Mathematics is one of the sciences that brings the most headaches because in this science accuracy prevails, there are no greys, it is either white or black, to put it simply. Solving mathematical calculations, no matter how simple they are, such as the fundamental operations (addition, subtraction, multiplication and division) requires accuracy. Luckily, there are calculators that often give quick solutions, but we don’t always have one at hand or we don’t get exactly what we’re looking for. To solve problems, we often need to know how to do division. For example, a problem may require a division that could be solved with a calculator. Suppose I have €1400 to distribute among 7 people, it is known that we must divide 1400 / 7 and obtain the result that will be exactly €200 each because the division is exact, or in other words the remainder of the division is zero.
But what would happen if instead of €1,400 I have €1,950 and I have to distribute it among the same 7 people, logically each one will get more but it could also be that I have money left over. If I do the division with the calculator: 1950 / 7 I will obtain €278.57143, that is to say that the division in this case is not exact. If we know how to make a division “by hand” we will be able to know how much each one has left (€278) and what is the rest of the division, that is, what is left over for me (in this case €4).
Let’s test if it’s true: €278 x 7 + €4 = €1,946 + €4 = € 1,950, which is what we had to share.
We will teach you how to do divisions with the corresponding algorithm and we will give you some tricks so that you can work with the calculator.
What do you need to do divisions?
- Numbers to divide
- Paper and pencil
- Calculator
Instructions for division
- Dividing two numbers is finding how many times the divisor fits in the dividend, that result is called the quotient and what remains of the division, if we are talking about exact division, is the remainder. Dividing is the opposite of multiplying, so this gives us a great advantage: we can verify if the result obtained is correct.
- In mathematics there are many types of numerical divisions depending on the numerical field in which we work, for example in the natural numbers, which are the ones we learn from a young age, there is only exact division, instead we can work within the so-called real numbers with fractions, decimals and irrationals. Each one with its own algorithm and its difficulties.
- We will see how to do a division with natural numbers first by one figure, then with two because the procedure is the same for any number as long as we are not working with decimal numbers.
- Suppose we want to divide 2354 :3 =
- We raise the division and we begin by asking ourselves: can I divide the first digit of the dividend by the divisor, that is, can 2 be divided by 3? The answer is no because the 3 does not fit even once in the two, it is greater. Then we will take two digits of the dividend, that is 23. Now 23 can be divided by 3. We ask ourselves: How many times does 3 fit into 23? The answer is 7 because 3 x 7 = 21, if he had answered 8 he would exceed it because 3 x 8 = 24. We put the 7 below the division line and we already have the first number of the quotient. Now we must multiply 7 x 3 = 21 and we place the result under 23 and subtract: 23 – 21 = 2 (we write it down).
- Now we must lower the next figure, 5, which with the two that we had left over before will form 25. We repeat the question: How many times does 3 fit into 25? The answer is 8 because 3 x 8 is 24 and if I put 9 it would happen to me. We write the 8 in the quotient after the 7 we already had. We multiply 8 x 3 = 24 again and write it under the 25 and subtract. 25 – 24 = 1. We write it down and lower the last digit, which will be a 4. We form 14. How many times does 3 enter 14? The answer is 4, we write it in the quotient and multiply 4 x 3 = 12 again, we write 12 and subtract: 14 – 12 = 2. This number is the remainder of the division which must always be less than the divisor. The quotient was 784and the rest
- If we want to check that the division is done correctly, we can multiply the quotient by the divisor, then we add the rest and it will give us the dividend.
- Look: 784 x 3 + 2 = 2352 +2 = 2354. Checked!
- If we want to divide by two figures, we must start by taking two figures from the dividend, if we see that it is less than the divisor, we will take 3 figures. For example: 14503: 70 =
- Since 14 is less than 70, we must take the first three figures, that is, 145, divide by 70 and this will result in 2, we write it in the quotient, multiply 2 x 70 = 140, write it and subtract: 145 -140 = 5 , then we lower the next figure that is a 0, we form the number 50 that we must divide by 70 but since it is less than the we place a 0 in the quotient. Finally we lower the last figure and we will have 503 formed. How many times does 70 fit into 503? The answer is 7, we put it in the quotient and continue as usual. The quotient will be 207 and the remainder 13 (remember that it must always be less than the divisor).
- We check: 207 x 70 + 13 = 14490 + 13 = 14503.
- If you want to do it with a calculator directly and you want to do the integer division, that is, find the quotient and the remainder, do the following:
- Divide 14503: 70 = 207, 1857143…… The quotient is 207, that is, the integer part of that division. To obtain the remainder, do the following: subtract the integer part from that number as it is on the calculator display, that is: 207.1857143….- 207 = 0.1857143 and multiply that result by the divisor, that is, by 70 and you will get the rest: 0.1857143 x 70 = 13
- Take the test with the first division we did.
Tips for making divisions
- Remember that when you do the verification you will have a multiplication and an addition, do not forget that the multiplication is solved first and then the addition.
- Practice a lot dividing by one, two, three figures since the procedure is the same.
- It can also be very useful for you to learn how to teach division or learn to memorize the multiplication tables.