Year 5: Short division with exchanging

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   2	6	8

2. Divide the tens. Always start on the left, with the biggest place value.
   6 ÷ 2 = 3
   Write 3 above the 6.
3. Divide the ones. Move to the next digit on the right.
   Nothing was carried, so there are just 8 ones.
   8 ÷ 2: 4 × 2 = 8. Write 4 above the 8.
   Nothing is left over, so there is no remainder.
4. Read the answer. Read the digits above the line from left to right.

   	3	4
   2	6	8

   
   68 ÷ 2 = 34
5. Write the answer.
   68 ÷ 2 = 34

Check. Multiply back: 34 × 2 = 30 × 2 + 4 × 2 = 60 + 8 = 68. ✓

Watch out. Start on the left, with the biggest place value. Carry any remainder to the next digit.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   3	9	3

2. Divide the tens. Always start on the left, with the biggest place value.
   9 ÷ 3 = 3
   Write 3 above the 9.
3. Divide the ones. Move to the next digit on the right.
   Nothing was carried, so there are just 3 ones.
   3 ÷ 3: 1 × 3 = 3. Write 1 above the 3.
   Nothing is left over, so there is no remainder.
4. Read the answer. Read the digits above the line from left to right.

   	3	1
   3	9	3

   
   93 ÷ 3 = 31
5. Write the answer.
   93 ÷ 3 = 31

Check. Multiply back: 31 × 3 = 30 × 3 + 1 × 3 = 90 + 3 = 93. ✓

Watch out. Start on the left, with the biggest place value. Carry any remainder to the next digit.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   6	6	6

2. Divide the tens. Always start on the left, with the biggest place value.
   6 ÷ 6 = 1
   Write 1 above the 6.
3. Divide the ones. Move to the next digit on the right.
   Nothing was carried, so there are just 6 ones.
   6 ÷ 6: 1 × 6 = 6. Write 1 above the 6.
   Nothing is left over, so there is no remainder.
4. Read the answer. Read the digits above the line from left to right.

   	1	1
   6	6	6

   
   66 ÷ 6 = 11
5. Write the answer.
   66 ÷ 6 = 11

Check. Multiply back: 11 × 6 = 10 × 6 + 1 × 6 = 60 + 6 = 66. ✓

Watch out. Start on the left, with the biggest place value. Carry any remainder to the next digit.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   4	6	4

2. Divide the tens. Always start on the left, with the biggest place value.
   6 ÷ 4 = 1, remainder 2
   Write 1 above the 6.
   Exchange the remainder: 2 tens become 20 ones. Carry 2 to the next digit.
3. Divide the ones. Move to the next digit on the right. Add the 2 that was carried.
   The carried 2 makes 20 ones. With the 4 ones there are 20 + 4 = 24 ones.
   24 ÷ 4: 6 × 4 = 24. Write 6 above the 4.
   Nothing is left over, so there is no remainder.
4. Read the answer. Read the digits above the line from left to right.

   	1	6
   4	6	24

   
   64 ÷ 4 = 16
5. Write the answer.
   64 ÷ 4 = 16

Check. Multiply back: 16 × 4 = 10 × 4 + 6 × 4 = 40 + 24 = 64. ✓

Watch out. Start on the left, with the biggest place value. Carry any remainder to the next digit.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   3	8	7

2. Divide the tens. Always start on the left, with the biggest place value.
   8 ÷ 3 = 2, remainder 2
   Write 2 above the 8.
   Exchange the remainder: 2 tens become 20 ones. Carry 2 to the next digit.
3. Divide the ones. Move to the next digit on the right. Add the 2 that was carried.
   The carried 2 makes 20 ones. With the 7 ones there are 20 + 7 = 27 ones.
   27 ÷ 3: 9 × 3 = 27. Write 9 above the 7.
   Nothing is left over, so there is no remainder.
4. Read the answer. Read the digits above the line from left to right.

   	2	9
   3	8	27

   
   87 ÷ 3 = 29
5. Write the answer.
   87 ÷ 3 = 29

Check. Multiply back: 29 × 3 = 20 × 3 + 9 × 3 = 60 + 27 = 87. ✓

Watch out. Start on the left, with the biggest place value. Carry any remainder to the next digit.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   8	9	6

2. Divide the tens. Always start on the left, with the biggest place value.
   9 ÷ 8 = 1, remainder 1
   Write 1 above the 9.
   Exchange the remainder: 1 ten becomes 10 ones. Carry 1 to the next digit.
3. Divide the ones. Move to the next digit on the right. Add the 1 that was carried.
   The carried 1 makes 10 ones. With the 6 ones there are 10 + 6 = 16 ones.
   16 ÷ 8: 2 × 8 = 16. Write 2 above the 6.
   Nothing is left over, so there is no remainder.
4. Read the answer. Read the digits above the line from left to right.

