Dividing is one of the four basic operations of arithmetic, along with addition, subtraction, and multiplication, but it is also one of the most complicated. Dividing consists of repeatedly subtracting a number or, in other words, how many times does one number contain another. For example, in the division of 40:4 it means that how many times the number 40, which is the largest, contains the smallest, which is 4, and in this case the result says that 10 times.
The first number, the big one, is called the dividend; the number we divide is called divisor; the result of that division is the quotient; and the remainder is what is left over, so to speak, from that division, since not all operations are integers, because 40:4 has a remainder of 0, but 41:4 would have some remainder number and it would be different to 0.
You can always find out if a division is correct with a multiply operation. What you would have to do would be to multiply the divisor by the quotient and add the remainder. If that operation results in the dividend, we have done it right.
There are simple and complex divisions. The simple ones are of only one number and whose solution can be quickly verified if it is correct or not; and the complex ones are those in which the divisor has more than two digits. In addition, then there are the divisions that are integers and the remainder is 0 and others that result in a decimal number.
Let’s take as an example of simple division and with remainder 0 the one at the beginning of 40:4. It doesn’t have much complication. Now, to know how to do complex ones with a remainder different from 0, let’s take 567:23 as an example.
- We have to place the 567 on the left side, leaving a separation gap and on the right, inside a box that is like a rectangle but without the top and right sides, the divider. Of course, always leaving space.
- Since 5 is smaller than 23, we cannot start dividing like this, we have to take the first two figures, that is, 56. In the event that those first two figures were smaller than 23, we would have to take the three figures. Then we have to divide 56:23. We test what number multiplied by 23 gives a number close to 56 and does not exceed it. With the 1 we are too far away, so we would try the 2. We would place the 2 under the box of 23 and we would do: 2 × 3 is equal to 6, so in the dividend, under the 6 of 567, we mentally place the 6 and we subtract it, as 6-6 is 0, under the 6 of 567 we put a 0. We multiply 2×2 which is 4 and make 5 of 567, minus 4, is equal to 1, so we put a 1 under the 5 and to the left of 0. Now we put the 7 of 567 next to the 10, so we have to divide 107:23. Since 10 is smaller than 23.
- We do the second division and think what number multiplied by 23 is close to 107 and does not exceed it. We try 4, because 2 times 2 is 8 and is close to 10 of 107, and 5 × 2 is 10 and would go over. So it would be 4×3, the 3 of 23, and it gives 12, so under the 7 of 107 we place the 2, and we are left with the fact that we took 1. We multiply 4×2, which is 8, we add the one that we took and this gives 9, so under the 10 of 107 we place the 9.
- Now on the dividend side we have 107 and below 92. We have to subtract this. 107-92=15, so now we have to divide 15:23, but here we see that 15 is smaller. So in this case we would put a 0 to the right of 15, leaving 150, and in the quotient we would put a comma (,) next to 24. This means that the result is going to be decimal. In case we do not want to continue with the division, the result would be 24 and the remainder would be 15.
- We divide 150:23, as 15 is very small we have to take the three figures. And we do the same thing again, we think what number multiplied by 23 gives 150 without going overboard. The 7 would be too much because 7 × 2 is 14 and it would be very fair, so we try the 6 and make 6 × 3 which is 18, we place the 8 under the 0 of 150 and we remember that we take 1; now we do 6×2 which is 12, plus the 1 which is 13 and we put the 13 under the 15. Now we have 150-132 on the dividend side and we do the subtraction, which gives 18. If we want to continue with the division we would have to lower a 0 again to the right of 18 so that it stays at 180 and continue testing. Otherwise, we would have 24.6 as a result and the remainder 18.
- To finish the division and make it clear what the rest is, we have to put it in a kind of box or crescent. Then we would have as a result of 567:23 a quotient of 24.6 and a remainder of 18. If we want we can check with a multiplication if we have done it correctly. What we would have to do is multiply the divisor, which is 23, by the quotient, which is 24.6, and add the remainder, which is 18. Since we have not finished the division since it is decimal, the result of this operation will be close to 567 but It won’t be exact, because we haven’t finished it.
If the divisor has more than two figures, the same thing would be done, always taking from the dividend a number that is higher than the divisor. If in the statement of a mathematical problem they tell us to go only up to the first decimal, we would leave the operation as it has been with 24.6 and if they ask us for two decimal places we would continue it.
Tips for dividing
- Place all the figures correctly because if it is a division with many figures you will end up messing up.
- Leave a large space between the dividend and the divisor because if you have to lower many numbers or have many figures after the decimal, you will have to put many 0s in the dividend and if you have stuck it too much to the divisor you will not have space to do the operation well.
- The divisions are one of the most complex operations, so do it slowly because otherwise the result will be incorrect.
- To choose the numbers of the quotient, you may always be between 2, try the largest of them and if you see that you go too far, keep the small one, but do not go for one first if you are not very clear, because although With 24.5 it would not have been bad, 24.6 is much more correct.
- Do the little house or crescent on the rest to signal that you are done. Just like when you decide the dividend figures with which you are going to start, do it too, this time instead of below the number, by the head. This way you will have the most organized operation and if you make a mistake it will be easier to find in which step it was.
What do you need to divide?
- Paper
- Pencil