Long Division Practice Questions with Worked Answers

Les exercices

1. Exercice 1Base2 points

   96 ÷ 4

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   24

   1. 14 into 9 goes 2, remainder 1. Write 2 above the 9.
   2. 2Bring down the 6 to make 16.
   3. 34 into 16 goes 4, remainder 0. Write 4 above the 6.
   4. 4Check: 24 × 4 = 96
2. Exercice 2Base2 points

   84 ÷ 6

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   14

   1. 16 into 8 goes 1, remainder 2. Write 1 above the 8.
   2. 2Bring down the 4 to make 24.
   3. 36 into 24 goes 4 exactly. Write 4 above the 4.
   4. 4Check: 14 × 6 = 84
3. Exercice 3Base3 points

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

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

   1. 14 into 9 goes 2, remainder 1. Write 2 above the 9.
   2. 2Bring down the 3 to make 13.
   3. 34 into 13 goes 3, remainder 1. Write 3 above the 3.
   4. 4The remainder is 1 out of 4, so 23 r 1 = 23 1/4 = 23.25.
   5. 5Check: 23 × 4 + 1 = 92 + 1 = 93
4. Exercice 4Standard2 points

   738 ÷ 6

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   123

   1. 16 into 7 goes 1, remainder 1. Write 1 above the 7.
   2. 2Bring down the 3 to make 13. 6 into 13 goes 2, remainder 1.
   3. 3Bring down the 8 to make 18. 6 into 18 goes 3, remainder 0.
   4. 4Check: 123 × 6 = 738
5. Exercice 5Standard3 points

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

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

   1. 18 into 9 goes 1, remainder 1. Write 1 above the 9.
   2. 2Bring down the 4 to make 14. 8 into 14 goes 1, remainder 6.
   3. 3Bring down the 7 to make 67. 8 into 67 goes 8, remainder 3.
   4. 4The remainder is 3 out of 8, and 3 ÷ 8 = 0.375, which terminates.
   5. 5Check: 118 × 8 + 3 = 944 + 3 = 947
6. Exercice 6Standard3 points

   1000 ÷ 16

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

   1. 116 does not go into 1 or into 10, so divide into 100.
   2. 216 × 6 = 96, remainder 4. Write 6 above the first 0.
   3. 3Bring down the last 0 to make 40. 16 × 2 = 32, remainder 8.
   4. 4The remainder is 8 out of 16, which is a half, so the answer is 62.5.
   5. 5Check: 62 × 16 + 8 = 992 + 8 = 1000
7. Exercice 7Standard3 points

   6042 ÷ 6

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   1007

   1. 16 into 6 goes 1, remainder 0. Write 1 above the first 6.
   2. 2Bring down the 0. 6 into 0 goes 0 - write that 0 in the answer, do not skip the column.
   3. 3Bring down the 4. 6 into 4 goes 0, remainder 4. Write a second 0 in the answer.
   4. 4Bring down the 2 to make 42. 6 into 42 goes 7, remainder 0.
   5. 5Check: 1007 × 6 = 6042
8. Exercice 8Standard4 points

   5824 ÷ 14

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   416

   1. 1Write the multiples of 14 down the side first: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140.
   2. 214 does not go into 5, so divide into 58. 14 × 4 = 56, remainder 2. Write 4 above the 8.
   3. 3Bring down the 2 to make 22. 14 × 1 = 14, remainder 8.
   4. 4Bring down the 4 to make 84. 14 × 6 = 84, remainder 0.
   5. 5Check: 416 × 14 = 5824
9. Exercice 9Approfondi4 points

   7854 ÷ 17

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   462

   1. 1Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170.
   2. 217 does not go into 7, so divide into 78. 17 × 4 = 68, remainder 10. Write 4 above the 8.
   3. 3Bring down the 5 to make 105. 17 × 6 = 102, remainder 3.
   4. 4Bring down the 4 to make 34. 17 × 2 = 34, remainder 0.
   5. 5Check: 462 × 17 = 7854
10. Exercice 10Approfondi5 points

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

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

    1. 1Multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, 240.
    2. 224 does not go into 9, so divide into 90. 24 × 3 = 72, remainder 18. Write 3 above the 0.
    3. 3Bring down the 1 to make 181. 24 × 7 = 168, remainder 13.
    4. 4Bring down the 3 to make 133. 24 × 5 = 120, remainder 13.
    5. 513 ÷ 24 = 0.541666..., which recurs, so the decimal form is rounded: 375.54 to 2 d.p.
    6. 6Check: 375 × 24 + 13 = 9000 + 13 = 9013

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.