   	1	2
   8	9	16

   
   96 ÷ 8 = 12
5. Write the answer.
   96 ÷ 8 = 12

Check. Multiply back: 12 × 8 = 10 × 8 + 2 × 8 = 80 + 16 = 96. ✓

Watch out. Start on the left, with the biggest place value. Carry any remainder to the next digit.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   5	7	5

2. Divide the tens. Always start on the left, with the biggest place value.
   7 ÷ 5 = 1, remainder 2
   Write 1 above the 7.
   Exchange the remainder: 2 tens become 20 ones. Carry 2 to the next digit.
3. Divide the ones. Move to the next digit on the right. Add the 2 that was carried.
   The carried 2 makes 20 ones. With the 5 ones there are 20 + 5 = 25 ones.
   25 ÷ 5: 5 × 5 = 25. Write 5 above the 5.
   Nothing is left over, so there is no remainder.
4. Read the answer. Read the digits above the line from left to right.

   	1	5
   5	7	25

   
   75 ÷ 5 = 15
5. Write the answer.
   75 ÷ 5 = 15

Check. Multiply back: 15 × 5 = 10 × 5 + 5 × 5 = 50 + 25 = 75. ✓

Watch out. Start on the left, with the biggest place value. Carry any remainder to the next digit.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   4	5	8

2. Divide the tens. Always start on the left, with the biggest place value.
   5 ÷ 4 = 1, remainder 1
   Write 1 above the 5.
   Exchange the remainder: 1 ten becomes 10 ones. Carry 1 to the next digit.
3. Divide the ones. Move to the next digit on the right. Add the 1 that was carried.
   The carried 1 makes 10 ones. With the 8 ones there are 10 + 8 = 18 ones.
   18 ÷ 4: 4 × 4 = 16, and 18 − 16 = 2. Write 4 above the 8.
   The remainder is 2.
4. Read the answer. Read the digits above the line from left to right.

   	1	4	r 2
   4	5	18

   
   58 ÷ 4 = 14 r 2
5. Write the answer.
   58 ÷ 4 = 14 r 2

Check. Multiply back: 14 × 4 = 10 × 4 + 4 × 4 = 40 + 16 = 56
56 + 2 (the remainder) = 58. ✓

Watch out. The remainder must always be smaller than the number you divide by (4). If it is not, you can divide again.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   6	8	3

2. Divide the tens. Always start on the left, with the biggest place value.
   8 ÷ 6 = 1, remainder 2
   Write 1 above the 8.
   Exchange the remainder: 2 tens become 20 ones. Carry 2 to the next digit.
3. Divide the ones. Move to the next digit on the right. Add the 2 that was carried.
   The carried 2 makes 20 ones. With the 3 ones there are 20 + 3 = 23 ones.
   23 ÷ 6: 3 × 6 = 18, and 23 − 18 = 5. Write 3 above the 3.
   The remainder is 5.
4. Read the answer. Read the digits above the line from left to right.

   	1	3	r 5
   6	8	23

   
   83 ÷ 6 = 13 r 5
5. Write the answer.
   83 ÷ 6 = 13 r 5

Check. Multiply back: 13 × 6 = 10 × 6 + 3 × 6 = 60 + 18 = 78
78 + 5 (the remainder) = 83. ✓

Watch out. The remainder must always be smaller than the number you divide by (6). If it is not, you can divide again.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   3	7	1

2. Divide the tens. Always start on the left, with the biggest place value.
   7 ÷ 3 = 2, remainder 1
   Write 2 above the 7.
   Exchange the remainder: 1 ten becomes 10 ones. Carry 1 to the next digit.
3. Divide the ones. Move to the next digit on the right. Add the 1 that was carried.
   The carried 1 makes 10 ones. With the 1 ones there are 10 + 1 = 11 ones.
   11 ÷ 3: 3 × 3 = 9, and 11 − 9 = 2. Write 3 above the 1.
   The remainder is 2.
4. Read the answer. Read the digits above the line from left to right.

