THE division and the operationmathbasic harder. Its algorithm is often confusing and it takes a lot of training to master a technique to perform it. In order to facilitate calculations involving divisions, we list some tips and tricks. Not all tips can be used in every case of division, but knowing them can improve your reasoning for dealing with this kind of problem.
We suggest reading the text "Rest of Division”, which will provide a good basis for understanding the content discussed in this article.
First tip: Know the multiplication table
THE times tables is a list of all the results of multiplications between two numbers, these numbers ranging from zero to 10. The important thing is not to memorize this list (although this will help speed up the calculations of division and others), but understand how it is produced.
In a division, whenever the divisor is greater than 10, it is necessary to build a part of the times tables of this divisor to make this operation feasible. This procedure can be done mentally or in writing, but it is always done.
In other words, to learn how to share, it is essential to know multiply.
Second tip: divisibility criteria
A "hand on the wheel" for the division are the divisibility criteria. Through them, it is possible to find out if a numberédivisible on the other without having to divide them.
A number is divisible by four, for example, whenever its last two digits form a number that is also divisible by four. A number is divisible by three whenever the sum of its digits makes a number that is divisible by three.
These criteria can be used to speed up calculations of least common multiple, greatest common divider, numerical factorizations, calculation of roots, between others. In addition, there are also issues that are only interested in discussing the divisibility of numbers or the restgivesdivision. Knowing these criteria can streamline the entire process of answering them.
Third tip: Estimate the result
In some entrance exams, many public exams and in Enem, there are issues that involve only the interpretationininformation and an operation performed on data obtained in this interpretation.
so much in division as with any other basic math operation, always estimate the final result to “verify” your calculations.
When interpreting a question, for example, we find that it is necessary to perform the sum:
1232 + 937
Before performing the sum, we can say that the result will be close to 2000. If we find a result greater than 3000, for example, it is already possible to guarantee that the calculation or interpretation is wrong. The same goes for the division.
First trick: numbers ending in zero
When divider and dividend are numbers ending in zero, we can simplify them just by eliminating the zeros. The rule for this is: eliminate in the dividend the same amount of zeros eliminated in the divisor. For example:
40000 | 2000
has the same result as the division:
40000 | 2000
i.e:
40 | 2
Note that we did not “cut” all available zeros, as the divisor had fewer zeros than the dividend.
Second trick: factor and simplify
Whenever divider and dividend are not cousins to each other, it is possible factor them out and simplify them. Numbers cousins between them they have no common dividers. To make this process even easier, we can still write the division as a fraction. Look at the example:
384:64
both numbers are divisible by 2, by 4, by 16 (to find this out, you can use divisibility criteria). Factoring them into prime factors and writing them in the form of fraction, we will have:
27.3
26
Simplifying the fraction, we will have:
2·3 = 6
Third trick: numbers ending in 5
Every time that divider and dividend go multiples of 5, we can multiply them by 2 and use the first trick given in this article: eliminate the final zero.
In the 245:35 division, for example, we will have:
245·2 = 490 = 49 =7
35·2 70 7
By Luiz Paulo Silva
Graduated in Mathematics
Source: Brazil School - https://brasilescola.uol.com.br/matematica/dicas-macetes-para-calculos-divisao.htm