Year 5: What do we do with 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	4	5

2. Divide the tens. 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 ten. Write 0 (a 0 at the front is not part of the answer).
   Exchange the 4 tens for 40 ones. Carry 4 to the next digit.
3. Divide the ones. Move to the next digit on the right. Add the 4 that was carried.
   The carried 4 makes 40 ones. With the 5 ones there are 40 + 5 = 45 ones.
   45 ÷ 6: 7 × 6 = 42, and 45 − 42 = 3. Write 7 above the 5.
   The remainder is 3.
4. Read the answer. Ignore any 0 at the front of the answer.

   	0	7	r 3
   6	4	45

   
   45 ÷ 6 = 7 r 3
5. Write the answer.
   45 ÷ 6 = 7 r 3

Check. Multiply back: 7 × 6 = 42
42 + 3 (the remainder) = 45. ✓

Watch out. The first digit is smaller than 6: write 0 and carry it. The remainder is always smaller than 6.

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	1	0	0

2. Divide the hundreds. Always start on the left, with the biggest place value.
   1 ÷ 7: 1 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 1 hundred for 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 0 tens there are 10 + 0 = 10 tens.
   10 ÷ 7: 1 × 7 = 7, and 10 − 7 = 3. Write 1 above the 0.
   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 0 ones there are 30 + 0 = 30 ones.
   30 ÷ 7: 4 × 7 = 28, and 30 − 28 = 2. Write 4 above the 0.
   The remainder is 2.
5. Read the answer. Ignore any 0 at the front of the answer.

   	0	1	4	r 2
   7	1	10	30

   
   100 ÷ 7 = 14 r 2
6. Write the answer.
   100 ÷ 7 = 14 r 2

Check. Multiply back: 14 × 7 = 10 × 7 + 4 × 7 = 70 + 28 = 98
98 + 2 (the remainder) = 100. ✓

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	2	5	0

2. Divide the hundreds. Always start on the left, with the biggest place value.
   2 ÷ 8: 2 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 2 hundreds for 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 5 tens there are 20 + 5 = 25 tens.
   25 ÷ 8: 3 × 8 = 24, and 25 − 24 = 1. Write 3 above the 5.
   Exchange: 1 ten becomes 10 ones. Carry 1 to the next digit.
4. 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 0 ones there are 10 + 0 = 10 ones.
   10 ÷ 8: 1 × 8 = 8, and 10 − 8 = 2. Write 1 above the 0.
   The remainder is 2.
5. Read the answer. Ignore any 0 at the front of the answer.

   	0	3	1	r 2
   8	2	25	10

   
   250 ÷ 8 = 31 r 2
6. Write the answer.
   250 ÷ 8 = 31 r 2

Check. Multiply back: 31 × 8 = 30 × 8 + 1 × 8 = 240 + 8 = 248
248 + 2 (the remainder) = 250. ✓

Watch out. The first digit is smaller than 8: write 0 and carry it. The remainder is always smaller than 8.

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. Divide, then think about what the remainder means in the story. The answer might be rounded up, rounded down, or be the remainder itself.

1. Draw a bar model. We split 53 into groups of 8. Some may be left over.
2. Choose the operation. We want to know how many groups of 8 fit into 53, so divide.
   53 ÷ 8
3. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   8	5	3

4. Divide the tens. Always start on the left, with the biggest place value.
   5 ÷ 8: 5 is smaller than 8, so we cannot give each share a whole ten. Write 0 (a 0 at the front is not part of the answer).
   Exchange the 5 tens for 50 ones. Carry 5 to the next digit.
5. 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 3 ones there are 50 + 3 = 53 ones.
   53 ÷ 8: 6 × 8 = 48, and 53 − 48 = 5. Write 6 above the 3.
   The remainder is 5.
6. Read the answer. Ignore any 0 at the front of the answer.

   	0	6	r 5
   8	5	53

   
   53 ÷ 8 = 6 r 5
7. Say what the remainder means. 53 ÷ 8 = 6 remainder 5: that is 6 full minibuses and 5 children left over.
   6 full minibuses + 5 left over
8. Decide what to do with the remainder. The 5 left over still need somewhere to go, so one more minibus is needed. We round the answer up.
   6 + 1 = 7
9. Write the answer. Include the unit.
   7 minibuses

Check. 6 × 8 = 48 and 48 + 5 = 53. ✓

Watch out. Do not round down here. The 5 left over would have no minibus.

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. Divide, then think about what the remainder means in the story. The answer might be rounded up, rounded down, or be the remainder itself.

