Long Division worksheet

1. Exact decimal (repeating block in brackets): 346.(153846)

1. Start with 45, the first part of 4,500 that is at least 13. 13 goes into it 3 times; multiply and subtract

   $45-3\times 13$$=6$

2. Bring down the next digit, 0, to make 60. 13 goes into it 4 times; multiply and subtract

   $60-4\times 13$$=8$

3. Bring down the next digit, 0, to make 80. 13 goes into it 6 times; multiply and subtract

   $80-6\times 13$$=2$

4. The remainder 2 is not 0, so write a decimal point after 346 and keep going by bringing down zeros

   $\text{346.}$

5. Decimal place 1: bring down a 0 to make 20. 13 goes into it 1 time

   $20-1\times 13$$=7$

6. Decimal place 2: bring down a 0 to make 70. 13 goes into it 5 times

   $70-5\times 13$$=5$

7. Decimal place 3: bring down a 0 to make 50. 13 goes into it 3 times

   $50-3\times 13$$=11$

8. Decimal place 4: bring down a 0 to make 110. 13 goes into it 8 times

   $110-8\times 13$$=6$

9. Decimal place 5: bring down a 0 to make 60. 13 goes into it 4 times

   $60-4\times 13$$=8$

10. Decimal place 6: bring down a 0 to make 80. 13 goes into it 6 times

    $80-6\times 13$$=2$

11. The remainder 2 has come up before, after the decimal point, so from there the same 6 digits repeat forever (shown in brackets)

