Year 6: Short division (the bus stop method)

Key words. Short division (the bus stop method) divides by a one-digit number. A small carried remainder is written above the next digit. It is the number left over, and it is worth ten times more in the next column.

Method. Use short division. Work from left to right, one digit at a time. Carry any remainder into the next digit.

1. Set out the bus stop layout. The number goes inside the bus stop and the divisor, 7, goes outside it.
   7 ) 4,839
2. Divide the digit 4 (digit 1 of 4). Start with the first digit on the left.
   4 ÷ 7 = 0 remainder 4. Write 0 on top and carry the remainder 4.
3. Divide the digit 8 (digit 2 of 4). Each remainder is smaller than the divisor. Carry it to the next digit to the right.
   Carry the remainder 4 to the next digit to make 48 = 48. 48 ÷ 7 = 6 remainder 6. Write 6 on top and carry 6.
4. Divide the digit 3 (digit 3 of 4). Each remainder is smaller than the divisor. Carry it to the next digit to the right.
   Carry the remainder 6 to the next digit to make 63 = 63. 63 ÷ 7 = 9 remainder 0. Write 9 on top and carry 0.
5. Divide the digit 9 (digit 4 of 4). Each remainder is smaller than the divisor. Carry it to the next digit to the right.
   Carry the remainder 0 to the next digit to make 09 = 9. 9 ÷ 7 = 1 remainder 2. Write 1 on top and carry 2.
6. Read the answer from the bus stop layout. The quotient is the top row of numbers. The last remainder is left over.

   		4	6	0
   7	4	8	3	9
   	0	6	9	1

   
   Answer 691 r 2

Check. 7 × 691 = 4,837, and 4,837 + 2 = 4,839. ✓

Watch out. A carried remainder must be smaller than the divisor. If you get a remainder that is too big, check your times table.

Key words. Short division (the bus stop method) divides by a one-digit number. A small carried remainder is written above the next digit. It is the number left over, and it is worth ten times more in the next column.

Method. Use short division. Work from left to right, one digit at a time. Carry any remainder into the next digit.

1. Set out the bus stop layout. The number goes inside the bus stop and the divisor, 6, goes outside it.
   6 ) 6,215
2. Divide the digit 6 (digit 1 of 4). Start with the first digit on the left.
   6 ÷ 6 = 1 remainder 0. Write 1 on top and carry the remainder 0.
3. Divide the digit 2 (digit 2 of 4). Each remainder is smaller than the divisor. Carry it to the next digit to the right.
   Carry the remainder 0 to the next digit to make 02 = 2. 2 ÷ 6 = 0 remainder 2. Write 0 on top and carry 2.
4. Divide the digit 1 (digit 3 of 4). Each remainder is smaller than the divisor. Carry it to the next digit to the right.
   Carry the remainder 2 to the next digit to make 21 = 21. 21 ÷ 6 = 3 remainder 3. Write 3 on top and carry 3.
5. Divide the digit 5 (digit 4 of 4). Each remainder is smaller than the divisor. Carry it to the next digit to the right.
   Carry the remainder 3 to the next digit to make 35 = 35. 35 ÷ 6 = 5 remainder 5. Write 5 on top and carry 5.
6. Read the answer from the bus stop layout. The quotient is the top row of numbers. The last remainder is left over.

   		0	2	3
   6	6	2	1	5
   	1	0	3	5

   
   Answer 1,035 r 5

Check. 6 × 1,035 = 6,210, and 6,210 + 5 = 6,215. ✓

Watch out. A carried remainder must be smaller than the divisor. If you get a remainder that is too big, check your times table.

Key words. Short division (the bus stop method) divides by a one-digit number. A small carried remainder is written above the next digit. It is the number left over, and it is worth ten times more in the next column.

Method. Use short division. Work from left to right, one digit at a time. Carry any remainder into the next digit.

1. Set out the bus stop layout. The number goes inside the bus stop and the divisor, 4, goes outside it.
   4 ) 8,004
2. Divide the digit 8 (digit 1 of 4). Start with the first digit on the left.
   8 ÷ 4 = 2 remainder 0. Write 2 on top and carry the remainder 0.
3. Divide the digit 0 (digit 2 of 4). Each remainder is smaller than the divisor. Carry it to the next digit to the right.
   Carry the remainder 0 to the next digit to make 00 = 0. 0 ÷ 4 = 0 remainder 0. Write 0 on top and carry 0.
4. Divide the digit 0 (digit 3 of 4). Each remainder is smaller than the divisor. Carry it to the next digit to the right.
   Carry the remainder 0 to the next digit to make 00 = 0. 0 ÷ 4 = 0 remainder 0. Write 0 on top and carry 0.
5. Divide the digit 4 (digit 4 of 4). Each remainder is smaller than the divisor. Carry it to the next digit to the right.
   Carry the remainder 0 to the next digit to make 04 = 4. 4 ÷ 4 = 1 remainder 0. Write 1 on top and carry 0.
6. Read the answer from the bus stop layout. The quotient is the top row of numbers. The last remainder is left over.