1. Draw a bar model. We split 130 into groups of 9. Some may be left over.
2. Choose the operation. We want to know how many groups of 9 fit into 130, so divide.
   130 ÷ 9
3. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   9	1	3	0

4. Divide the hundreds. Always start on the left, with the biggest place value.
   1 ÷ 9: 1 is smaller than 9, 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 ÷ 9: 1 × 9 = 9, and 13 − 9 = 4. Write 1 above the 3.
   Exchange: 4 tens become 40 ones. Carry 4 to the next digit.
6. Divide the ones. Move to the next digit on the right. Add the 4 that was carried.
   The carried 4 makes 40 ones. With the 0 ones there are 40 + 0 = 40 ones.
   40 ÷ 9: 4 × 9 = 36, and 40 − 36 = 4. Write 4 above the 0.
   The remainder is 4.
7. Read the answer. Ignore any 0 at the front of the answer.

   	0	1	4	r 4
   9	1	13	40

   
   130 ÷ 9 = 14 r 4
8. Say what the remainder means. 130 ÷ 9 = 14 remainder 4: that is 14 full trips and 4 books left over.
   14 full trips + 4 left over
9. Decide what to do with the remainder. The 4 left over still need somewhere to go, so one more trip is needed. We round the answer up.
   14 + 1 = 15
10. Write the answer. Include the unit.
    15 trips

Check. 14 × 9 = 126 and 126 + 4 = 130. ✓

Watch out. Do not round down here. The 4 left over would have no trip.

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. Divide, then think about what the remainder means in the story. The answer might be rounded up, rounded down, or be the remainder itself.

1. Draw a bar model. We split 37 into groups of 4. Some may be left over.
2. Choose the operation. We want to know how many groups of 4 fit into 37, so divide.
   37 ÷ 4
3. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   4	3	7

4. Divide the tens. Always start on the left, with the biggest place value.
   3 ÷ 4: 3 is smaller than 4, so we cannot give each share a whole ten. Write 0 (a 0 at the front is not part of the answer).
   Exchange the 3 tens for 30 ones. Carry 3 to the next digit.
5. 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 7 ones there are 30 + 7 = 37 ones.
   37 ÷ 4: 9 × 4 = 36, and 37 − 36 = 1. Write 9 above the 7.
   The remainder is 1.
6. Read the answer. Ignore any 0 at the front of the answer.

   	0	9	r 1
   4	3	37

   
   37 ÷ 4 = 9 r 1
7. Say what the remainder means. 37 ÷ 4 = 9 remainder 1: that is 9 full tables and 1 people left over.
   9 full tables + 1 left over
8. Decide what to do with the remainder. The 1 left over still need somewhere to go, so one more table is needed. We round the answer up.
   9 + 1 = 10
9. Write the answer. Include the unit.
   10 tables

Check. 9 × 4 = 36 and 36 + 1 = 37. ✓

Watch out. Do not round down here. The 1 left over would have no table.

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. Divide, then think about what the remainder means in the story. The answer might be rounded up, rounded down, or be the remainder itself.

1. Draw a bar model. We split 70 into groups of 8. Some may be left over.
2. Choose the operation. We want to know how many groups of 8 fit into 70, so divide.
   70 ÷ 8
3. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   8	7	0

4. Divide the tens. Always start on the left, with the biggest place value.
   7 ÷ 8: 7 is smaller than 8, so we cannot give each share a whole ten. Write 0 (a 0 at the front is not part of the answer).
   Exchange the 7 tens for 70 ones. Carry 7 to the next digit.
5. Divide the ones. Move to the next digit on the right. Add the 7 that was carried.
   The carried 7 makes 70 ones. With the 0 ones there are 70 + 0 = 70 ones.
   70 ÷ 8: 8 × 8 = 64, and 70 − 64 = 6. Write 8 above the 0.
   The remainder is 6.
6. Read the answer. Ignore any 0 at the front of the answer.

   	0	8	r 6
   8	7	70

   
   70 ÷ 8 = 8 r 6
7. Say what the remainder means. 70 ÷ 8 = 8 remainder 6: that is 8 full sweets and 6 pence left over.
   8 full sweets + 6 left over
8. Decide what to do with the remainder. Only full sweets count. The 6 left over cannot make another one. We round the answer down (we ignore the remainder).
   8 full sweets
9. Write the answer. Include the unit.
   8 sweets

Check. 8 × 8 = 64 and 64 + 6 = 70. ✓

Watch out. Do not round up here: the extra sweet would not be full.