    $\text{346.(153846)}$

12. Rounded to 12 decimal places (half up), using the next digit

    $\text{4,500 ÷ 13 ≈ 346.153846153846}$

2. Answer: 283 R 4

1. Start with 34, the first part of 3,400 that is at least 12. 12 goes into it 2 times; multiply and subtract

   $34-2\times 12$$=10$

2. Bring down the next digit, 0, to make 100. 12 goes into it 8 times; multiply and subtract

   $100-8\times 12$$=4$

3. Bring down the next digit, 0, to make 40. 12 goes into it 3 times; multiply and subtract

   $40-3\times 12$$=4$

4. No digits are left to bring down, so the quotient is 283 and the last subtraction leaves the remainder

   $\text{3,400 ÷ 12 = 283 R 4}$

5. Check: quotient × divisor + remainder gives back the dividend

   $\text{283 × 12 + 4}$$=\mathrm{3,400}$

3. Answer: 395 R 10

1. Start with 47, the first part of 4,750 that is at least 12. 12 goes into it 3 times; multiply and subtract

   $47-3\times 12$$=11$

2. Bring down the next digit, 5, to make 115. 12 goes into it 9 times; multiply and subtract

   $115-9\times 12$$=7$

3. Bring down the next digit, 0, to make 70. 12 goes into it 5 times; multiply and subtract

   $70-5\times 12$$=10$

4. No digits are left to bring down, so the quotient is 395 and the last subtraction leaves the remainder

   $\text{4,750 ÷ 12 = 395 R 10}$

5. Check: quotient × divisor + remainder gives back the dividend

   $\text{395 × 12 + 10}$$=\mathrm{4,750}$

4. Answer: 454 R 6

1. Start with 50, the first part of 5,000 that is at least 11. 11 goes into it 4 times; multiply and subtract

   $50-4\times 11$$=6$

2. Bring down the next digit, 0, to make 60. 11 goes into it 5 times; multiply and subtract

   $60-5\times 11$$=5$

3. Bring down the next digit, 0, to make 50. 11 goes into it 4 times; multiply and subtract

   $50-4\times 11$$=6$

4. No digits are left to bring down, so the quotient is 454 and the last subtraction leaves the remainder

   $\text{5,000 ÷ 11 = 454 R 6}$

5. Check: quotient × divisor + remainder gives back the dividend

   $\text{454 × 11 + 6}$$=\mathrm{5,000}$

5. Answer: 468 R 6

1. Start with 37, the first part of 3,750 that is at least 8. 8 goes into it 4 times; multiply and subtract

   $37-4\times 8$$=5$

2. Bring down the next digit, 5, to make 55. 8 goes into it 6 times; multiply and subtract

   $55-6\times 8$$=7$

3. Bring down the next digit, 0, to make 70. 8 goes into it 8 times; multiply and subtract

   $70-8\times 8$$=6$

4. No digits are left to bring down, so the quotient is 468 and the last subtraction leaves the remainder

   $\text{3,750 ÷ 8 = 468 R 6}$

5. Check: quotient × divisor + remainder gives back the dividend

   $\text{468 × 8 + 6}$$=\mathrm{3,750}$

6. Exact decimal (repeating block in brackets): 357.(142857)

1. Start with 50, the first part of 5,000 that is at least 14. 14 goes into it 3 times; multiply and subtract

   $50-3\times 14$$=8$

2. Bring down the next digit, 0, to make 80. 14 goes into it 5 times; multiply and subtract

   $80-5\times 14$$=10$

3. Bring down the next digit, 0, to make 100. 14 goes into it 7 times; multiply and subtract

   $100-7\times 14$$=2$

4. The remainder 2 is not 0, so write a decimal point after 357 and keep going by bringing down zeros

   $\text{357.}$

5. Decimal place 1: bring down a 0 to make 20. 14 goes into it 1 time

   $20-1\times 14$$=6$

6. Decimal place 2: bring down a 0 to make 60. 14 goes into it 4 times

   $60-4\times 14$$=4$

7. Decimal place 3: bring down a 0 to make 40. 14 goes into it 2 times

   $40-2\times 14$$=12$

8. Decimal place 4: bring down a 0 to make 120. 14 goes into it 8 times

   $120-8\times 14$$=8$

9. Decimal place 5: bring down a 0 to make 80. 14 goes into it 5 times

   $80-5\times 14$$=10$

10. Decimal place 6: bring down a 0 to make 100. 14 goes into it 7 times

    $100-7\times 14$$=2$

11. The remainder 2 has come up before, after the decimal point, so from there the same 6 digits repeat forever (shown in brackets)

    $\text{357.(142857)}$

12. Rounded to 14 decimal places (half up), using the next digit

    $\text{5,000 ÷ 14 ≈ 357.14285714285714}$

7. Answer: 266 R 10

1. Start with 40, the first part of 4,000 that is at least 15. 15 goes into it 2 times; multiply and subtract

   $40-2\times 15$$=10$

2. Bring down the next digit, 0, to make 100. 15 goes into it 6 times; multiply and subtract

   $100-6\times 15$$=10$

3. Bring down the next digit, 0, to make 100. 15 goes into it 6 times; multiply and subtract

   $100-6\times 15$$=10$

4. No digits are left to bring down, so the quotient is 266 and the last subtraction leaves the remainder

   $\text{4,000 ÷ 15 = 266 R 10}$

5. Check: quotient × divisor + remainder gives back the dividend

   $\text{266 × 15 + 10}$$=\mathrm{4,000}$

8. Exact decimal: 520

1. Start with 52, the first part of 5,200 that is at least 10. 10 goes into it 5 times; multiply and subtract

   $52-5\times 10$$=2$

2. Bring down the next digit, 0, to make 20. 10 goes into it 2 times; multiply and subtract

   $20-2\times 10$$=0$

3. Bring down the next digit, 0, to make 0. 10 goes into it 0 times; multiply and subtract

   $0-0\times 10$$=0$

4. Rounded to 11 decimal places (half up), using the next digit

   $\text{5,200 ÷ 10 ≈ 520.00000000000}$

9. Exact decimal (repeating block in brackets): 363.(63)

1. Start with 40, the first part of 4,000 that is at least 11. 11 goes into it 3 times; multiply and subtract

   $40-3\times 11$$=7$

2. Bring down the next digit, 0, to make 70. 11 goes into it 6 times; multiply and subtract

   $70-6\times 11$$=4$

3. Bring down the next digit, 0, to make 40. 11 goes into it 3 times; multiply and subtract

   $40-3\times 11$$=7$

4. The remainder 7 is not 0, so write a decimal point after 363 and keep going by bringing down zeros

   $\text{363.}$

5. Decimal place 1: bring down a 0 to make 70. 11 goes into it 6 times

   $70-6\times 11$$=4$

6. Decimal place 2: bring down a 0 to make 40. 11 goes into it 3 times

   $40-3\times 11$$=7$

7. The remainder 7 has come up before, after the decimal point, so from there the same 2 digits repeat forever (shown in brackets)

   $\text{363.(63)}$

8. Rounded to 8 decimal places (half up), using the next digit

   $\text{4,000 ÷ 11 ≈ 363.63636364}$

10. Answer: 418 R 2

1. Start with 46, the first part of 4,600 that is at least 11. 11 goes into it 4 times; multiply and subtract

   $46-4\times 11$$=2$

2. Bring down the next digit, 0, to make 20. 11 goes into it 1 time; multiply and subtract

   $20-1\times 11$$=9$

3. Bring down the next digit, 0, to make 90. 11 goes into it 8 times; multiply and subtract

   $90-8\times 11$$=2$

4. No digits are left to bring down, so the quotient is 418 and the last subtraction leaves the remainder

   $\text{4,600 ÷ 11 = 418 R 2}$

5. Check: quotient × divisor + remainder gives back the dividend

   $\text{418 × 11 + 2}$$=\mathrm{4,600}$