   	2	3	r 2
   3	7	11

   
   71 ÷ 3 = 23 r 2
5. Write the answer.
   71 ÷ 3 = 23 r 2

Check. Multiply back: 23 × 3 = 20 × 3 + 3 × 3 = 60 + 9 = 69
69 + 2 (the remainder) = 71. ✓

Watch out. The remainder must always be smaller than the number you divide by (3). If it is not, you can divide again.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   7	9	4

2. Divide the tens. Always start on the left, with the biggest place value.
   9 ÷ 7 = 1, remainder 2
   Write 1 above the 9.
   Exchange the remainder: 2 tens become 20 ones. Carry 2 to the next digit.
3. Divide the ones. Move to the next digit on the right. Add the 2 that was carried.
   The carried 2 makes 20 ones. With the 4 ones there are 20 + 4 = 24 ones.
   24 ÷ 7: 3 × 7 = 21, and 24 − 21 = 3. Write 3 above the 4.
   The remainder is 3.
4. Read the answer. Read the digits above the line from left to right.

   	1	3	r 3
   7	9	24

   
   94 ÷ 7 = 13 r 3
5. Write the answer.
   94 ÷ 7 = 13 r 3

Check. Multiply back: 13 × 7 = 10 × 7 + 3 × 7 = 70 + 21 = 91
91 + 3 (the remainder) = 94. ✓

Watch out. The remainder must always be smaller than the number you divide by (7). If it is not, you can divide again.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   3	9	3	6

2. Divide the hundreds. Always start on the left, with the biggest place value.
   9 ÷ 3 = 3
   Write 3 above the 9.
3. Divide the tens. Move to the next digit on the right.
   Nothing was carried, so there are just 3 tens.
   3 ÷ 3: 1 × 3 = 3. Write 1 above the 3.
4. Divide the ones. Move to the next digit on the right.
   Nothing was carried, so there are just 6 ones.
   6 ÷ 3: 2 × 3 = 6. Write 2 above the 6.
   Nothing is left over, so there is no remainder.
5. Read the answer. Read the digits above the line from left to right.

   	3	1	2
   3	9	3	6

   
   936 ÷ 3 = 312
6. Write the answer.
   936 ÷ 3 = 312

Check. Multiply back: 312 × 3 = 300 × 3 + 10 × 3 + 2 × 3 = 900 + 30 + 6 = 936. ✓

Watch out. Start on the left, with the biggest place value. Carry any remainder to the next digit.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   5	7	2	5

2. Divide the hundreds. Always start on the left, with the biggest place value.
   7 ÷ 5 = 1, remainder 2
   Write 1 above the 7.
   Exchange the remainder: 2 hundreds become 20 tens. Carry 2 to the next digit.
3. Divide the tens. Move to the next digit on the right. Add the 2 that was carried.
   The carried 2 makes 20 tens. With the 2 tens there are 20 + 2 = 22 tens.
   22 ÷ 5: 4 × 5 = 20, and 22 − 20 = 2. Write 4 above the 2.
   Exchange: 2 tens become 20 ones. Carry 2 to the next digit.
4. Divide the ones. Move to the next digit on the right. Add the 2 that was carried.
   The carried 2 makes 20 ones. With the 5 ones there are 20 + 5 = 25 ones.
   25 ÷ 5: 5 × 5 = 25. Write 5 above the 5.
   Nothing is left over, so there is no remainder.
5. Read the answer. Read the digits above the line from left to right.

   	1	4	5
   5	7	22	25

   
   725 ÷ 5 = 145
6. Write the answer.
   725 ÷ 5 = 145

Check. Multiply back: 145 × 5 = 100 × 5 + 40 × 5 + 5 × 5 = 500 + 200 + 25 = 725. ✓

Watch out. Start on the left, with the biggest place value. Carry any remainder to the next digit.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   7	6	1	6

2. Divide the hundreds. Always start on the left, with the biggest place value.
   6 ÷ 7: 6 is smaller than 7, so we cannot give each share a whole hundred. Write 0 (a 0 at the front is not part of the answer).
   Exchange the 6 hundreds for 60 tens. Carry 6 to the next digit.
3. Divide the tens. Move to the next digit on the right. Add the 6 that was carried.
   The carried 6 makes 60 tens. With the 1 tens there are 60 + 1 = 61 tens.
   61 ÷ 7: 8 × 7 = 56, and 61 − 56 = 5. Write 8 above the 1.
   Exchange: 5 tens become 50 ones. Carry 5 to the next digit.
4. Divide the ones. Move to the next digit on the right. Add the 5 that was carried.
   The carried 5 makes 50 ones. With the 6 ones there are 50 + 6 = 56 ones.
   56 ÷ 7: 8 × 7 = 56. Write 8 above the 6.
   Nothing is left over, so there is no remainder.
5. Read the answer. Ignore any 0 at the front of the answer.

