A fraction is the expression of a quantity divided by another, and a proper fraction represents the object parts that take a object whole.

The classic example is that of a cheese that matches portions.
In the picture, we have made 8 portions, 3 roses and 5 green.

If we take the 3 roses, represents 3 portions of eight in which we have divided the cheese, ie   3 / 8  of the cheese, and if we take the 5 green , represents 5 portions of eight in which we have divided the cheese, ie   5 / 8   of the cheese.

The parts we take (3-5)  are called   numerator (top)   and the parts that divide the cheese  ( 8 ) denominator (bottom).

CLASSIFICATION OF FRACTIONS

Fractions can be classified in different ways, in the following table shows the characteristics of the most important.

Type	Features	Examples
Proper	The numerator is smaller than the denominator	1 / 2, 7 / 9
Improper	The numerator is greater than the denominator	4 / 3, 5 / 2
Whole	The numerator equals the denominator; represent an integer	6 / 6 = 1
Homogeneous	They have the same denominator	2 / 5, 4 / 5
Heterogeneous	They have different denominator	3 / 7, 2 / 8
Equivalents	When they have the same value. Two fractions are equivalent if their cross product are equal	2/3 y 4/6 2x6 = 3x4

If a fraction we multiply or divide the numerator and denominator by the same number, we get a fraction equivalent to the first, as both have the same value. Example:

1		(1 x 4)		4				3		(3 : 3)		1
—	=	———	=	—	=	0,5 ;		—	=	———	=	—	=	0,2
2		(2 x 4)		8				15		(15 : 3)		5

Reduce or simplify a fraction is to find the smallest equivalent fraction; therefore, we divide the numerator and denominator by the factors common to both.
A fraction in which the numerator and denominator have no factors in common (other than 1) is said to be irreducible or in its lowest terms.

ADDITION AND SUBTRACTION OF FRACTIONS

The first rule of addition is that only homogeneous fractions (with the same denominator) can be added.
If the fractions have the same denominator, add or subtract the numerators and put the same denominator.
Example:

3		2		(3 + 2)		5		5		2		(5 – 2)		3
—	+	—	=	———	=	— ;		—	–	—	=	———	=	—
6		6		6		6		7		7		7		7

If the fractions have different denominator (heterogeneous), the first thing we have to do is transformed into homogeneous (equalize the denominators). To achieve this, we seek two fractions equivalent to those given by multiplying the numerator and denominator each by the denominator of the other. Once you get the same denominator, we proceed as above, add or subtract the numerators and put the common denominator.
Example:

2		3		(2 x 7)		(3 x 5)		14		15		29
—	+	—	=	———	+	———	=	——	+	——	=	——
5		7		(5 x 7)		(7 x 5)		35		35		35

MULTIPLICATION OF FRACTIONS

The product of various fractions is equal to another fraction whose numerator is the product of the numerators and denominator is the product of the denominators.
Example:

3		4		2		(3 x 4 x 2)		24			2
—	x	—	x	—	=	————	=	——	simplifying	=	—
4		5		3		(4 x 5 x 3)		60			5

FRACTION OF A NUMBER

Calculate the fraction of a number is the same as multiplying the fraction by that number.
Example: Calculate the 2 / 3 of 60 :

2				2				(2 x 60)		120
—	of	60	=	—	x	60	=	———	=	——	=	40
3				3				3		3

DIVISION OF FRACTIONS

The quotient of two fractions is another fraction whose numerator is the product of the first numerator by the denominator of the second, and the denominator is the product of the denominator of the first by the numerator of the second.
Example:

4		3		(4 x 5)		20
—	:	—	=	———	=	——
9		5		(9 x 3)		27

In the games, the fraction line we will write with the slash " / ", by simplicity in the handling of the keyboard.

The games in the menu on the left will help you learn fractions.

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