
   4,060 ends in 1 zero. ✓
2. Make every digit 10 times smaller. Dividing by 10 makes each digit 10 times smaller. That moves it 1 place to the right.
   4 thousands become 4 hundreds
   6 tens become 6 ones
3. Show it in a place-value table. The last 1 zero falls off the end.

   	Th	H	T	O
   4,060	4	0	6	0
   ÷ 10	→ 1 place right
   406		4	0	6

4. Write the answer.
   4,060 ÷ 10 = 406

Check. Multiply back: 406 × 10 = 4,060. ✓

Watch out. Move the digits 1 place to the right. Check the answer is 10 times smaller.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To divide by 10, move every digit 1 place to the right. A number that ends in 1 zero will divide exactly.

1. Look at the end of the number. Are there at least 1 zero? Every digit moves 1 place to the right, so the ones column must be able to hold the moved digits. A number that ends in 1 zero divides exactly.
   9,000 ends in 3 zeros. ✓
2. Make every digit 10 times smaller. Dividing by 10 makes each digit 10 times smaller. That moves it 1 place to the right.
   9 thousands become 9 hundreds
3. Show it in a place-value table. The last 1 zero falls off the end.

   	Th	H	T	O
   9,000	9	0	0	0
   ÷ 10	→ 1 place right
   900		9	0	0

4. Write the answer.
   9,000 ÷ 10 = 900

Check. Multiply back: 900 × 10 = 9,000. ✓

Watch out. Take away 1 zero from the end. Do not take away every zero: 600 ÷ 10 is 60, not 6.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To divide by 100, move every digit 2 places to the right. A number that ends in 2 zeros will divide exactly.

1. Look at the end of the number. Are there at least 2 zeros? Every digit moves 2 places to the right, so the ones column must be able to hold the moved digits. A number that ends in 2 zeros divides exactly.
   600 ends in 2 zeros. ✓
2. Make every digit 100 times smaller. Dividing by 100 makes each digit 100 times smaller. That moves it 2 places to the right.
   6 hundreds become 6 ones
3. Show it in a place-value table. The last 2 zeros fall off the end.

   	Th	H	T	O
   600		6	0	0
   ÷ 100	→ 2 places right
   6				6

4. Write the answer.
   600 ÷ 100 = 6

Check. Multiply back: 6 × 100 = 600. ✓

Watch out. Move the digits 2 places to the right. Check the answer is 100 times smaller.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To divide by 100, move every digit 2 places to the right. A number that ends in 2 zeros will divide exactly.

1. Look at the end of the number. Are there at least 2 zeros? Every digit moves 2 places to the right, so the ones column must be able to hold the moved digits. A number that ends in 2 zeros divides exactly.
   4,700 ends in 2 zeros. ✓
2. Make every digit 100 times smaller. Dividing by 100 makes each digit 100 times smaller. That moves it 2 places to the right.
   4 thousands become 4 tens
   7 hundreds become 7 ones
3. Show it in a place-value table. The last 2 zeros fall off the end.

   	Th	H	T	O
   4,700	4	7	0	0
   ÷ 100	→ 2 places right
   47			4	7

4. Write the answer.
   4,700 ÷ 100 = 47

Check. Multiply back: 47 × 100 = 4,700. ✓

Watch out. Move the digits 2 places to the right. Check the answer is 100 times smaller.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To divide by 100, move every digit 2 places to the right. A number that ends in 2 zeros will divide exactly.

1. Look at the end of the number. Are there at least 2 zeros? Every digit moves 2 places to the right, so the ones column must be able to hold the moved digits. A number that ends in 2 zeros divides exactly.
   3,000 ends in 3 zeros. ✓
2. Make every digit 100 times smaller. Dividing by 100 makes each digit 100 times smaller. That moves it 2 places to the right.
   3 thousands become 3 tens
3. Show it in a place-value table. The last 2 zeros fall off the end.