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. Divide, then think about what the remainder means in the story. The answer might be rounded up, rounded down, or be the remainder itself.

1. Draw a bar model. We split 100 into groups of 7. Some may be left over.
2. Choose the operation. We want to know how many groups of 7 fit into 100, so divide.
   100 ÷ 7
3. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   7	1	0	0

4. Divide the hundreds. Always start on the left, with the biggest place value.
   1 ÷ 7: 1 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 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 0 tens there are 10 + 0 = 10 tens.
   10 ÷ 7: 1 × 7 = 7, and 10 − 7 = 3. Write 1 above the 0.
   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 0 ones there are 30 + 0 = 30 ones.
   30 ÷ 7: 4 × 7 = 28, and 30 − 28 = 2. Write 4 above the 0.
   The remainder is 2.
7. Read the answer. Ignore any 0 at the front of the answer.

   	0	1	4	r 2
   7	1	10	30

   
   100 ÷ 7 = 14 r 2
8. Say what the remainder means. 100 ÷ 7 = 14 remainder 2: that is 14 full gifts and 2 cm left over.
   14 full gifts + 2 left over
9. Decide what to do with the remainder. Only full gifts count. The 2 left over cannot make another one. We round the answer down (we ignore the remainder).
   14 full gifts
10. Write the answer. Include the unit.
    14 gifts

Check. 14 × 7 = 98 and 98 + 2 = 100. ✓

Watch out. Do not round up here: the extra gift would not be full.

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. Divide, then think about what the remainder means in the story. The answer might be rounded up, rounded down, or be the remainder itself.

1. Draw a bar model. We split 150 into groups of 4. Some may be left over.
2. Choose the operation. We want to know how many groups of 4 fit into 150, so divide.
   150 ÷ 4
3. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   4	1	5	0

4. Divide the hundreds. Always start on the left, with the biggest place value.
   1 ÷ 4: 1 is smaller than 4, 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 5 tens there are 10 + 5 = 15 tens.
   15 ÷ 4: 3 × 4 = 12, and 15 − 12 = 3. Write 3 above the 5.
   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 0 ones there are 30 + 0 = 30 ones.
   30 ÷ 4: 7 × 4 = 28, and 30 − 28 = 2. Write 7 above the 0.
   The remainder is 2.
7. Read the answer. Ignore any 0 at the front of the answer.

   	0	3	7	r 2
   4	1	15	30

   
   150 ÷ 4 = 37 r 2
8. Say what the remainder means. 150 ÷ 4 = 37 remainder 2: that is 37 full boxes and 2 cakes left over.
   37 full boxes + 2 left over
9. Decide what to do with the remainder. Only full boxes count. The 2 left over cannot make another one. We round the answer down (we ignore the remainder).
   37 full boxes
10. Write the answer. Include the unit.
    37 boxes

Check. 37 × 4 = 148 and 148 + 2 = 150. ✓

Watch out. Do not round up here: the extra box would not be full.

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. Divide, then think about what the remainder means in the story. The answer might be rounded up, rounded down, or be the remainder itself.

1. Draw a bar model. We split 58 into groups of 7. Some may be left over.
2. Choose the operation. We want to know how many groups of 7 fit into 58, so divide.
   58 ÷ 7
3. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   7	5	8

4. Divide the tens. 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 ten. Write 0 (a 0 at the front is not part of the answer).
   Exchange the 5 tens for 50 ones. Carry 5 to the next digit.
5. 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 8 ones there are 50 + 8 = 58 ones.
   58 ÷ 7: 8 × 7 = 56, and 58 − 56 = 2. Write 8 above the 8.
   The remainder is 2.
6. Read the answer. Ignore any 0 at the front of the answer.

   	0	8	r 2
   7	5	58

   
   58 ÷ 7 = 8 r 2
7. Say what the remainder means. 58 ÷ 7 = 8 remainder 2: that is 8 full baskets and 2 apples left over.
   8 full baskets + 2 left over
8. Decide what to do with the remainder. The question asks how many are left over. That is the remainder itself.
   2 apples left over
9. Write the answer. Include the unit.
   2 apples

Check. 8 × 7 = 56 and 56 + 2 = 58. ✓

Watch out. The answer is the remainder, not the number of full groups.

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. Divide, then think about what the remainder means in the story. The answer might be rounded up, rounded down, or be the remainder itself.

