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Long Division Practice Questions with Worked Answers

Ten divisions from 96 ÷ 4 up to 9013 ÷ 24, set out line by line, with every remainder written three ways: as a remainder, a fraction and a decimal.

The short answer

Ten divisions worked line by line, from 96 ÷ 4 to 9013 ÷ 24. Six divide exactly and four leave a remainder, and each remainder is written three ways: as r, as a fraction of the divisor, and as a decimal. Two have a two-digit divisor and one has zeros inside the answer.

The questions

  1. Question 1Foundation2 marks

    96 ÷ 4

    Show the working

    24

    1. 4 into 9 goes 2, remainder 1. Write 2 above the 9.
    2. Bring down the 6 to make 16.
    3. 4 into 16 goes 4, remainder 0. Write 4 above the 6.
    4. Check: 24 × 4 = 96
  2. Question 2Foundation2 marks

    84 ÷ 6

    Show the working

    14

    1. 6 into 8 goes 1, remainder 2. Write 1 above the 8.
    2. Bring down the 4 to make 24.
    3. 6 into 24 goes 4 exactly. Write 4 above the 4.
    4. Check: 14 × 6 = 84
  3. Question 3Foundation3 marks

    93 ÷ 4. Give the remainder as a whole number, as a fraction and as a decimal.

    Show the working

    23 r 1, or 23 1/4, or 23.25

    1. 4 into 9 goes 2, remainder 1. Write 2 above the 9.
    2. Bring down the 3 to make 13.
    3. 4 into 13 goes 3, remainder 1. Write 3 above the 3.
    4. The remainder is 1 out of 4, so 23 r 1 = 23 1/4 = 23.25.
    5. Check: 23 × 4 + 1 = 92 + 1 = 93
  4. Question 4Core2 marks

    738 ÷ 6

    Show the working

    123

    1. 6 into 7 goes 1, remainder 1. Write 1 above the 7.
    2. Bring down the 3 to make 13. 6 into 13 goes 2, remainder 1.
    3. Bring down the 8 to make 18. 6 into 18 goes 3, remainder 0.
    4. Check: 123 × 6 = 738
  5. Question 5Core3 marks

    947 ÷ 8. Give the answer as a mixed number and as a decimal.

    Show the working

    118 r 3, or 118 3/8, or 118.375

    1. 8 into 9 goes 1, remainder 1. Write 1 above the 9.
    2. Bring down the 4 to make 14. 8 into 14 goes 1, remainder 6.
    3. Bring down the 7 to make 67. 8 into 67 goes 8, remainder 3.
    4. The remainder is 3 out of 8, and 3 ÷ 8 = 0.375, which terminates.
    5. Check: 118 × 8 + 3 = 944 + 3 = 947
  6. Question 6Core3 marks

    1000 ÷ 16

    Show the working

    62 r 8, or 62 1/2, or 62.5

    1. 16 does not go into 1 or into 10, so divide into 100.
    2. 16 × 6 = 96, remainder 4. Write 6 above the first 0.
    3. Bring down the last 0 to make 40. 16 × 2 = 32, remainder 8.
    4. The remainder is 8 out of 16, which is a half, so the answer is 62.5.
    5. Check: 62 × 16 + 8 = 992 + 8 = 1000
  7. Question 7Core3 marks

    6042 ÷ 6

    Show the working

    1007

    1. 6 into 6 goes 1, remainder 0. Write 1 above the first 6.
    2. Bring down the 0. 6 into 0 goes 0 - write that 0 in the answer, do not skip the column.
    3. Bring down the 4. 6 into 4 goes 0, remainder 4. Write a second 0 in the answer.
    4. Bring down the 2 to make 42. 6 into 42 goes 7, remainder 0.
    5. Check: 1007 × 6 = 6042
  8. Question 8Core4 marks

    5824 ÷ 14

    Show the working

    416

    1. Write the multiples of 14 down the side first: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140.
    2. 14 does not go into 5, so divide into 58. 14 × 4 = 56, remainder 2. Write 4 above the 8.
    3. Bring down the 2 to make 22. 14 × 1 = 14, remainder 8.
    4. Bring down the 4 to make 84. 14 × 6 = 84, remainder 0.
    5. Check: 416 × 14 = 5824
  9. Question 9Stretch4 marks

    7854 ÷ 17

    Show the working

    462

    1. Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170.
    2. 17 does not go into 7, so divide into 78. 17 × 4 = 68, remainder 10. Write 4 above the 8.
    3. Bring down the 5 to make 105. 17 × 6 = 102, remainder 3.
    4. Bring down the 4 to make 34. 17 × 2 = 34, remainder 0.
    5. Check: 462 × 17 = 7854
  10. Question 10Stretch5 marks

    9013 ÷ 24. Give the remainder as a whole number, as a fraction and as a decimal to 2 decimal places.