   	Th	H	T	O
   3,000	3	0	0	0
   ÷ 100	→ 2 places right
   30			3	0

4. Write the answer.
   3,000 ÷ 100 = 30

Check. Multiply back: 30 × 100 = 3,000. ✓

Watch out. Take away 2 zeros from the end. Do not take away every zero: 600 ÷ 10 is 60, not 6.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To divide by 100, move every digit 2 places to the right. A number that ends in 2 zeros will divide exactly.

1. Look at the end of the number. Are there at least 2 zeros? Every digit moves 2 places to the right, so the ones column must be able to hold the moved digits. A number that ends in 2 zeros divides exactly.
   9,500 ends in 2 zeros. ✓
2. Make every digit 100 times smaller. Dividing by 100 makes each digit 100 times smaller. That moves it 2 places to the right.
   9 thousands become 9 tens
   5 hundreds become 5 ones
3. Show it in a place-value table. The last 2 zeros fall off the end.

   	Th	H	T	O
   9,500	9	5	0	0
   ÷ 100	→ 2 places right
   95			9	5

4. Write the answer.
   9,500 ÷ 100 = 95

Check. Multiply back: 95 × 100 = 9,500. ✓

Watch out. Move the digits 2 places to the right. Check the answer is 100 times smaller.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To divide by 100, move every digit 2 places to the right. A number that ends in 2 zeros will divide exactly.

1. Look at the end of the number. Are there at least 2 zeros? Every digit moves 2 places to the right, so the ones column must be able to hold the moved digits. A number that ends in 2 zeros divides exactly.
   7,200 ends in 2 zeros. ✓
2. Make every digit 100 times smaller. Dividing by 100 makes each digit 100 times smaller. That moves it 2 places to the right.
   7 thousands become 7 tens
   2 hundreds become 2 ones
3. Show it in a place-value table. The last 2 zeros fall off the end.

   	Th	H	T	O
   7,200	7	2	0	0
   ÷ 100	→ 2 places right
   72			7	2

4. Write the answer.
   7,200 ÷ 100 = 72

Check. Multiply back: 72 × 100 = 7,200. ✓

Watch out. Move the digits 2 places to the right. Check the answer is 100 times smaller.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To divide by 100, move every digit 2 places to the right. A number that ends in 2 zeros will divide exactly.

1. Look at the end of the number. Are there at least 2 zeros? Every digit moves 2 places to the right, so the ones column must be able to hold the moved digits. A number that ends in 2 zeros divides exactly.
   8,000 ends in 3 zeros. ✓
2. Make every digit 100 times smaller. Dividing by 100 makes each digit 100 times smaller. That moves it 2 places to the right.
   8 thousands become 8 tens
3. Show it in a place-value table. The last 2 zeros fall off the end.

   	Th	H	T	O
   8,000	8	0	0	0
   ÷ 100	→ 2 places right
   80			8	0

4. Write the answer.
   8,000 ÷ 100 = 80

Check. Multiply back: 80 × 100 = 8,000. ✓

Watch out. Take away 2 zeros from the end. Do not take away every zero: 600 ÷ 10 is 60, not 6.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To multiply by 10, move every digit 1 place to the left and put a zero in the empty place on the right. Do not just “add a zero”: it is the digits that move.

1. Say what each digit is worth. The digits have different values because of their columns.
   5 tens
   6 ones
2. Make every digit 10 times bigger. Multiplying by 10 makes each digit 10 times bigger. That moves it 1 place to the left.
   5 tens become 5 hundreds
   6 ones become 6 tens
3. Show it in a place-value table. The 1 gap on the right is empty, so we put a zero there.

   	Th	H	T	O
   56			5	6
   × 10	← 1 place left
   560		5	6	0

4. Write the answer. The zero place holders keep every digit in the right column.
   56 × 10 = 560

Check. Divide back: 560 ÷ 10 = 56. ✓

Watch out. Move the digits, then fill the empty place with a zero. Check the answer is 10 times bigger.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To divide by 10, move every digit 1 place to the right. A number that ends in 1 zero will divide exactly.

