Boba Maths

Year 6 · Arithmetic skills · Skill 6D

Skill 6D: Long division with remainders

Use long division to divide by 2-digit numbers and write the remainder as a fraction.

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Each file is an editable Word document (.docx) with 25 questions in five columns. It opens in Word, Google Docs, Pages and LibreOffice, so you can change questions or add working space before printing.

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Worked examples

Long division with remainders works in exactly the same way. The amount left at the end is the remainder, which can be written as a fraction of the divisor.

Example 1

A remainder that simplifies

2,194 ÷ 52

  1. Write out the multiples of 52 first. They make every step quicker.
    52 × 1 = 5252 × 2 = 10452 × 3 = 15652 × 4 = 20852 × 5 = 26052 × 6 = 31252 × 7 = 36452 × 8 = 41652 × 9 = 468
  2. Set out the division, then work from the left. At each step, find the biggest multiple of the divisor that fits, subtract it, and bring down the next digit.
               4 2
52 )   2 1 9 4
     − 2 0 8
     - - - -
         1 1 4
       − 1 0 4
       - - - -
           1 0
    1. 219 ÷ 52: 52 × 4 = 208, which is the biggest multiple that fits. 219 − 208 = 11.
    2. 114 ÷ 52: 52 × 2 = 104, which is the biggest multiple that fits. 114 − 104 = 10.
  4. 10 is left over. Write it as a fraction of the divisor: 10⁄52, which simplifies to 5⁄26 (divide the top and bottom by 2).
  5. So 2,194 ÷ 52 = 42 5⁄26 (or 42 remainder 10). Check: 42 × 52 + 10 = 2,194.

Answer: 425⁄26

Example 2

A remainder that does not simplify

3,205 ÷ 41

  1. Write out the multiples of 41 first. They make every step quicker.
    41 × 1 = 4141 × 2 = 8241 × 3 = 12341 × 4 = 16441 × 5 = 20541 × 6 = 24641 × 7 = 28741 × 8 = 32841 × 9 = 369
  2. Set out the division, then work from the left. At each step, find the biggest multiple of the divisor that fits, subtract it, and bring down the next digit.
               7 8
41 )   3 2 0 5
     − 2 8 7
     - - - -
         3 3 5
       − 3 2 8
       - - - -
             7
    1. 320 ÷ 41: 41 × 7 = 287, which is the biggest multiple that fits. 320 − 287 = 33.
    2. 335 ÷ 41: 41 × 8 = 328, which is the biggest multiple that fits. 335 − 328 = 7.
  4. 7 is left over. Write it as a fraction of the divisor: 7⁄41, which cannot be simplified.
  5. So 3,205 ÷ 41 = 78 7⁄41 (or 78 remainder 7). Check: 78 × 41 + 7 = 3,205.

Answer: 787⁄41

Top tips

  • Write the remainder over the divisor, then simplify.
  • Make sure the remainder is smaller than the divisor.
  • Check: answer × divisor + remainder = the starting number.

Watch out for

  • Leaving a remainder that is bigger than the divisor (you can fit in another).
  • Forgetting to simplify the fraction.

Try some questions

These are from the worksheet. Work each one out, then open it to check.

  1. 1,875 ÷ 24 =
    Show the answer

    781⁄8 (or 78 r 3)

  2. 3,027 ÷ 36 =
    Show the answer

    841⁄12 (or 84 r 3)

  3. 4,221 ÷ 57 =
    Show the answer

    741⁄19 (or 74 r 3)

  4. 6,219 ÷ 84 =
    Show the answer

    741⁄28 (or 74 r 3)

All arithmetic skills

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Arithmetic skills overview · Year 6 overview