   		0	0	0
   4	8	0	0	4
   	2	0	0	1

   
   Answer 2,001

Check. 4 × 2,001 = 8,004. ✓

Watch out. A carried remainder must be smaller than the divisor. If you get a remainder that is too big, check your times table.

Key words. Short division (the bus stop method) divides by a one-digit number. A small carried remainder is written above the next digit. It is the number left over, and it is worth ten times more in the next column.

Method. Use short division. Work from left to right, one digit at a time. Carry any remainder into the next digit.

1. Set out the bus stop layout. The number goes inside the bus stop and the divisor, 7, goes outside it.
   7 ) 3,597
2. Divide the digit 3 (digit 1 of 4). Start with the first digit on the left.
   3 ÷ 7 = 0 remainder 3. Write 0 on top and carry the remainder 3.
3. Divide the digit 5 (digit 2 of 4). Each remainder is smaller than the divisor. Carry it to the next digit to the right.
   Carry the remainder 3 to the next digit to make 35 = 35. 35 ÷ 7 = 5 remainder 0. Write 5 on top and carry 0.
4. Divide the digit 9 (digit 3 of 4). Each remainder is smaller than the divisor. Carry it to the next digit to the right.
   Carry the remainder 0 to the next digit to make 09 = 9. 9 ÷ 7 = 1 remainder 2. Write 1 on top and carry 2.
5. Divide the digit 7 (digit 4 of 4). Each remainder is smaller than the divisor. Carry it to the next digit to the right.
   Carry the remainder 2 to the next digit to make 27 = 27. 27 ÷ 7 = 3 remainder 6. Write 3 on top and carry 6.
6. Read the answer from the bus stop layout. The quotient is the top row of numbers. The last remainder is left over.

   		3	0	2
   7	3	5	9	7
   	0	5	1	3

   
   Answer 513 r 6

Check. 7 × 513 = 3,591, and 3,591 + 6 = 3,597. ✓

Watch out. A carried remainder must be smaller than the divisor. If you get a remainder that is too big, check your times table.

Method. Divide by 3, then divide the answer by 4. Combine the two remainders to find the true remainder.

1. Write 12 as two numbers to multiply. Dividing by 12 is the same as dividing by 3 and then by 4.
   12 = 3 × 4
2. Divide by 3 first. Use short division and keep the remainder.

   		0	0	0
   3	3	3	6	0
   	1	1	2	0

   
   3,360 ÷ 3 = 1120 remainder 0
3. Divide the answer, 1120, by 4. Use short division again.

   		1	3	0
   4	1	1	2	0
   	0	2	8	0

   
   1,120 ÷ 4 = 280 remainder 0
4. Work out the total remainder. The 0 left over from the second division is worth 3 each in the first division. So multiply 0 by 3, then add the first remainder 0.
   3 × 0 + 0 = 0 + 0 = 0
5. Write the answer.
   280

Check. 12 × 280 = 3,360, and 3,360 + 0 = 3,360. ✓

Watch out. The second remainder is worth 3 in the first division, so you must multiply it by 3. Do not just add the two remainders.

Method. Divide by 3, then divide the answer by 5. Combine the two remainders to find the true remainder.

1. Write 15 as two numbers to multiply. Dividing by 15 is the same as dividing by 3 and then by 5.
   15 = 3 × 5
2. Divide by 3 first. Use short division and keep the remainder.

   		1	2	2
   3	4	7	0	0
   	1	5	6	6

   
   4,700 ÷ 3 = 1566 remainder 2
3. Divide the answer, 1566, by 5. Use short division again.

   		1	0	1
   5	1	5	6	6
   	0	3	1	3

   
   1,566 ÷ 5 = 313 remainder 1
4. Work out the total remainder. The 1 left over from the second division is worth 3 each in the first division. So multiply 1 by 3, then add the first remainder 2.
   3 × 1 + 2 = 3 + 2 = 5
5. Write the answer.
   313 r 5

Check. 15 × 313 = 4,695, and 4,695 + 5 = 4,700. ✓

Watch out. The second remainder is worth 3 in the first division, so you must multiply it by 3. Do not just add the two remainders.

Key words. Short division (the bus stop method) divides by a one-digit number. A small carried remainder is written above the next digit. It is the number left over, and it is worth ten times more in the next column.

Method. Use short division. Work from left to right, one digit at a time. Carry any remainder into the next digit.