1. Look at the end of the number. Are there at least 1 zero? Every digit moves 1 place to the right, so the ones column must be able to hold the moved digits. A number that ends in 1 zero divides exactly.
   300 ends in 2 zeros. ✓
2. Make every digit 10 times smaller. Dividing by 10 makes each digit 10 times smaller. That moves it 1 place to the right.
   3 hundreds become 3 tens
3. Show it in a place-value table. The last 1 zero falls off the end.

   	Th	H	T	O
   300		3	0	0
   ÷ 10	→ 1 place right
   30			3	0

4. Write the answer.
   300 ÷ 10 = 30

Check. Multiply back: 30 × 10 = 300. ✓

Watch out. Take away 1 zero from the end. Do not take away every zero: 600 ÷ 10 is 60, not 6.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To multiply by 100, move every digit 2 places to the left and put 2 zeros in the empty places on the right. Do not just “add a zero”: it is the digits that move.

1. Say what each digit is worth. The digits have different values because of their columns.
   7 ones
2. Make every digit 100 times bigger. Multiplying by 100 makes each digit 100 times bigger. That moves it 2 places to the left.
   7 ones become 7 hundreds
3. Show it in a place-value table. The 2 gaps on the right are empty, so we put zeros there.

   	Th	H	T	O
   7				7
   × 100	← 2 places left
   700		7	0	0

4. Write the answer. The zero place holders keep every digit in the right column.
   7 × 100 = 700

Check. Divide back: 700 ÷ 100 = 7. ✓

Watch out. Move the digits, then fill the empty places with zeros. Check the answer is 100 times bigger.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To divide by 100, move every digit 2 places to the right. A number that ends in 2 zeros will divide exactly.

1. Look at the end of the number. Are there at least 2 zeros? Every digit moves 2 places to the right, so the ones column must be able to hold the moved digits. A number that ends in 2 zeros divides exactly.
   2,900 ends in 2 zeros. ✓
2. Make every digit 100 times smaller. Dividing by 100 makes each digit 100 times smaller. That moves it 2 places to the right.
   2 thousands become 2 tens
   9 hundreds become 9 ones
3. Show it in a place-value table. The last 2 zeros fall off the end.

   	Th	H	T	O
   2,900	2	9	0	0
   ÷ 100	→ 2 places right
   29			2	9

4. Write the answer.
   2,900 ÷ 100 = 29

Check. Multiply back: 29 × 100 = 2,900. ✓

Watch out. Move the digits 2 places to the right. Check the answer is 100 times smaller.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To multiply by 10, move every digit 1 place to the left and put a zero in the empty place on the right. Do not just “add a zero”: it is the digits that move.

1. Say what each digit is worth. The digits have different values because of their columns.
   4 hundreds
   1 ten
2. Make every digit 10 times bigger. Multiplying by 10 makes each digit 10 times bigger. That moves it 1 place to the left.
   4 hundreds become 4 thousands
   1 ten becomes 1 hundred
3. Show it in a place-value table. The 1 gap on the right is empty, so we put a zero there.

   	Th	H	T	O
   410		4	1	0
   × 10	← 1 place left
   4,100	4	1	0	0

4. Write the answer. The zero place holders keep every digit in the right column.
   410 × 10 = 4,100

Check. Divide back: 4,100 ÷ 10 = 410. ✓

Watch out. The zeros are place holders. Count them: 410 × 10 must end with 1 zero more than the zeros 410 already ends with.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To divide by 10, move every digit 1 place to the right. A number that ends in 1 zero will divide exactly.

1. Look at the end of the number. Are there at least 1 zero? Every digit moves 1 place to the right, so the ones column must be able to hold the moved digits. A number that ends in 1 zero divides exactly.
   6,000 ends in 3 zeros. ✓
2. Make every digit 10 times smaller. Dividing by 10 makes each digit 10 times smaller. That moves it 1 place to the right.
   6 thousands become 6 hundreds
3. Show it in a place-value table. The last 1 zero falls off the end.

