Despite the fact that most people think math science complex, it is not so.Many mathematical operations quite easy to understand, especially if you know the rules and formulas.So, knowing the multiplication table, you can quickly multiply in the mind large numbers.The main thing - to train constantly and do not forget the rules of multiplication.The same can be said of the division.
Let us analyze the division of whole numbers, fractions and negative.Let's remember the basic rules, techniques and methods.
Operation division
Let's start with the definition of names and numbers that are involved in this operation.This will greatly facilitate further presentation and perception of information.
Division - one of the four basic mathematical operations.Its study begins in elementary school.That's when children show the first example of division of the number, explain the rules.
The operation involved two numbers: the dividend and divisor.The first - a number that is divided, and the second - at which divide.The result of division is private.
There are several notations for recording the operation ":", "/" and the horizontal line - a record as a fraction when the dividend is at the top and at the bottom, below the line - divider.
Terms
In the study of a particular mathematical operation requires the teacher to acquaint students with the basic rules that you should know.However, they are not always remembered as nice as we would like.That is why we decided to refresh your memory of the four fundamental rights.
basic rules of division of numbers that should always remember:
1. divide by zero is impossible.The rule to remember in the first place.
2. Share a zero can be any number, but in the end will always be zero.
3. If the number is divided by one, we will get the same number.
4. If the number is divided by itself, we will get one.
As you can see, the rules are quite simple and easy to remember.Although some people may forget this simple rule, as the impossibility of dividing by zero, or confuse them with the division of the number zero.
signs of divisibility of the number
One of the most useful rules - a sign on which is determined by the possibility of dividing the natural number to another without a trace.Thus, isolated signs of divisibility by 2, 3, 5, 6, 9, 10. Let us examine them in detail.They essentially make it easier to perform operations on numbers.Also give an example for each rule dividing the number by the number.
These are general-attributes are widely used by mathematicians.
Divisibility by 2
easiest to memorize the sign.Number which ends with an even number (2, 4, 6, 8) or 0 are always evenly divisible by two.Pretty easy to remember and use.Thus, the number 236 ends in an even number, and hence divided into two evenly.
verify: 236: 2 = 118. In fact, the 236 is divisible by 2 without remainder.
This rule is the most well known not only for adults but also for children.
Divisibility by 3
How to perform a division of the number 3?Remember the following rule.
number evenly divisible by 3 in the event that the sum of its digits is a multiple of three.For example, take the number 381. The sum of all digits will be 12. This number is a multiple of three, and then divided by 3 without remainder.
also check this example.381: 3 = 127, then all right.
Divisibility of numbers 5
There is also simple.Divided into five without a remainder can only those numbers that end in the 5 or 0. For example, consider the number of such as 705 or 800. The first end 5, the second - to zero, so they are both divisible by 5. It is onefrom the simple rule that allows you to quickly divide by digit 5.
verify this feature on these examples: 405: 5 = 81;600: 5 = 120. As you can see, the sign acts.
Severability 6
If you want to find out whether a number is divisible by 6, then you first need to find out whether it is divided by 2, and then - to the 3. If so, then the number can be evenly divided by 6. For example,number 216 and divided by 2, as ends in an even number, and 3, as the sum of the digits is 9.
verify: 216: 6 = 36. The example shows that this feature works.
Severability 9
also talk about how to implement the division of numbers to 9. At this number divided those integers, the sum of digits is a multiple of 9. Similarly, the rule of divide by 3. For example, the number 918. Putting all the numbers and get18 - multiple of 9. Thus, it is divided into 9 without residue.
Solve this example to check: 918: 9 = 102.
Severability 10
latter feature that is worth knowing.On 10 share only those numbers that end in 0. This pattern is quite simple and easy to remember.For example, 500: 10 = 50.
That's all the main features.Remember them, you can make your life easier.Of course, there are other numbers for which there are signs of divisibility, but we'll highlight just the main ones.
Table division
In mathematics there is not only the multiplication table, but the table division.Once you learn it, you can easily perform the operation.In fact, the division table is a table multiplication vice versa.Be it on your own is not difficult.To this should be rewritten every line of the multiplication tables in this way:
1. Put the product of the number in the first place.
2. Put a sign of division and write the second factor from the table.
3. After the equal sign write the first factor.
For example, consider the following line from the multiplication table: 2 * 3 = 6. Now rewrite it according to the algorithm and get 6 รท 3 = 2.
Quite often, children are asked to draw up their own table, thus developing their memory and attention.
If you do not have time to write it, you can use the provided in the article.
Forms division
talk a little bit about the kinds of division.
To begin with, it is possible to allocate the division of whole numbers and fractions.In the first case we can speak about operations with whole numbers and decimals, while the second - only fractional numbers.When this can be both fractional numerator or divisor, or both simultaneously.This separation is due to the fact that the operations on fractions differ from integer operations.
Next we'll talk about dividing fractions more.
Based on the numbers involved in the operation, there are two kinds of division: in the single digits and ambiguity.The simplest division is considered to be in the single digits.Here, you will not need to carry out lengthy calculations.Besides well may help dividing table.Share the same on the other - two-, three-digit numbers - harder.
Consider the examples of these types of division:
14: 7 = 2 (division by one-digit number).
240: 12 = 20 (divide by two-digit number).
45387: 123 = 369 (division by three-digit number).
last division can be identified, which involves positive and negative numbers.When working with the latest should know the rules by which it assigns the result is positive or negative value.
When dividing numbers with different signs (dividend - the number is positive, the divisor - negative, or vice versa), we get a negative number.When dividing numbers with the same sign (and the dividend and the divisor - positive or vice versa) - we get a positive number.
Consider for illustration the following examples:
21: (- 7) = -3
-36: 6 = (-6)
-48: (-8) = 6.
division of fractions
So,we are pulled down the basic rules, gave an example of dividing the number by the number, now let's talk about how to correctly perform the same operations with fractions.
Although the division of fractions at first seems rather heavy thing, in fact, work with them is not so difficult.Dividing fractions is performed almost as well as multiplication, but with one difference.
To divide fractions, you must first multiply the numerator by the denominator of the dividend and the divider to fix the result in the form of the numerator of the quotient.Then multiply the denominator of the dividend by the divisor of the numerator and denominator to record the result as private.
can be made easier.Rewrite the fraction divider, interchanging the numerator by the denominator, and then multiply the resulting number.
example, to separate the two fractions: 4/5: 3/9.To start overturn divider we get 9/3.Now multiply fractions: 4/5 * 9/3 = 36/15.
As you can see, it's pretty easy, and no more difficult than the division into single digits.Examples of the actions with fractions solved simply, if you do not forget this rule.
Conclusions
Division - one of the mathematical operations that every child learns in elementary school.There are certain rules that you should know the techniques in order to facilitate this operation.The division is a residue and without, is the division of negative and fractional numbers.Remember
features of this mathematical operation quite easily.We are dismantled most important moments, not considered one example of dividing the number by the number of even talked about how to work with fractional numbers.
If you want to improve your knowledge of mathematics, we advise you remember these simple rules.In addition, we can advise you develop memory and numeracy in mind, performing mathematical dictations or just trying to calculate the quotient of two orally random numbers.Believe me, these skills will never be superfluous.