1. Set out the bus stop layout. The number goes inside the bus stop and the divisor, 6, goes outside it.
   6 ) 2,850
2. Divide the digit 2 (digit 1 of 4). Start with the first digit on the left.
   2 ÷ 6 = 0 remainder 2. Write 0 on top and carry the remainder 2.
3. Divide the digit 8 (digit 2 of 4). Each remainder is smaller than the divisor. Carry it to the next digit to the right.
   Carry the remainder 2 to the next digit to make 28 = 28. 28 ÷ 6 = 4 remainder 4. Write 4 on top and carry 4.
4. Divide the digit 5 (digit 3 of 4). Each remainder is smaller than the divisor. Carry it to the next digit to the right.
   Carry the remainder 4 to the next digit to make 45 = 45. 45 ÷ 6 = 7 remainder 3. Write 7 on top and carry 3.
5. Divide the digit 0 (digit 4 of 4). Each remainder is smaller than the divisor. Carry it to the next digit to the right.
   Carry the remainder 3 to the next digit to make 30 = 30. 30 ÷ 6 = 5 remainder 0. Write 5 on top and carry 0.
6. Read the answer from the bus stop layout. The quotient is the top row of numbers. The last remainder is left over.

   		2	4	3
   6	2	8	5	0
   	0	4	7	5

   
   Answer 475

Check. 6 × 475 = 2,850. ✓

Watch out. A carried remainder must be smaller than the divisor. If you get a remainder that is too big, check your times table.

Method. Divide the money by 7 with short division. Then say what the remainder means.

1. Set out the division. Each friend gets the same amount.
   £3,826 ÷ 7
2. Use short division. The answer is the amount each friend gets, and the remainder is the money left over.

   		3	3	4
   7	3	8	2	6
   	0	5	4	6

   
   £546 remainder £4
3. Write the answer. The remainder is money that cannot be shared, so it is left over.
   Each friend gets £546 and £4 is left over.

Check. 7 × 546 = 3,822, and 3,822 + 4 = 3,826. ✓

Watch out. The remainder is in pounds here, because we divided pounds. It is not in pence.

Key words. Short division (the bus stop method) divides by a one-digit number. A small carried remainder is written above the next digit. It is the number left over, and it is worth ten times more in the next column.

Method. Use short division. Work from left to right, one digit at a time. Carry any remainder into the next digit.

1. Set out the bus stop layout. The number goes inside the bus stop and the divisor, 8, goes outside it.
   8 ) 1,035
2. Divide the digit 1 (digit 1 of 4). Start with the first digit on the left.
   1 ÷ 8 = 0 remainder 1. Write 0 on top and carry the remainder 1.
3. Divide the digit 0 (digit 2 of 4). Each remainder is smaller than the divisor. Carry it to the next digit to the right.
   Carry the remainder 1 to the next digit to make 10 = 10. 10 ÷ 8 = 1 remainder 2. Write 1 on top and carry 2.
4. Divide the digit 3 (digit 3 of 4). Each remainder is smaller than the divisor. Carry it to the next digit to the right.
   Carry the remainder 2 to the next digit to make 23 = 23. 23 ÷ 8 = 2 remainder 7. Write 2 on top and carry 7.
5. Divide the digit 5 (digit 4 of 4). Each remainder is smaller than the divisor. Carry it to the next digit to the right.
   Carry the remainder 7 to the next digit to make 75 = 75. 75 ÷ 8 = 9 remainder 3. Write 9 on top and carry 3.
6. Read the answer from the bus stop layout. The quotient is the top row of numbers. The last remainder is left over.

   		1	2	7
   8	1	0	3	5
   	0	1	2	9

   
   Answer 129 r 3

Check. 8 × 129 = 1,032, and 1,032 + 3 = 1,035. ✓

Watch out. A carried remainder must be smaller than the divisor. If you get a remainder that is too big, check your times table.

Method. Check Ruby's answer by multiplying 6 by 895 and adding the remainder.

1. Multiply the divisor by the quotient. Work out 6 × 895.
   6 × 895 = 5,370
2. Add the remainder. Add the remainder 2 to the answer.
   5,370 + 2 = 5,372
3. Compare with the number we started with. The check gives the number we started with, and the remainder is smaller than 6.
   5,372 = 5,372, and 2 is smaller than 6. ✓

Check. 6 × 895 + 2 = 5,372. ✓

Watch out. A short division check is the same as a long division check: divisor × quotient + remainder.

Method. Work backwards. Multiply the quotient by the divisor, then add the remainder.

1. Multiply the quotient by the divisor. The number is 8 groups of the quotient, plus the remainder.
   437 × 8 = 3,496
2. Add the remainder. The remainder 5 was left over, so add it.
   3,496 + 5 = 3,501
3. Check with short division. Divide the number by 8. It should give 437 remainder 5.

   		3	3	6
   8	3	5	0	1
   	0	4	3	7

   
   3,501 ÷ 8 = 437 remainder 5

Check. 8 × 437 + 5 = 3,501. ✓

Watch out. Check the number has four digits, as the question says.