   	Th	H	T	O
   6,000	6	0	0	0
   ÷ 10	→ 1 place right
   600		6	0	0

4. Write the answer.
   6,000 ÷ 10 = 600

Check. Multiply back: 600 × 10 = 6,000. ✓

Watch out. Take away 1 zero from the end. Do not take away every zero: 600 ÷ 10 is 60, not 6.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To multiply by 100, move every digit 2 places to the left and put 2 zeros in the empty places on the right. Do not just “add a zero”: it is the digits that move.

1. Say what each digit is worth. The digits have different values because of their columns.
   8 tens
   3 ones
2. Make every digit 100 times bigger. Multiplying by 100 makes each digit 100 times bigger. That moves it 2 places to the left.
   8 tens become 8 thousands
   3 ones become 3 hundreds
3. Show it in a place-value table. The 2 gaps on the right are empty, so we put zeros there.

   	Th	H	T	O
   83			8	3
   × 100	← 2 places left
   8,300	8	3	0	0

4. Write the answer. The zero place holders keep every digit in the right column.
   83 × 100 = 8,300

Check. Divide back: 8,300 ÷ 100 = 83. ✓

Watch out. Move the digits, then fill the empty places with zeros. Check the answer is 100 times bigger.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To divide by 100, move every digit 2 places to the right. A number that ends in 2 zeros will divide exactly.

1. Look at the end of the number. Are there at least 2 zeros? Every digit moves 2 places to the right, so the ones column must be able to hold the moved digits. A number that ends in 2 zeros divides exactly.
   500 ends in 2 zeros. ✓
2. Make every digit 100 times smaller. Dividing by 100 makes each digit 100 times smaller. That moves it 2 places to the right.
   5 hundreds become 5 ones
3. Show it in a place-value table. The last 2 zeros fall off the end.

   	Th	H	T	O
   500		5	0	0
   ÷ 100	→ 2 places right
   5				5

4. Write the answer.
   500 ÷ 100 = 5

Check. Multiply back: 5 × 100 = 500. ✓

Watch out. Move the digits 2 places to the right. Check the answer is 100 times smaller.

Method. Look at where the digits start and where they finish. The direction and the number of places tell you whether it is multiply or divide, and by what.

1. Read the top number and the bottom number. The top row is the starting number. The bottom row is the answer.
   Top: 38.   Bottom: 380.
2. Look at the arrows. The digits move 1 place to the left. Moving to the left makes numbers bigger.
   1 place to the left means × 10.
3. Write the calculation.
   38 × 10 = 380

Check. Divide back: 380 ÷ 10 = 38. ✓

Watch out. Digits moving to the left means multiply. Digits moving to the right means divide.

Method. Look at where the digits start and where they finish. The direction and the number of places tell you whether it is multiply or divide, and by what.

1. Read the top number and the bottom number. The top row is the starting number. The bottom row is the answer.
   Top: 6,700.   Bottom: 67.
2. Look at the arrows. The digits move 2 places to the right. Moving to the right makes numbers smaller.
   2 places to the right means ÷ 100.
3. Write the calculation.
   6,700 ÷ 100 = 67

Check. Multiply back: 67 × 100 = 6,700. ✓

Watch out. Digits moving to the left means multiply. Digits moving to the right means divide.

Method. Look at where the digits start and where they finish. The direction and the number of places tell you whether it is multiply or divide, and by what.

1. Read the top number and the bottom number. The top row is the starting number. The bottom row is the answer.
   Top: 52.   Bottom: 5,200.
2. Look at the arrows. The digits move 2 places to the left. Moving to the left makes numbers bigger.
   2 places to the left means × 100.
3. Write the calculation.
   52 × 100 = 5,200

Check. Divide back: 5,200 ÷ 100 = 52. ✓

Watch out. Digits moving to the left means multiply. Digits moving to the right means divide.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. Find out how far the digits move. One place to the left is × 10. Two places to the left is × 100.

1. Compare the two numbers. 45 is on one side, 4,500 is the answer.
   45 → 4,500
2. Count how many places the digits moved. Each digit of 45 moved to the left. Count the places.