1. Draw a bar model. We split 100 into groups of 9. Some may be left over.
2. Choose the operation. We want to know how many groups of 9 fit into 100, so divide.
   100 ÷ 9
3. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   9	1	0	0

4. Divide the hundreds. Always start on the left, with the biggest place value.
   1 ÷ 9: 1 is smaller than 9, 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 0 tens there are 10 + 0 = 10 tens.
   10 ÷ 9: 1 × 9 = 9, and 10 − 9 = 1. Write 1 above the 0.
   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 0 ones there are 10 + 0 = 10 ones.
   10 ÷ 9: 1 × 9 = 9, and 10 − 9 = 1. Write 1 above the 0.
   The remainder is 1.
7. Read the answer. Ignore any 0 at the front of the answer.

   	0	1	1	r 1
   9	1	10	10

   
   100 ÷ 9 = 11 r 1
8. Say what the remainder means. 100 ÷ 9 = 11 remainder 1: that is 11 full players and 1 cards left over.
   11 full players + 1 left over
9. Decide what to do with the remainder. The question asks how many are left over. That is the remainder itself.
   1 card left over
10. Write the answer. Include the unit.
    1 card

Check. 11 × 9 = 99 and 99 + 1 = 100. ✓

Watch out. The answer is the remainder, not the number of full groups.

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. Divide, then think about what the remainder means in the story. The answer might be rounded up, rounded down, or be the remainder itself.

1. Draw a bar model. We split 200 into groups of 6. Some may be left over.
2. Choose the operation. We want to know how many groups of 6 fit into 200, so divide.
   200 ÷ 6
3. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   6	2	0	0

4. Divide the hundreds. Always start on the left, with the biggest place value.
   2 ÷ 6: 2 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 2 hundreds for 20 tens. Carry 2 to the next digit.
5. 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 0 tens there are 20 + 0 = 20 tens.
   20 ÷ 6: 3 × 6 = 18, and 20 − 18 = 2. Write 3 above the 0.
   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 0 ones there are 20 + 0 = 20 ones.
   20 ÷ 6: 3 × 6 = 18, and 20 − 18 = 2. Write 3 above the 0.
   The remainder is 2.
7. Read the answer. Ignore any 0 at the front of the answer.

   	0	3	3	r 2
   6	2	20	20

   
   200 ÷ 6 = 33 r 2
8. Say what the remainder means. 200 ÷ 6 = 33 remainder 2: that is 33 full necklaces and 2 beads left over.
   33 full necklaces + 2 left over
9. Decide what to do with the remainder. The question asks how many are left over. That is the remainder itself.
   2 beads left over
10. Write the answer. Include the unit.
    2 beads

Check. 33 × 6 = 198 and 198 + 2 = 200. ✓

Watch out. The answer is the remainder, not the number of full groups.

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. Divide, then think about what the remainder means in the story. The answer might be rounded up, rounded down, or be the remainder itself.

1. Draw a bar model. We split 75 into groups of 4. Some may be left over.
2. Choose the operation. We want to know how many groups of 4 fit into 75, so divide.
   75 ÷ 4
3. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   4	7	5

4. Divide the tens. Always start on the left, with the biggest place value.
   7 ÷ 4 = 1, remainder 3
   Write 1 above the 7.
   Exchange the remainder: 3 tens become 30 ones. Carry 3 to the next digit.
5. 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 ÷ 4: 8 × 4 = 32, and 35 − 32 = 3. Write 8 above the 5.
   The remainder is 3.
6. Read the answer. Read the digits above the line from left to right.

   	1	8	r 3
   4	7	35

   
   75 ÷ 4 = 18 r 3
7. Say what the remainder means. 75 ÷ 4 = 18 remainder 3: that is 18 full strips and 3 cm left over.
   18 full strips + 3 left over
8. Decide what to do with the remainder. Only full strips count. The 3 left over cannot make another one. We round the answer down (we ignore the remainder).
   18 full strips
9. Write the answer. Include the unit.
   18 strips

Check. 18 × 4 = 72 and 72 + 3 = 75. ✓

Watch out. Do not round up here: the extra strip would not be full.

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. Divide, then think about what the remainder means in the story. The answer might be rounded up, rounded down, or be the remainder itself.

1. Draw a bar model. We split 75 into groups of 4. Some may be left over.
2. Choose the operation. We want to know how many groups of 4 fit into 75, so divide.
   75 ÷ 4
3. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   4	7	5

4. Divide the tens. Always start on the left, with the biggest place value.
   7 ÷ 4 = 1, remainder 3
   Write 1 above the 7.
   Exchange the remainder: 3 tens become 30 ones. Carry 3 to the next digit.
5. 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 ÷ 4: 8 × 4 = 32, and 35 − 32 = 3. Write 8 above the 5.
   The remainder is 3.
6. Read the answer. Read the digits above the line from left to right.

