Process of division in a column consists in consecutive performance of elementary arithmetic actions. To learn to divide in a column, it is necessary just to practice in it several times. We will consider a division algorithm in a column on the following examples - we will divide in a column integers without the rest, from the rest and the fractional numbers presented in the form of decimal fraction.
It is required to you
- - handle or pencil,
- - sheet of paper in a cage.
Instruction
1. Exact division. Let's divide 1265 into 55. Draw a short vertical line, height in several cages down. From this line carry out a perpendicular to the right. Letter "T" which is filled up on the left side turned out. Over a horizontal part of the filled-up letter "T" the divider (55), and to the left of it is written in the same line, behind a vertical part of letter "T" – a dividend (1265). Usually, at first the dividend registers, the division sign in a column (letter "T" which is filled up on one side), and after a divider is put then.
2. Define what part of a dividend (counting goes on seniority of categories from left to right) is divided into a divider. That is: 1 on 55 – no, 12 on 55 – no, 126 on 55 – yes. Number 126 is called an incomplete dividend.
3. Ponder by what number N it is necessary to increase a divider that the number equal or as close as possible (but not bigger) to the size of an incomplete dividend turned out. That is: 1*55 – it is not enough, 3*55=165 – there is a bit too much. So, our choice – number 2. We write down it under a divider (below a horizontal part of the filled-up letter "T").
4. Increase 2 by 55 and write down the received number 110 strictly under figures of an incomplete dividend – from left to right: 1 under 1, 1 under 2 and 0 under 6. From above 126, from below 110. Draw under the 110th short horizontal line.
5. Subtract from the 126th 110. 16 will turn out. Write down figures accurately one under another under the drawn line. That is, from left to right: under figure 1 of number 110 – it is empty, under figure 1 – 1 and under figure 0 – 6. Number 16 is the rest which has to be less divider. If it appeared more divider, number N was chosen incorrectly – it is necessary to increase it and to repeat the previous actions.
6. Demolish the following figure of a dividend (figure 5) and write down it to the right of number 16. 165 turned out.
7. Repeat actions of the third step for the relation 165 to 55, that is find number Q at multiplication of a divider by which, the number as close as possible to 165 turns out (but not bigger it). This number 3 – 165 is divided into 55 without the rest. Write down figure 3 to the right of figure 2 below the line which is carried out under a divider. It is also the answer: private the relations of 1265 to 55 it is equal to 23.
8. Division with remainder. Let's divide 1276 into 55. Repeat the same actions, as at exact division. Number N is still equal 2, but the difference between 127 and 110 is equal to 17. We take down 6 and we define number Q. It is also still equal 3, but the rest appears now: 176 – 165 = 11. The rest 11 less than 55, it seems, everything is normal. But there is nothing to take down more …
9. Add zero to the right of a dividend and put a comma, after figure 3 in private (that number which turns out during division, and registers below the line, carried out under a divider).
10. Demolish zero added in a dividend (write down it to the right of 11) and check whether there is an opportunity to divide the turned-out number into a divider. The answer – yes: 2 (we will designate it, as number G) to increase by 55 equally 110. The answer - 23.2. If there would not be enough zero demolished in the previous step in order that the rest with the added zero appeared more divider, it would be necessary to add one more zero in a dividend and to put 0 in the private ambassador of a comma (23.0 would turn out...).
11. Division in a column of decimal fractions. Transfer a comma to the identical number of signs to the right in a dividend and a divider so that both there, and there were integers. Further – a division algorithm the same.