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Long division

You learn long division: dividing a big number bit by bit, from left to right.

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How to work it out

  1. Find multiples of the divisor.
  2. Divide, multiply, subtract, and bring down the next digit until complete.
1×2×3×5×10×
612183060

A worked example

438 ÷ 6

  1. Make a list: 6, 12, 30, 60.
  2. The 4 is too small, so take 43: 6 goes in 7 times, 6 × 7 = 42, and 1 is left over.
  3. Bring down the 8: 18.
  4. 6 goes in 3 times, 6 × 3 = 18, and 0 is left over.
  5. The answer is 73.
More examples

952 ÷ 7

  1. Take 9: 7 goes in once, and 2 is left over.
  2. Bring down the 5: 25.
  3. 7 goes in 3 times, 7 × 3 = 21, and 4 is left over.
  4. Bring down the 2: 42.
  5. 7 goes in 6 times, 7 × 6 = 42.
  6. The answer is 136.

738 ÷ 5

  1. Take 7: 5 goes in once, and 2 is left over.
  2. Bring down the 3: 23.
  3. 5 goes in 4 times, 5 × 4 = 20, and 3 is left over.
  4. Bring down the 8: 38.
  5. 5 goes in 7 times, 5 × 7 = 35, and 3 is left over.
  6. There are no more digits to bring down, so that 3 is the remainder.
  7. The answer is 147 remainder 3.

Watch out

  • You forget a 0 in the answer when a part is too small: for 624 ÷ 6 you write 14 instead of 104.

    If the number does not go into a part, write a 0 in the answer and bring down the next digit.

  • You forget to take what is left over on to the next part.

    Put what is left over in front of the next digit: 2 left over and a 5 brought down makes 25.

Tips

  • The list of 1, 2, 5 and 10 times the number shows how many times it goes in.
  • Check with multiplication: 73 × 6 = 438.

Exceptions

  • If the remainder is 0, the division comes out exactly and you do not write a remainder.

Why it works

Dividing a big number all at once is too much. So you divide a small part at a time, and take what is left over on to the next digit. If something is left after the last digit, that is the remainder: the part the number did not fit into. A list of 1, 2, 5 and 10 times the number helps you see how many times it goes in, without guessing.