   	1	8	r 3
   4	7	35

   
   75 ÷ 4 = 18 r 3
7. Say what the remainder means. 75 ÷ 4 = 18 remainder 3: that is 18 full teams and 3 pupils left over.
   18 full teams + 3 left over
8. Decide what to do with the remainder. The 3 left over still need somewhere to go, so one more team is needed. We round the answer up.
   18 + 1 = 19
9. Write the answer. Include the unit.
   19 teams

Check. 18 × 4 = 72 and 72 + 3 = 75. ✓

Watch out. Do not round down here. The 3 left over would have no team.

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. Divide, then think about what the remainder means in the story. The answer might be rounded up, rounded down, or be the remainder itself.

1. Draw a bar model. We split 75 into groups of 4. Some may be left over.
2. Choose the operation. We want to know how many groups of 4 fit into 75, so divide.
   75 ÷ 4
3. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   4	7	5

4. Divide the tens. Always start on the left, with the biggest place value.
   7 ÷ 4 = 1, remainder 3
   Write 1 above the 7.
   Exchange the remainder: 3 tens become 30 ones. Carry 3 to the next digit.
5. 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 ÷ 4: 8 × 4 = 32, and 35 − 32 = 3. Write 8 above the 5.
   The remainder is 3.
6. Read the answer. Read the digits above the line from left to right.

   	1	8	r 3
   4	7	35

   
   75 ÷ 4 = 18 r 3
7. Say what the remainder means. 75 ÷ 4 = 18 remainder 3: that is 18 full teams and 3 pupils left over.
   18 full teams + 3 left over
8. Decide what to do with the remainder. The question asks how many are left over. That is the remainder itself.
   3 pupils left over
9. Write the answer. Include the unit.
   3 pupils

Check. 18 × 4 = 72 and 72 + 3 = 75. ✓

Watch out. The answer is the remainder, not the number of full groups.

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. Divide, then think about what the remainder means in the story. The answer might be rounded up, rounded down, or be the remainder itself.

1. Draw a bar model. We split 206 into groups of 5. Some may be left over.
2. Choose the operation. We want to know how many groups of 5 fit into 206, so divide.
   206 ÷ 5
3. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   5	2	0	6

4. Divide the hundreds. Always start on the left, with the biggest place value.
   2 ÷ 5: 2 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 2 hundreds for 20 tens. Carry 2 to the next digit.
5. 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 0 tens there are 20 + 0 = 20 tens.
   20 ÷ 5: 4 × 5 = 20. Write 4 above the 0.
6. Divide the ones. Move to the next digit on the right.
   Nothing was carried, so there are just 6 ones.
   6 ÷ 5: 1 × 5 = 5, and 6 − 5 = 1. Write 1 above the 6.
   The remainder is 1.
7. Read the answer. Ignore any 0 at the front of the answer.

   	0	4	1	r 1
   5	2	20	6

   
   206 ÷ 5 = 41 r 1
8. Say what the remainder means. 206 ÷ 5 = 41 remainder 1: that is 41 full sheets and 1 stickers left over.
   41 full sheets + 1 left over
9. Decide what to do with the remainder. The 1 left over still need somewhere to go, so one more sheet is needed. We round the answer up.
   41 + 1 = 42
10. Write the answer. Include the unit.
    42 sheets

Check. 41 × 5 = 205 and 205 + 1 = 206. ✓

Watch out. Do not round down here. The 1 left over would have no sheet.

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. Divide to find the whole number and the remainder. The remainder can be written as a fraction (remainder over divisor) or carried on as a decimal.

1. Divide with a remainder. First divide as usual and find the remainder.

   	4	r 1
   2	9

   
   9 ÷ 2 = 4 remainder 1
2. Write the remainder as a fraction. The 1 left over is shared into 2 equal parts, so each share gets 12 of one more.
   12
   9 ÷ 2 = 4 r 1 = 412
3. Write the remainder as a decimal. Add a point and 1 zero, and carry on dividing. The 1 left over becomes 10 tenths.

   	4	.	5
   2	9	.	10

   
   9 ÷ 2 = 4.5
4. Write all three answers. They all mean the same amount.
   4 r 1  =  412  =  4.5

Check. 4.5 × 2 = 9. ✓

Watch out. The fraction is the remainder over the divisor, not over the original number.

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. Divide to find the whole number and the remainder. The remainder can be written as a fraction (remainder over divisor) or carried on as a decimal.