   	0	8	8
   7	6	61	56

   
   616 ÷ 7 = 88
6. Write the answer.
   616 ÷ 7 = 88

Check. Multiply back: 88 × 7 = 80 × 7 + 8 × 7 = 560 + 56 = 616. ✓

Watch out. If the first digit is smaller than 7, write 0 above it (not in the final answer) and carry the digit to the next place.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   6	4	5	6

2. Divide the hundreds. Always start on the left, with the biggest place value.
   4 ÷ 6: 4 is smaller than 6, so we cannot give each share a whole hundred. Write 0 (a 0 at the front is not part of the answer).
   Exchange the 4 hundreds for 40 tens. Carry 4 to the next digit.
3. Divide the tens. Move to the next digit on the right. Add the 4 that was carried.
   The carried 4 makes 40 tens. With the 5 tens there are 40 + 5 = 45 tens.
   45 ÷ 6: 7 × 6 = 42, and 45 − 42 = 3. Write 7 above the 5.
   Exchange: 3 tens become 30 ones. Carry 3 to the next digit.
4. Divide the ones. Move to the next digit on the right. Add the 3 that was carried.
   The carried 3 makes 30 ones. With the 6 ones there are 30 + 6 = 36 ones.
   36 ÷ 6: 6 × 6 = 36. Write 6 above the 6.
   Nothing is left over, so there is no remainder.
5. Read the answer. Ignore any 0 at the front of the answer.

   	0	7	6
   6	4	45	36

   
   456 ÷ 6 = 76
6. Write the answer.
   456 ÷ 6 = 76

Check. Multiply back: 76 × 6 = 70 × 6 + 6 × 6 = 420 + 36 = 456. ✓

Watch out. If the first digit is smaller than 6, write 0 above it (not in the final answer) and carry the digit to the next place.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   8	6	7	2

2. Divide the hundreds. Always start on the left, with the biggest place value.
   6 ÷ 8: 6 is smaller than 8, so we cannot give each share a whole hundred. Write 0 (a 0 at the front is not part of the answer).
   Exchange the 6 hundreds for 60 tens. Carry 6 to the next digit.
3. Divide the tens. Move to the next digit on the right. Add the 6 that was carried.
   The carried 6 makes 60 tens. With the 7 tens there are 60 + 7 = 67 tens.
   67 ÷ 8: 8 × 8 = 64, and 67 − 64 = 3. Write 8 above the 7.
   Exchange: 3 tens become 30 ones. Carry 3 to the next digit.
4. Divide the ones. Move to the next digit on the right. Add the 3 that was carried.
   The carried 3 makes 30 ones. With the 2 ones there are 30 + 2 = 32 ones.
   32 ÷ 8: 4 × 8 = 32. Write 4 above the 2.
   Nothing is left over, so there is no remainder.
5. Read the answer. Ignore any 0 at the front of the answer.

   	0	8	4
   8	6	67	32

   
   672 ÷ 8 = 84
6. Write the answer.
   672 ÷ 8 = 84

Check. Multiply back: 84 × 8 = 80 × 8 + 4 × 8 = 640 + 32 = 672. ✓

Watch out. If the first digit is smaller than 8, write 0 above it (not in the final answer) and carry the digit to the next place.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   5	7	3	5

2. Divide the hundreds. Always start on the left, with the biggest place value.
   7 ÷ 5 = 1, remainder 2
   Write 1 above the 7.
   Exchange the remainder: 2 hundreds become 20 tens. Carry 2 to the next digit.
3. Divide the tens. Move to the next digit on the right. Add the 2 that was carried.
   The carried 2 makes 20 tens. With the 3 tens there are 20 + 3 = 23 tens.
   23 ÷ 5: 4 × 5 = 20, and 23 − 20 = 3. Write 4 above the 3.
   Exchange: 3 tens become 30 ones. Carry 3 to the next digit.
4. Divide the ones. Move to the next digit on the right. Add the 3 that was carried.
   The carried 3 makes 30 ones. With the 5 ones there are 30 + 5 = 35 ones.
   35 ÷ 5: 7 × 5 = 35. Write 7 above the 5.
   Nothing is left over, so there is no remainder.
5. Read the answer. Read the digits above the line from left to right.