   	Th	H	T	O
   45			4	5
   × 100	← 2 places left
   4,500	4	5	0	0

3. Say what the number is. Digits that move 2 places to the left mean × 100.
   45 × 100 = 4,500

Check. 45 × 100 = 4,500. ✓

Watch out. Put your answer back in the box and read the whole sentence. It must be true.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. Find out how far the digits move. One place to the left is × 10. Two places to the left is × 100.

1. Compare the two numbers. 8 is on one side, 80 is the answer.
   8 → 80
2. Count how many places the digits moved. Each digit of 8 moved to the left. Count the places.

   	Th	H	T	O
   8				8
   × 10	← 1 place left
   80			8	0

3. Say what the number is. Digits that move 1 place to the left mean × 10.
   8 × 10 = 80

Check. 8 × 10 = 80. ✓

Watch out. Put your answer back in the box and read the whole sentence. It must be true.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. Multiplying and dividing undo each other. Divide the answer by 10 to find the missing number.

1. Use the opposite (inverse) operation. ? × 10 = 370, so 370 ÷ 10 gives the missing number.
   370 ÷ 10
2. Move the digits 1 place to the right. Dividing by 10 makes each digit 10 times smaller.

   	Th	H	T	O
   370		3	7	0
   ÷ 10	→ 1 place right
   37			3	7

3. Write the missing number.
   37 × 10 = 370

Check. 37 × 10 = 370. ✓

Watch out. Put your answer back in the box and read the whole sentence. It must be true.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. Multiplying and dividing undo each other. Divide the answer by 100 to find the missing number.

1. Use the opposite (inverse) operation. ? × 100 = 6,200, so 6,200 ÷ 100 gives the missing number.
   6,200 ÷ 100
2. Move the digits 2 places to the right. Dividing by 100 makes each digit 100 times smaller.

   	Th	H	T	O
   6,200	6	2	0	0
   ÷ 100	→ 2 places right
   62			6	2

3. Write the missing number.
   62 × 100 = 6,200

Check. 62 × 100 = 6,200. ✓

Watch out. Put your answer back in the box and read the whole sentence. It must be true.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. Multiplying and dividing undo each other. Multiply 54 by 10 to find the missing number.

1. Use the opposite (inverse) operation. The missing number is 10 times bigger than 54.
   54 × 10
2. Move the digits 1 place to the left. Multiplying by 10 makes each digit 10 times bigger.

   	Th	H	T	O
   54			5	4
   × 10	← 1 place left
   540		5	4	0

3. Write the missing number.
   540 ÷ 10 = 54

Check. 540 ÷ 10 = 54. ✓

Watch out. Put your answer back in the box and read the whole sentence. It must be true.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. Find out how far the digits move. One place to the right is ÷ 10. Two places to the right is ÷ 100.

1. Compare the two numbers. 900 is divided by the missing number to make 9.
   900 → 9
2. Count how many places the digits moved. Each digit of 900 moved to the right.

   	Th	H	T	O
   900		9	0	0
   ÷ 100	→ 2 places right
   9				9

3. Say what the number is. Digits that move 2 places to the right mean ÷ 100.
   900 ÷ 100 = 9

Check. 9 × 100 = 900. ✓

Watch out. Put your answer back in the box and read the whole sentence. It must be true.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To multiply by 10, move every digit 1 place to the left and put a zero in the empty place on the right. Do not just “add a zero”: it is the digits that move.

1. Say what each digit is worth. The digits have different values because of their columns.
   7 tens
   6 ones
2. Make every digit 10 times bigger. Multiplying by 10 makes each digit 10 times bigger. That moves it 1 place to the left.
   7 tens become 7 hundreds
   6 ones become 6 tens
3. Show it in a place-value table. The 1 gap on the right is empty, so we put a zero there.

   	Th	H	T	O
   76			7	6
   × 10	← 1 place left
   760		7	6	0

4. Write the answer. The zero place holders keep every digit in the right column.
   76 × 10 = 760

Check. Divide back: 760 ÷ 10 = 76. ✓

Watch out. Move the digits, then fill the empty place with a zero. Check the answer is 10 times bigger.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To multiply by 100, move every digit 2 places to the left and put 2 zeros in the empty places on the right. Do not just “add a zero”: it is the digits that move.