1. Divide with a remainder. First divide as usual and find the remainder.

   	0	2	r 3
   5	1	13

   
   13 ÷ 5 = 2 remainder 3
2. Write the remainder as a fraction. The 3 left over is shared into 5 equal parts, so each share gets 35 of one more.
   35
   13 ÷ 5 = 2 r 3 = 235
3. Write the remainder as a decimal. Add a point and 1 zero, and carry on dividing. The 3 left over becomes 30 tenths.

   	0	2	.	6
   5	1	13	.	30

   
   13 ÷ 5 = 2.6
4. Write all three answers. They all mean the same amount.
   2 r 3  =  235  =  2.6

Check. 2.6 × 5 = 13. ✓

Watch out. The fraction is the remainder over the divisor, not over the original number.

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. Divide to find the whole number and the remainder. The remainder can be written as a fraction (remainder over divisor) or carried on as a decimal.

1. Divide with a remainder. First divide as usual and find the remainder.

   	0	r 3
   4	3

   
   3 ÷ 4 = 0 remainder 3
2. Write the remainder as a fraction. The 3 left over is shared into 4 equal parts, so each share gets 34 of one more.
   34
   3 ÷ 4 = 0 r 3 = 34
3. Write the remainder as a decimal. Add a point and 2 zeros, and carry on dividing. The 3 left over becomes 30 tenths.

   	0	.	7	5
   4	3	.	30	20

   
   3 ÷ 4 = 0.75
4. Write all three answers. They all mean the same amount.
   0 r 3  =  34  =  0.75

Check. 0.75 × 4 = 3. ✓

Watch out. The fraction is the remainder over the divisor, not over the original number.

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. Divide the pounds. If there is a remainder, carry on dividing into tenths and hundredths (10p and 1p).

1. Choose the operation. £15 is shared equally between 4, so divide by 4. Money needs 2 decimal places (pounds and pence), so we add a point and 2 zeros.
   15 ÷ 4
2. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left. We write a decimal point and 2 zeros after the 15. They do not change its value, but they give us places to carry the remainder into.

   4	1	5	.	0	0

3. Divide the tens. Always start on the left, with the biggest place value.
   1 ÷ 4: 1 is smaller than 4, so we cannot give each share a whole ten. Write 0 (a 0 at the front is not part of the answer).
   Exchange the 1 ten for 10 ones. Carry 1 to the next digit.
4. 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 5 ones there are 10 + 5 = 15 ones.
   15 ÷ 4: 3 × 4 = 12, and 15 − 12 = 3. Write 3 above the 5.
   Exchange: 3 ones become 30 tenths. Carry 3 to the next digit.
5. Divide the tenths. Move to the next digit on the right. Add the 3 that was carried.
   The carried 3 makes 30 tenths. With the 0 tenths there are 30 + 0 = 30 tenths.
   30 ÷ 4: 7 × 4 = 28, and 30 − 28 = 2. Write 7 above the 0.
   Exchange: 2 tenths become 20 hundredths. Carry 2 to the next digit.
6. Divide the hundredths. Move to the next digit on the right. Add the 2 that was carried.
   The carried 2 makes 20 hundredths. With the 0 hundredths there are 20 + 0 = 20 hundredths.
   20 ÷ 4: 5 × 4 = 20. Write 5 above the 0.
   Nothing is left over, so the division is exact.
7. Read the answer. Read the digits above the line from left to right. The point in the answer is straight above the point in the bus stop.

   	0	3	.	7	5
   4	1	15	.	30	20

   
   15 ÷ 4 = 3.75
8. Write the answer in pounds and pence. Give the answer to 2 decimal places.
   £3.75

Check. £3.75 × 4 = £15. ✓

Watch out. Write money with 2 decimal places: £3.50, not £3.5.

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. Divide the pounds. If there is a remainder, carry on dividing into tenths and hundredths (10p and 1p).

1. Choose the operation. £7 is shared equally between 2, so divide by 2. Money needs 2 decimal places (pounds and pence), so we add a point and 2 zeros.
   7 ÷ 2
2. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left. We write a decimal point and 2 zeros after the 7. They do not change its value, but they give us places to carry the remainder into.