   	1	4	7
   5	7	23	35

   
   735 ÷ 5 = 147
6. Write the answer.
   735 ÷ 5 = 147

Check. Multiply back: 147 × 5 = 100 × 5 + 40 × 5 + 7 × 5 = 500 + 200 + 35 = 735. ✓

Watch out. Start on the left, with the biggest place value. Carry any remainder to the next digit.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   4	6	2	5

2. Divide the hundreds. Always start on the left, with the biggest place value.
   6 ÷ 4 = 1, remainder 2
   Write 1 above the 6.
   Exchange the remainder: 2 hundreds become 20 tens. Carry 2 to the next digit.
3. Divide the tens. Move to the next digit on the right. Add the 2 that was carried.
   The carried 2 makes 20 tens. With the 2 tens there are 20 + 2 = 22 tens.
   22 ÷ 4: 5 × 4 = 20, and 22 − 20 = 2. Write 5 above the 2.
   Exchange: 2 tens become 20 ones. Carry 2 to the next digit.
4. Divide the ones. Move to the next digit on the right. Add the 2 that was carried.
   The carried 2 makes 20 ones. With the 5 ones there are 20 + 5 = 25 ones.
   25 ÷ 4: 6 × 4 = 24, and 25 − 24 = 1. Write 6 above the 5.
   The remainder is 1.
5. Read the answer. Read the digits above the line from left to right.

   	1	5	6	r 1
   4	6	22	25

   
   625 ÷ 4 = 156 r 1
6. Write the answer.
   625 ÷ 4 = 156 r 1

Check. Multiply back: 156 × 4 = 100 × 4 + 50 × 4 + 6 × 4 = 400 + 200 + 24 = 624
624 + 1 (the remainder) = 625. ✓

Watch out. The remainder must always be smaller than the number you divide by (4). If it is not, you can divide again.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   6	8	7	4

2. Divide the hundreds. Always start on the left, with the biggest place value.
   8 ÷ 6 = 1, remainder 2
   Write 1 above the 8.
   Exchange the remainder: 2 hundreds become 20 tens. Carry 2 to the next digit.
3. Divide the tens. Move to the next digit on the right. Add the 2 that was carried.
   The carried 2 makes 20 tens. With the 7 tens there are 20 + 7 = 27 tens.
   27 ÷ 6: 4 × 6 = 24, and 27 − 24 = 3. Write 4 above the 7.
   Exchange: 3 tens become 30 ones. Carry 3 to the next digit.
4. Divide the ones. Move to the next digit on the right. Add the 3 that was carried.
   The carried 3 makes 30 ones. With the 4 ones there are 30 + 4 = 34 ones.
   34 ÷ 6: 5 × 6 = 30, and 34 − 30 = 4. Write 5 above the 4.
   The remainder is 4.
5. Read the answer. Read the digits above the line from left to right.

   	1	4	5	r 4
   6	8	27	34

   
   874 ÷ 6 = 145 r 4
6. Write the answer.
   874 ÷ 6 = 145 r 4

Check. Multiply back: 145 × 6 = 100 × 6 + 40 × 6 + 5 × 6 = 600 + 240 + 30 = 870
870 + 4 (the remainder) = 874. ✓

Watch out. The remainder must always be smaller than the number you divide by (6). If it is not, you can divide again.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   7	5	9	3

2. Divide the hundreds. Always start on the left, with the biggest place value.
   5 ÷ 7: 5 is smaller than 7, so we cannot give each share a whole hundred. Write 0 (a 0 at the front is not part of the answer).
   Exchange the 5 hundreds for 50 tens. Carry 5 to the next digit.
3. Divide the tens. Move to the next digit on the right. Add the 5 that was carried.
   The carried 5 makes 50 tens. With the 9 tens there are 50 + 9 = 59 tens.
   59 ÷ 7: 8 × 7 = 56, and 59 − 56 = 3. Write 8 above the 9.
   Exchange: 3 tens become 30 ones. Carry 3 to the next digit.
4. Divide the ones. Move to the next digit on the right. Add the 3 that was carried.
   The carried 3 makes 30 ones. With the 3 ones there are 30 + 3 = 33 ones.
   33 ÷ 7: 4 × 7 = 28, and 33 − 28 = 5. Write 4 above the 3.
   The remainder is 5.
5. Read the answer. Ignore any 0 at the front of the answer.

