Short division

To divide a large number by a {1}-digit number you can set it out like this:

Short division sum showing 918 ÷ 6 = 153
  1. 6 goes into 9 once with 3 remaining (remainder 3), so put 1 above the hundreds column and carry the 3 to the tens column.
  2. 6 goes into 31 five times, remainder 1, so put 5 above the tens column and carry the 1 to the units column.
  3. 6 goes into 18 exactly three times, so put 3 above the units column.

So, {918}\div{6}={153}

Sometimes, a number does not divide into another number exactly.

In this case, we can either give the answer as a whole number along with a remainder, or we can give the answer as a decimal. The decimal answer may be a terminating decimal or a recurring decimal. Often, decimal answers may be rounded to a required number of decimal places.

For example:

{964}\div{7}

Method 1 - answer as a whole number with a remainder.

Short division diagram
  1. 7 goes into 9 once with 2 remaining (remainder 2), so put 1 above the hundreds column and carry the 2 to the tens column.
  2. 7 goes into 26 three times, remainder 5, so put 3 above the tens column and carry the 5 to the units column.
  3. 7 goes into 54 seven times, remainder 5, so put 7 above the units column and have a remainder of 5.

So, 964 \div 7 = 137 remainder 5.

We write this with an r for 'remainder', so it looks like this:

{964}\div{7}={137~r5}

Method 2 - decimal answer, rounded to {1} decimal place.

Short division sum showing 964 ÷ 7 = 137.714...
  1. 7 goes into 9 once with 2 remaining (remainder 2), so put 1 above the hundreds column and carry the 2 to the tens column.
  2. 7 goes into 26 three times, remainder 5, so put 3 above the tens column and carry the 5 to the units column.
  3. 7 goes into 54 seven times, remainder 5, so put 7 above the units column and carry the 5 to the tenths column (writing the {964} as {964.000} as {7} does not divide into it exactly).
  4. {7} goes into {50} seven times, remainder {1}, so put {7} above the tenths column and carry the {1} to the hundredths column.
  5. {7} goes into {10} once, remainder {3}, etc

So, {964}\div{7}={137.714...}

{=137.7} (correct to {1} decimal place).

This method is called short division.