Let’s divide 32 into 240. We set the problem out as before: 32
We begin by dividing both numbers by 10. Then, 3 divides into 24 eight times, with 0 remainder. The
0 remainder is carried to the next digit, 0, making a new working number of 0. We adjust for the 2 in 32
by multiplying the last digit of our answer by the 2 in 32 and subtracting from our working number, 0.
Eight times 2 is 16. Zero minus 16 is −16. We can’t work with −16 so the last digit of our answer was
too high.
(We can easily see this, as 8 times 30 is exactly 240. We are not dividing by 30, but by 32. The
answer is correct for 30, but clearly it is not correct for 32. Because each answer is only an estimate, we
can see in this case we will have to drop our answer by 1.)
We change the answer to 7, so: 7 × 3 = 21, with 3 remainder.
Our calculation looks like this:
We now multiply:
7 × 2 = 14
Then we subtract from 30:
30 − 14 = 16
The answer is 7 with 16 remainder.
If we want to take the answer to one decimal place, we now divide 16 by 3 for the next digit of the
answer. Three divides into 16 five times, with 1 remainder. The 1 is carried to the next digit to make 10.
We multiply the last answer, 5, by the 2 in 32 to get an answer of 10. Subtract 10 from our working
number 10 to get an answer of 0. There is no remainder. The answer is exactly 7.5.
The problem now looks like this:
This is not difficult, but you need to keep in mind that you have to allow for the subtraction from the
remainder.
Reverse technique — rounding off upwards
Let’s see how direct long division works for dividing by numbers with a high units digit, such as 39. We