   	0	8	4	r 5
   7	5	59	33

   
   593 ÷ 7 = 84 r 5
6. Write the answer.
   593 ÷ 7 = 84 r 5

Check. Multiply back: 84 × 7 = 80 × 7 + 4 × 7 = 560 + 28 = 588
588 + 5 (the remainder) = 593. ✓

Watch out. The first digit is smaller than 7: write 0 and carry it. The remainder is always smaller than 7.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   8	9	9	9

2. Divide the hundreds. Always start on the left, with the biggest place value.
   9 ÷ 8 = 1, remainder 1
   Write 1 above the 9.
   Exchange the remainder: 1 hundred becomes 10 tens. Carry 1 to the next digit.
3. Divide the tens. Move to the next digit on the right. Add the 1 that was carried.
   The carried 1 makes 10 tens. With the 9 tens there are 10 + 9 = 19 tens.
   19 ÷ 8: 2 × 8 = 16, and 19 − 16 = 3. Write 2 above the 9.
   Exchange: 3 tens become 30 ones. Carry 3 to the next digit.
4. Divide the ones. Move to the next digit on the right. Add the 3 that was carried.
   The carried 3 makes 30 ones. With the 9 ones there are 30 + 9 = 39 ones.
   39 ÷ 8: 4 × 8 = 32, and 39 − 32 = 7. Write 4 above the 9.
   The remainder is 7.
5. Read the answer. Read the digits above the line from left to right.

   	1	2	4	r 7
   8	9	19	39

   
   999 ÷ 8 = 124 r 7
6. Write the answer.
   999 ÷ 8 = 124 r 7

Check. Multiply back: 124 × 8 = 100 × 8 + 20 × 8 + 4 × 8 = 800 + 160 + 32 = 992
992 + 7 (the remainder) = 999. ✓

Watch out. The remainder must always be smaller than the number you divide by (8). If it is not, you can divide again.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. The 5 hundreds are too few to share between 6, so they were exchanged for 50 tens. Add them to the 3 tens that are there.

1. Use the carried 5. The small 5 in front of the 3 means 5 hundreds became 50 tens. With the 3 tens there are 50 + 3 = 53 tens.
   50 + 3 = 53 tens
2. Divide. Use the 6 times table.
   53 ÷ 6 = 8 remainder 5, because 8 × 6 = 48 and 53 − 48 = 5
   Write 8 above the 3.
   

   	0	8
   6	5	53	54

Check. 8 × 6 = 48. ✓

Watch out. The carried digit is added to the digit it is in front of, as tens.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. The remainder from the last step is carried to the next digit.

1. Find the remainder. From the last step: 53 ÷ 6 = 8 remainder 5.
   53 − 48 = 5
2. Carry the remainder. 5 tens are exchanged for 50 ones, so the 5 is written small in front of the 4 in the ones place.

   	0	8
   6	5	53	54

Check. The ones column now has 50 + 4 = 54 ones.

Watch out. The carried number is the remainder.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   6	5	3	4

2. Divide the hundreds. Always start on the left, with the biggest place value.
   5 ÷ 6: 5 is smaller than 6, so we cannot give each share a whole hundred. Write 0 (a 0 at the front is not part of the answer).
   Exchange the 5 hundreds for 50 tens. Carry 5 to the next digit.
3. Divide the tens. Move to the next digit on the right. Add the 5 that was carried.
   The carried 5 makes 50 tens. With the 3 tens there are 50 + 3 = 53 tens.
   53 ÷ 6: 8 × 6 = 48, and 53 − 48 = 5. Write 8 above the 3.
   Exchange: 5 tens become 50 ones. Carry 5 to the next digit.
4. Divide the ones. Move to the next digit on the right. Add the 5 that was carried.
   The carried 5 makes 50 ones. With the 4 ones there are 50 + 4 = 54 ones.
   54 ÷ 6: 9 × 6 = 54. Write 9 above the 4.
   Nothing is left over, so there is no remainder.
5. Read the answer. Ignore any 0 at the front of the answer.

   	0	8	9
   6	5	53	54

   
   534 ÷ 6 = 89
6. Write the answer.
   534 ÷ 6 = 89

Check. Multiply back: 89 × 6 = 80 × 6 + 9 × 6 = 480 + 54 = 534. ✓

Watch out. If the first digit is smaller than 6, write 0 above it (not in the final answer) and carry the digit to the next place.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Count what is in each group.

1. Count the tens rods in one group. Look at one group and count the green rods.
   2 tens
2. Count the ones. Count the small red squares in one group. These came from the exchange.
   3 ones
3. Read the number in each group. 2 tens and 3 ones make 23.
   23

Check. 23 × 4 = 92.