   2	7	.	0	0

3. Divide the ones. Always start on the left, with the biggest place value.
   7 ÷ 2 = 3, remainder 1
   Write 3 above the 7.
   Exchange the remainder: 1 one becomes 10 tenths. Carry 1 to the next digit.
4. Divide the tenths. Move to the next digit on the right. Add the 1 that was carried.
   The carried 1 makes 10 tenths. With the 0 tenths there are 10 + 0 = 10 tenths.
   10 ÷ 2: 5 × 2 = 10. Write 5 above the 0.
5. Divide the hundredths. Move to the next digit on the right.
   Nothing was carried, so there are just 0 hundredths.
   0 ÷ 2 = 0. Write 0 above. This 0 is a place holder, and it must stay in the answer.
   Nothing is left over, so the division is exact.
6. Read the answer. Read the digits above the line from left to right. The point in the answer is straight above the point in the bus stop.

   	3	.	5	0
   2	7	.	10	0

   
   7 ÷ 2 = 3.5
7. Write the answer in pounds and pence. Give the answer to 2 decimal places.
   £3.50

Check. £3.50 × 2 = £7. ✓

Watch out. Write money with 2 decimal places: £3.50, not £3.5.

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. Divide the pounds. If there is a remainder, carry on dividing into tenths and hundredths (10p and 1p).

1. Choose the operation. £18 is shared equally between 8, so divide by 8. Money needs 2 decimal places (pounds and pence), so we add a point and 2 zeros.
   18 ÷ 8
2. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left. We write a decimal point and 2 zeros after the 18. They do not change its value, but they give us places to carry the remainder into.

   8	1	8	.	0	0

3. Divide the tens. Always start on the left, with the biggest place value.
   1 ÷ 8: 1 is smaller than 8, so we cannot give each share a whole ten. Write 0 (a 0 at the front is not part of the answer).
   Exchange the 1 ten for 10 ones. Carry 1 to the next digit.
4. 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 ÷ 8: 2 × 8 = 16, and 18 − 16 = 2. Write 2 above the 8.
   Exchange: 2 ones become 20 tenths. Carry 2 to the next digit.
5. Divide the tenths. Move to the next digit on the right. Add the 2 that was carried.
   The carried 2 makes 20 tenths. With the 0 tenths there are 20 + 0 = 20 tenths.
   20 ÷ 8: 2 × 8 = 16, and 20 − 16 = 4. Write 2 above the 0.
   Exchange: 4 tenths become 40 hundredths. Carry 4 to the next digit.
6. Divide the hundredths. Move to the next digit on the right. Add the 4 that was carried.
   The carried 4 makes 40 hundredths. With the 0 hundredths there are 40 + 0 = 40 hundredths.
   40 ÷ 8: 5 × 8 = 40. Write 5 above the 0.
   Nothing is left over, so the division is exact.
7. Read the answer. Read the digits above the line from left to right. The point in the answer is straight above the point in the bus stop.

   	0	2	.	2	5
   8	1	18	.	20	40

   
   18 ÷ 8 = 2.25
8. Write the answer in pounds and pence. Give the answer to 2 decimal places.
   £2.25

Check. £2.25 × 8 = £18. ✓

Watch out. Write money with 2 decimal places: £3.50, not £3.5.

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. Look at the bar model. The orange box is the part that is left over.

1. Count the full boxes. There are 8 boxes of 9 cm. The dots in the picture stand for the boxes in between.
   75 ÷ 9 = 8 remainder 3
2. Say what the orange box is. It is the part that is not long enough for another full strip.

   	0	8	r 3
   9	7	75

   
   75 ÷ 9 = 8 r 3

Check. 8 × 9 = 72 and 72 + 3 = 75. ✓

Watch out. The remainder is smaller than 9.

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. Divide, then think about what the remainder means in the story. The answer might be rounded up, rounded down, or be the remainder itself.

1. Draw a bar model. We split 75 into groups of 9. Some may be left over.
2. Choose the operation. We want to know how many groups of 9 fit into 75, so divide.
   75 ÷ 9
3. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   9	7	5

4. Divide the tens. Always start on the left, with the biggest place value.
   7 ÷ 9: 7 is smaller than 9, so we cannot give each share a whole ten. Write 0 (a 0 at the front is not part of the answer).
   Exchange the 7 tens for 70 ones. Carry 7 to the next digit.
5. Divide the ones. Move to the next digit on the right. Add the 7 that was carried.
   The carried 7 makes 70 ones. With the 5 ones there are 70 + 5 = 75 ones.
   75 ÷ 9: 8 × 9 = 72, and 75 − 72 = 3. Write 8 above the 5.
   The remainder is 3.
6. Read the answer. Ignore any 0 at the front of the answer.

