What are the fractions called?
In mathematics, a fraction is a number consisting of one or several units of a unit. That is, the fraction is a part of one whole. For example, if you divide an object into 4 equal parts and take 1 of them, you will get a fraction 1/4, where 3 is the numerator, 4 is the denominator, and the result of this division (0.25) is the quotient. In the school curriculum various fractions are used, as they are called, depending on their type.
Ordinary, Decimal and Periodic Fractions
By way of writing, distinguish between ordinary and decimal fractions. In the first case, the fraction is also called simple. It consists of two natural numbers, separated by a horizontal or a slash, as in the image below.
The decimal fraction is an ordinary fraction with a denominator in the form of one followed by zeros, an example of such a fraction is shown in the following figure. However, such fractions are usually written without a denominator, and a comma (0.3) is used to denote parts from a whole. In this case, after the comma indicates as many digits as zeros in the denominator of a simple fraction.
The part of the decimal fraction that is located before the positional comma is called the whole part of the fraction, after it the decimal places. Moreover, the number of decimal places can be both finite (2,3) and infinite (2,333333).
In the latter case, we are talking about periodic fractions, since the repeating numbers were called the period. In this case, it is customary to enclose the period in letter, for example, 2, (3). This record is read as follows: two whole and three in the period. However, the periodic fractions can be rounded, then they are often called round fractions, although in mathematics it would be more correct to say - rounded fraction.
Correct, irregular and mixed fractions
A fraction is called correct when the module of the numerator is less than the module of the denominator(1/3, 2/5, 7/8), otherwise the fraction is called irregular (3/2, 9/7, 13/5). Including to the wrong fractions are counted fractions, where the numerator and denominator are equal to each other.
At the same time, any irregular fraction can be represented as a mixed one, an example of such a fraction is given below.
Here 1 is the integer part of the mixed number, and 1/2 is the fractional part. To convert a mixed number to a fraction, you must multiply the integer part by the denominator and add the numerator to the resulting value.As a result of such actions is the numerator of the ordinary fraction, while the denominator remains the same.
Reduced and Irreducible Fractions
When the numerator and denominator of a fraction can be divided into the same number (except one), the fraction is called contractible, in any other case - irreducible. For example:
- 3/9 - reduced fraction, since both the numerator and the denominator can be divided by 3;
- 3/5 is an irreducible fraction, since both numbers are simple, i.e. are divided only by themselves and by 1;
- 2/7 is an irreducible fraction, since there is no total number by which both the numerator and the denominator would be divided at the same time.
Compound and Reverse Fractions
Often, schoolchildren do not understand which fraction is called the inverse, and which fraction. It turns out, everything is quite simple. If we take the fraction 7/8 and swap the numerator and denominator, we get the fraction 8/7. Such fractions (7/8 and 8/7) are called inverse. Moreover, it should be noted that the product of such fractions is always equal to 1.
Composite fractions include expressions that include several features of a fraction. Examples of such fractions are given below.
In addition, there are positive and negative fractions.For designation of the last before the fraction is put the sign "-". At the same time, the “+” sign is usually not indicated, as with the positive numbers.