Watch out. Count carefully: each group is the same.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Look at the orange squares outside the groups.

1. Count the left-over ones. They are not in any group.
   2 left over
2. Write the division. 94 ÷ 4 = 23 remainder 2
   94 ÷ 4 = 23 r 2

Check. 23 × 4 = 92, and 92 + 2 = 94. ✓

Watch out. The remainder is smaller than 4.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Look at the orange squares outside the groups.

1. Count the left-over ones. They are not in any group.
   2 left over
2. Write the division. 94 ÷ 4 = 23 remainder 2
   94 ÷ 4 = 23 r 2

Check. 23 × 4 = 92, and 92 + 2 = 94. ✓

Watch out. The remainder is smaller than 4.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw a bar model, choose the operation, then work it out.

1. Draw a bar model. There are 6 equal shares. Each share is the same size.
2. Choose the operation. 138 is shared equally between 6, so divide by 6.
   138 ÷ 6
3. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   6	1	3	8

4. Divide the hundreds. Always start on the left, with the biggest place value.
   1 ÷ 6: 1 is smaller than 6, so we cannot give each share a whole hundred. Write 0 (a 0 at the front is not part of the answer).
   Exchange the 1 hundred for 10 tens. Carry 1 to the next digit.
5. Divide the tens. Move to the next digit on the right. Add the 1 that was carried.
   The carried 1 makes 10 tens. With the 3 tens there are 10 + 3 = 13 tens.
   13 ÷ 6: 2 × 6 = 12, and 13 − 12 = 1. Write 2 above the 3.
   Exchange: 1 ten becomes 10 ones. Carry 1 to the next digit.
6. Divide the ones. Move to the next digit on the right. Add the 1 that was carried.
   The carried 1 makes 10 ones. With the 8 ones there are 10 + 8 = 18 ones.
   18 ÷ 6: 3 × 6 = 18. Write 3 above the 8.
   Nothing is left over, so there is no remainder.
7. Read the answer. Ignore any 0 at the front of the answer.

   	0	2	3
   6	1	13	18

   
   138 ÷ 6 = 23
8. Write the answer. Include the unit.
   23 stickers

Check. Multiply back: 23 × 6 = 20 × 6 + 3 × 6 = 120 + 18 = 138. ✓

Watch out. If the first digit is smaller than 6, write 0 above it (not in the final answer) and carry the digit to the next place.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw a bar model, choose the operation, then work it out.

1. Draw a bar model. Each box is a group of 5. We count how many boxes make 375.
2. Choose the operation. We find how many groups of 5 fit into 375, so divide by 5.
   375 ÷ 5
3. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   5	3	7	5

4. Divide the hundreds. Always start on the left, with the biggest place value.
   3 ÷ 5: 3 is smaller than 5, so we cannot give each share a whole hundred. Write 0 (a 0 at the front is not part of the answer).
   Exchange the 3 hundreds for 30 tens. Carry 3 to the next digit.
5. Divide the tens. Move to the next digit on the right. Add the 3 that was carried.
   The carried 3 makes 30 tens. With the 7 tens there are 30 + 7 = 37 tens.
   37 ÷ 5: 7 × 5 = 35, and 37 − 35 = 2. Write 7 above the 7.
   Exchange: 2 tens become 20 ones. Carry 2 to the next digit.
6. Divide the ones. Move to the next digit on the right. Add the 2 that was carried.
   The carried 2 makes 20 ones. With the 5 ones there are 20 + 5 = 25 ones.
   25 ÷ 5: 5 × 5 = 25. Write 5 above the 5.
   Nothing is left over, so there is no remainder.
7. Read the answer. Ignore any 0 at the front of the answer.

   	0	7	5
   5	3	37	25

   
   375 ÷ 5 = 75
8. Write the answer. Include the unit.
   75 bags

Check. Multiply back: 75 × 5 = 70 × 5 + 5 × 5 = 350 + 25 = 375. ✓

Watch out. If the first digit is smaller than 5, write 0 above it (not in the final answer) and carry the digit to the next place.

Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.

Method. Draw a bar model, choose the operation, then work it out.