   	0	8	r 3
   9	7	75

   
   75 ÷ 9 = 8 r 3
7. Say what the remainder means. 75 ÷ 9 = 8 remainder 3: that is 8 full bows and 3 cm left over.
   8 full bows + 3 left over
8. Decide what to do with the remainder. Only full bows count. The 3 left over cannot make another one. We round the answer down (we ignore the remainder).
   8 full bows
9. Write the answer. Include the unit.
   8 bows

Check. 8 × 9 = 72 and 72 + 3 = 75. ✓

Watch out. Do not round up here: the extra bow would not be full.

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. The left-over piece is the remainder.

1. Find the remainder. 75 ÷ 9 = 8 remainder 3, so 8 pieces of 9 cm are cut and some ribbon is left.
   75 − 8 × 9 = 75 − 72 = 3
2. Write the answer with the unit. The remainder is in the same unit as the ribbon, centimetres.
   3 cm

Check. 72 + 3 = 75. ✓

Watch out. The remainder is smaller than 9 cm.

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. Share the pencils equally, so divide by 9.

1. Divide. Use short division.

   	0	2	2	r 2
   9	2	20	20

   
   200 ÷ 9 = 22 r 2
2. Read the answer. The whole number part is the amount each group gets. The remainder is what is left over.
   Each group gets 22 pencils. There are 2 left over.

Check. 22 × 9 = 198 and 198 + 2 = 200. ✓

Watch out. The remainder is smaller than 9.

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. Share the pencils equally, so divide by 9.

1. Divide. Use short division.

   	0	2	2	r 2
   9	2	20	20

   
   200 ÷ 9 = 22 r 2
2. Read the answer. The whole number part is the amount each group gets. The remainder is what is left over.
   Each group gets 22 pencils. There are 2 left over.

Check. 22 × 9 = 198 and 198 + 2 = 200. ✓

Watch out. The remainder is smaller than 9.

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. Look at the key words in the question. They tell you what to do with the remainder.

1. Find the key words. Read the question again. The key words show what to do with the remainder.
   “How many are needed?”
2. Decide. Everyone or everything must be included, so a part-filled group still needs a whole one.
   We round up.
3. Try it. An example makes it clear.
   coaches needed: 230 ÷ 50 = 4 r 30, so 5 coaches

Check. Read the question again and see if your answer makes sense.

Watch out. Always read the question again after you divide: the remainder means different things in different stories.

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. Look at the key words in the question. They tell you what to do with the remainder.

1. Find the key words. Read the question again. The key words show what to do with the remainder.
   “how many can she buy?”
2. Decide. Only complete (full) groups count, so ignore the remainder.
   We round down.
3. Try it. An example makes it clear.
   20 ÷ 3 = 6 r 2, so 6 packs

Check. Read the question again and see if your answer makes sense.

Watch out. Always read the question again after you divide: the remainder means different things in different stories.

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. Look at the key words in the question. They tell you what to do with the remainder.

1. Find the key words. Read the question again. The key words show what to do with the remainder.
   “how many are left over?”
2. Decide. The question asks for what is left over, which is the remainder itself.
   We use the remainder.
3. Try it. An example makes it clear.
   47 ÷ 5 = 9 r 2, so 2 sweets

Check. Read the question again and see if your answer makes sense.

Watch out. Always read the question again after you divide: the remainder means different things in different stories.

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. Look at the key words in the question. They tell you what to do with the remainder.

1. Find the key words. Read the question again. The key words show what to do with the remainder.
   “How many are needed?”
2. Decide. Everyone or everything must be included, so a part-filled group still needs a whole one.
   We round up.
3. Try it. An example makes it clear.
   130 ÷ 40 = 3 r 10, so 4 buses

Check. Read the question again and see if your answer makes sense.

Watch out. Always read the question again after you divide: the remainder means different things in different stories.

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.
   3 ÷ 5 = 0 r 3 and 3 is odd.
   8 ÷ 5 = 1 r 3 and 8 is even.
2. Look for one that does not work. One example that breaks the rule is called a counter-example.
   8 is even and leaves a remainder of 3 when divided by 5.
3. Explain why. A reason shows what is happening for every number, not just the ones we tried.
   The numbers 3, 8, 13, 18, 23… all leave remainder 3. They go odd, even, odd, even, so 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.

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.
   7 ÷ 2 = 3 r 1
   15 ÷ 2 = 7 r 1
   101 ÷ 2 = 50 r 1
2. Explain why. A reason shows what is happening for every number, not just the ones we tried.
   An even number is exactly 2 times something. A number that leaves remainder 1 is one more than a multiple of 2. That is odd. And every odd number leaves remainder 1.
3. Decide.
   Always

Check. Every odd number we tried had remainder 1. ✓

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