# The main property of fractions.

Speaking of math, one can not forget fraction.Their study paid a lot of attention and time.Think how many examples you had to solve in order to learn certain rules of work with fractions as you remember and apply the basic property of fractions.How many nerves were spent to find a common denominator, especially in the examples were more than two terms!

Let us remember that it is, and a little brush up on the basics and rules for working with fractions.

## Determining fractions

Let's start with the most important - determination.Fraction - a number which consists of one or more parts of the unit.Fraction is written as two numbers separated by a horizontal or the slash.The upper (or the first) is the numerator, and the bottom (second) - the denominator.

It is worth noting that the denominator indicates how many parts of the divided unit, and the numerator - the number of shares taken or parts.Often, fractions, if they are correct, less than unity.

Now let's look at the properties of these numbers and the basic rules that are used when working with them.But before we will analyze such a thing as "the basic property of rational fractions", will talk about the kinds of fractions and their features.

## What are fractions

There are several types of such numbers.This is especially common and decimal.The first are already given us a rational view of the number of entries by using either a horizontal slash.The second type of fractions is indicated by the so-called positional notation, is an indication of when the first part of the whole, and then, after the decimal point indicates the fractional part.

It is worth noting that in the same math used as decimal and common fractions.The main property of the fraction thus only valid for the second embodiment.In addition, common fractions distinguish right and wrong numbers.At first the numerator is always less than the denominator.Note also that this fraction is less than one.The improper fractions contrary - numerator over denominator, and she was more than one.Thus it can be distinguished from an integer.In this article we consider only ordinary fractions.

## Properties fractions

Any phenomenon, chemical, physical or mathematical, has its own characteristics and properties.No exception, and fractional numbers.They have one important feature, with which they can be carried out on certain operations.What is the main property of fractions?The rule states that if its numerator and denominator are multiplied or divided by the same rational number, we will get a new shot, the value of which is equal to the original.That is, by multiplying two fractional number 3/6 by 2, we obtain a new fraction of 6/12, and they are equal.

Based on this property, it is possible to reduce the fraction, as well as to select the common denominators for a particular pair of numbers.

## Operations

Although fractions seem to us to be more complex than the simple numbers, with them also to perform basic mathematical operations such as addition and subtraction, multiplication and division.In addition, there is a specific action, such as reducing fractions.Naturally, each of these actions is done according to certain rules.Knowledge of these laws easier to work with fractions, making it easier and more interesting.That's why we'll continue to look at the basic rules and sequence of actions when dealing with such numbers.

But before we talk about mathematical operations such as addition and subtraction, we explain an operation such as to bring to a common denominator.Here we just did and useful knowledge, a basic property of fractions exists.

## common denominator

In order to bring the number to a common denominator, you first need to find the least common multiple of the two denominators.That is the smallest number that is divisible by both two denominator without a trace.The easiest way to choose the LCM (least common multiple) - written out in line multiples for a single denominator, then the second, and to find among them the match number.In case NOC not found, that is, data numbers have a common multiple numbers must multiply them, and the resulting count value for the NOC.

So we found NOCs now have to find an additional factor.To do this, turn on the NOC to share denominators and write on each of them received number.Next, multiply the numerator and denominator for additional multiplier and record the results as a new fraction.If you doubt that you have received equal number still remember the main property of fractions.

now proceed directly to the mathematical operations on fractional numbers.Let's start with the most simple.There are several options for adding fractions.In the first case, both numbers have the same denominator.In this case, can only add up the numerators together.But the denominator does not change.For example, 1/5 + 3/5 = 4/5.

If the fractions have different denominators, you should bring them to the total, and only then perform addition.How to do it, we're just above dismantled.In this situation, you just come in handy basic property of fractions.The rule will bring the number to a common denominator.The value does not change.

Alternatively, it may happen that the fraction is mixed.Then, you must first be folded together the whole part, and then the fractions.

Multiply Multiply fractions requires no tricks, and to perform this action, necessary to know the main property of fractions.Suffice first multiply together the numerators and denominators.The product of the numerator will be the new numerator and the denominator - the new denominator.As you can see, nothing complicated.

The only thing you have to do - knowledge of multiplication tables, as well as care.In addition, after receiving the results, be sure to check whether you can reduce this number or not.For information on how to reduce fractions, we describe a little later.

## Subtraction

performing subtraction of fractions, should be guided by the same rules as for the addition.So, in numbers with the same denominator of the numerator of the reduced enough to take away the numerator deducted.In that case, if the fractions different denominators, you should bring them to the general and then perform the operation.As in a similar case with addition, you will need to use the main property of algebraic fractions and the skills to find the NOC and the common factors for the fractions.

## division

And the last, the most interesting operation when working with such numbers - division.It is pretty simple and does not cause any difficulties, even those who do not understand exactly how to work with fractions, especially to perform addition and subtraction.When dividing operating such a rule, as multiplication by the inverse fraction.The main property of the fraction, as in the case of the multiplication is involved for this operation would not.Let us examine in more detail.

When dividing numbers dividend remains unchanged.Fraction-splitter turns in the opposite, ie, the numerator by the denominator switch places.After this number multiplied together.

## reduction

So, we have already dismantled the definition and structure of fractions, their types, rules of operations on data numbers, found the main property of algebraic fractions.Now let's talk about an operation such as the reduction.Reduction of the fraction is the process of its transformation - the division of the numerator and denominator on the same number.Thus, the fraction is reduced without changing its properties.

Usually when making mathematical operation should look closely at the results obtained in the end and find out whether it is possible to reduce the resulting fraction or not.Keep in mind that the final result is always written does not require reduction of fractional number.

## Other operations

Finally, we note that we have listed, not all operations on fractional numbers, mentioning only the most well-known and necessary.Fractions can also equalize, convert to decimal and vice versa.But in this article we did not consider these operations as they are carried out in mathematics is much less than those that were listed above.

## Conclusions

we will talk about fractional numbers and operations with them.We dismantled and the main property of fractions, reducing fractions.But note that all these issues were discussed by us in passing.We have given only the most famous and used the rules gave the most important, in our opinion, advice.