1. Say what each digit is worth. The digits have different values because of their columns.
   9 ones
2. Make every digit 100 times bigger. Multiplying by 100 makes each digit 100 times bigger. That moves it 2 places to the left.
   9 ones become 9 hundreds
3. Show it in a place-value table. The 2 gaps on the right are empty, so we put zeros there.

   	Th	H	T	O
   9				9
   × 100	← 2 places left
   900		9	0	0

4. Write the answer. The zero place holders keep every digit in the right column.
   9 × 100 = 900

Check. Divide back: 900 ÷ 100 = 9. ✓

Watch out. Move the digits, then fill the empty places with zeros. Check the answer is 100 times bigger.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To divide by 10, move every digit 1 place to the right. A number that ends in 1 zero will divide exactly.

1. Look at the end of the number. Are there at least 1 zero? Every digit moves 1 place to the right, so the ones column must be able to hold the moved digits. A number that ends in 1 zero divides exactly.
   830 ends in 1 zero. ✓
2. Make every digit 10 times smaller. Dividing by 10 makes each digit 10 times smaller. That moves it 1 place to the right.
   8 hundreds become 8 tens
   3 tens become 3 ones
3. Show it in a place-value table. The last 1 zero falls off the end.

   	Th	H	T	O
   830		8	3	0
   ÷ 10	→ 1 place right
   83			8	3

4. Write the answer.
   830 ÷ 10 = 83

Check. Multiply back: 83 × 10 = 830. ✓

Watch out. Move the digits 1 place to the right. Check the answer is 10 times smaller.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To divide by 100, move every digit 2 places to the right. A number that ends in 2 zeros will divide exactly.

1. Look at the end of the number. Are there at least 2 zeros? Every digit moves 2 places to the right, so the ones column must be able to hold the moved digits. A number that ends in 2 zeros divides exactly.
   6,100 ends in 2 zeros. ✓
2. Make every digit 100 times smaller. Dividing by 100 makes each digit 100 times smaller. That moves it 2 places to the right.
   6 thousands become 6 tens
   1 hundred becomes 1 one
3. Show it in a place-value table. The last 2 zeros fall off the end.

   	Th	H	T	O
   6,100	6	1	0	0
   ÷ 100	→ 2 places right
   61			6	1

4. Write the answer.
   6,100 ÷ 100 = 61

Check. Multiply back: 61 × 100 = 6,100. ✓

Watch out. Move the digits 2 places to the right. Check the answer is 100 times smaller.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. Multiplying and dividing undo each other. Divide the answer by 100 to find the missing number.

1. Use the opposite (inverse) operation. ? × 100 = 6,300, so 6,300 ÷ 100 gives the missing number.
   6,300 ÷ 100
2. Move the digits 2 places to the right. Dividing by 100 makes each digit 100 times smaller.

   	Th	H	T	O
   6,300	6	3	0	0
   ÷ 100	→ 2 places right
   63			6	3

3. Write the missing number.
   63 × 100 = 6,300

Check. 63 × 100 = 6,300. ✓

Watch out. Put your answer back in the box and read the whole sentence. It must be true.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To divide by 10, move every digit 1 place to the right. A number that ends in 1 zero will divide exactly.

1. Look at the end of the number. Are there at least 1 zero? Every digit moves 1 place to the right, so the ones column must be able to hold the moved digits. A number that ends in 1 zero divides exactly.
   6,300 ends in 2 zeros. ✓
2. Make every digit 10 times smaller. Dividing by 10 makes each digit 10 times smaller. That moves it 1 place to the right.
   6 thousands become 6 hundreds
   3 hundreds become 3 tens
3. Show it in a place-value table. The last 1 zero falls off the end.

   	Th	H	T	O
   6,300	6	3	0	0
   ÷ 10	→ 1 place right
   630		6	3	0

4. Write the answer.
   6,300 ÷ 10 = 630

Check. Multiply back: 630 × 10 = 6,300. ✓

Watch out. Take away 1 zero from the end. Do not take away every zero: 600 ÷ 10 is 60, not 6.