    Show the working

    375 r 13, or 375 13/24, or 375.54 to 2 d.p.

    1. Multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, 240.
    2. 24 does not go into 9, so divide into 90. 24 × 3 = 72, remainder 18. Write 3 above the 0.
    3. Bring down the 1 to make 181. 24 × 7 = 168, remainder 13.
    4. Bring down the 3 to make 133. 24 × 5 = 120, remainder 13.
    5. 13 ÷ 24 = 0.541666..., which recurs, so the decimal form is rounded: 375.54 to 2 d.p.
    6. Check: 375 × 24 + 13 = 9000 + 13 = 9013

Where these go wrong

  • Putting the first digit of the answer above the wrong column, so 5824 ÷ 14 comes out as 4160 or as 41.6 with all the digits otherwise correct.
  • Dropping the zeros in 6042 ÷ 6 and writing 107 or 17. Every column of the dividend needs a digit in the answer, including the ones where the divisor does not go.
  • Leaving a remainder larger than the divisor at some stage, which always means the digit chosen was one too small.
  • Writing the remainder as a fraction of the dividend rather than of the divisor: 118 3/947 instead of 118 3/8.
  • Giving 375.54 for 9013 ÷ 24 without saying it is rounded, when 13/24 is 0.541666... and never terminates.

What each of these ten is built to catch

A set of ten divisions that all behave the same way teaches one thing ten times. These are chosen so that each stage of the ladder introduces exactly one new difficulty, and the difficulty is named rather than hidden.

If a child is getting most of them right and one particular type wrong, that is the useful information. Work the type, not the whole sheet again.

  • 96 ÷ 4 and 84 ÷ 6 - the plain cycle, two digits, no remainder
  • 93 ÷ 4 - the first remainder, written in all three forms
  • 738 ÷ 6 - three digits, so the cycle runs a third time
  • 947 ÷ 8 - a remainder that becomes an eighth, and a decimal that stops
  • 1000 ÷ 16 - a divisor that will not go into the leading digits at all
  • 6042 ÷ 6 - zeros inside the answer, the most-dropped digits in the method
  • 5824 ÷ 14 and 7854 ÷ 17 - two-digit divisors, where estimating replaces recall
  • 9013 ÷ 24 - a remainder whose decimal never stops

When the decimal does not stop

Three of the four remainders here convert to a decimal that terminates: 1 out of 4 is 0.25, 3 out of 8 is 0.375, 8 out of 16 is 0.5. The fourth does not. 13 out of 24 is 0.541666..., with the 6 repeating forever, and no amount of extra columns will close it.

The honest answer is to say so. Write 375 13/24 if an exact answer is wanted, or 375.54 to 2 decimal places if a decimal is wanted, and state that it has been rounded. What is not acceptable is writing 375.54 as though it were exact, because the next calculation that uses it will be slightly wrong and there will be no record of why.

Marking your own answers

There are two checks worth running and they catch different mistakes. Multiplying the answer back by the divisor and adding the remainder catches arithmetic slips. Estimating the size of the answer before starting catches misplaced digits, which the multiplication check will happily confirm if the multiplication is done just as carelessly.

For 5824 ÷ 14, the estimate is that 14 is close to 15, and 15 goes into 5824 roughly 400 times. An answer of 4160 or of 41.6 is then visibly wrong before any working is re-read. In our classes the estimate is written down first and circled, because a check that lives only in a student's head does not get done under exam pressure.

Common questions

Do I have to write out the multiples before starting?

Not for a single-digit divisor, where the multiples are recalled facts. For 14, 17 or 24 it saves more time than it costs. Listing ten multiples takes about twenty seconds and turns every stage of the division into a lookup rather than a guess-and-adjust.

Which form should the remainder be written in?

Whichever the question asks for. If it does not say, let the context decide: a count of whole objects takes r, a measurement takes the decimal, and an exact answer that will be used again takes the fraction. Only the fraction is exact when the decimal recurs, as in 9013 ÷ 24.

Is bus stop division the same as long division?

The bus stop layout is the short version, where the remainder at each stage is carried as a small digit rather than written out as a subtraction. The cycle is identical. Long division shows the multiply and subtract lines in full, which is what a two-digit divisor makes necessary.

When is long division taught in England?

Year 6. The national curriculum expects pupils to divide numbers up to four digits by a two-digit whole number using the formal written method, and to interpret remainders as whole numbers, as fractions, or by rounding, according to the context. Two of the questions here are exactly that specification.

Sources

  1. National curriculum in England: mathematics programmes of study — Department for Education

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