1. Draw a bar model. There are 8 equal shares. Each share is the same size.
2. Choose the operation. 432 is shared equally between 8, so divide by 8.
   432 ÷ 8
3. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   8	4	3	2

4. Divide the hundreds. Always start on the left, with the biggest place value.
   4 ÷ 8: 4 is smaller than 8, so we cannot give each share a whole hundred. Write 0 (a 0 at the front is not part of the answer).
   Exchange the 4 hundreds for 40 tens. Carry 4 to the next digit.
5. Divide the tens. Move to the next digit on the right. Add the 4 that was carried.
   The carried 4 makes 40 tens. With the 3 tens there are 40 + 3 = 43 tens.
   43 ÷ 8: 5 × 8 = 40, and 43 − 40 = 3. Write 5 above the 3.
   Exchange: 3 tens become 30 ones. Carry 3 to the next digit.
6. Divide the ones. Move to the next digit on the right. Add the 3 that was carried.
   The carried 3 makes 30 ones. With the 2 ones there are 30 + 2 = 32 ones.
   32 ÷ 8: 4 × 8 = 32. Write 4 above the 2.
   Nothing is left over, so there is no remainder.
7. Read the answer. Ignore any 0 at the front of the answer.

   	0	5	4
   8	4	43	32

   
   432 ÷ 8 = 54
8. Write the answer. Include the unit.
   54 chairs

Check. Multiply back: 54 × 8 = 50 × 8 + 4 × 8 = 400 + 32 = 432. ✓

Watch out. If the first digit is smaller than 8, write 0 above it (not in the final answer) and carry the digit to the next place.

Key words. The remainder is what is left over after you divide. The quotient is the answer to a division. Whether you round the answer up, round it down or use the remainder depends on the question.

Method. Break the problem into steps. Work out one thing at a time and write down what each answer means.

1. Choose the operation. Share the stickers equally between 7 children, so divide by 7.
   437 ÷ 7
2. Use short division. Divide one digit at a time.

   	0	6	2	r 3
   7	4	43	17

   
   437 ÷ 7 = 62 r 3
3. Say what the remainder means. Each child gets the whole number part. The remainder is what is left over after sharing.
   Each child gets 62. There are 3 left over.
4. Write the answer. Include the unit.
   62 stickers each and 3 left over

Check. 62 × 7 = 434, and 434 + 3 = 437. ✓

Watch out. The remainder is smaller than 7.

Key words. The remainder is what is left over after you divide. The quotient is the answer to a division. Whether you round the answer up, round it down or use the remainder depends on the question.

Method. Break the problem into steps. Work out one thing at a time and write down what each answer means.

1. Choose the operation. Share the stickers equally between 7 children, so divide by 7.
   437 ÷ 7
2. Use short division. Divide one digit at a time.

   	0	6	2	r 3
   7	4	43	17

   
   437 ÷ 7 = 62 r 3
3. Say what the remainder means. Each child gets the whole number part. The remainder is what is left over after sharing.
   Each child gets 62. There are 3 left over.
4. Write the answer. Include the unit.
   62 stickers each and 3 left over

Check. 62 × 7 = 434, and 434 + 3 = 437. ✓

Watch out. The remainder is smaller than 7.

Key words. A counter-example is one example that shows a statement is false.

Method. Try some examples. If the statement is true for every example you can find, ask why. If you find one that is false, it cannot be “always”.

1. Try some numbers. Test the statement with some examples.
   Divide by 6 and look at the remainders: 13 ÷ 6 = 2 r 1, 17 ÷ 6 = 2 r 5, 18 ÷ 6 = 3 r 0. They are 0, 1, 2, 3, 4 or 5.
2. Explain why. A reason shows what is happening for every number, not just the ones we tried.
   If the remainder was 6, there would be another whole group of 6 in it, so we could divide again. A remainder is always smaller than the divisor.
3. Decide.
   Never

Check. We never found a remainder of 6. ✓

Watch out. “Always” means every time. “Sometimes” needs one example that works and one that does not. “Never” means no example works.

Key words. A counter-example is one example that shows a statement is false.

Method. Try some examples. If the statement is true for every example you can find, ask why. If you find one that is false, it cannot be “always”.

1. Try some numbers. Test the statement with some examples.
   100 ÷ 2 = 50 (2 digits)
   200 ÷ 2 = 100 (3 digits)
2. Look for one that does not work. One example that breaks the rule is called a counter-example.
   200 ÷ 2 = 100 has 3 digits.
3. Explain why. A reason shows what is happening for every number, not just the ones we tried.
   Half of 100 to 199 is 50 to 99 (2 digits), but half of 200 or more is 100 or more (3 digits). It depends on the number.
4. Decide.
   Sometimes

Check. We found one example each way. ✓

Watch out. “Always” means every time. “Sometimes” needs one example that works and one that does not. “Never” means no example works.