1.04 Long division.

Division is based on the repeated subtraction of one number (a) from another (b). The result of a division gives the number of times a can be subtracted from b and may also include a remainder. The remainder is any amount left after a has been subtracted the maximum number of times from b.



As an alternative to expressing the result as a quotient with a remainder, we can also express the result as a fractional quotient with no remainder.

e.g. 5/2 = 2.5 (i.e. two "fits into" five two and a half times).

Note, when expressing quotients this way (i.e.with the use of decimal fractions) some answers will be approximate. This is because you can't express all fractions exactly in decimal. e.g. 1/3 would be expressed as 0.33. However 3 x 0.33 = 0.99 (but 3 x 1/3 = 1). Therefore 0.33 is only approximately equal to a third.

Procedure for carrying out long division.

The steps involved in long division are quite simple, but as it involves a series of repeated steps, it can appear to be quite complicated. The basic principal is to break the task into stages, with a simple division at each stage that gives a single digit result. Any remainder is carried over into the next stage. The final answer is made up of the digits produced from each individual stage.

You may need to read through the procedure below several times while stepping through example problems to master this method.

If divisor does not divide exactly into the dividend (i.e. the final stage produces a remainder), then you can produce an approximate result which is either rounded down or rounded up. You can decide how many decimal points to calculate the answer to, before rounding the final value. To do this add zeros after the decimal point to the dividend and carry out further steps of division using these digits, until you have produced the required number of decimal points in the quotient.
In the example below two zeros have been placed after the decimal point in the dividend. They will be used when required to produce an answer rounded down to two decimal points.

Note the calculation of the quotient and the remainder at each step are shown below. This is not normally shown in the working out for a question. However the subtraction to determine the remainder, usually is included within the main calculation as illustrated below. (The amount of working out included with the answer, makes the process look even more complicated!)


Press step to step through the calculation
Press reset to clear and set new calculation
divided by = remainder
e.g.          x  

The app above always rounds down the answer. In practice you should round up or down depending on the value of the third decimal place.
e.g. 3.252 should be rounded down to 3.25 and 3.256 should be rounded up to 3.26 .

Also the script is not "intelligent" enough to spot when it has found and exact answer early in the procedure and so carries on until every digit in the divisor as been processed.
e.g. 2800/ 14 just requires 1 step for the solution (28/14 = 2 with no remainder. So you would insert the remaining zeros to give a final value of 200).
The app however will continue to check the remaining zeros to "see" if they can be divided!