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# FRACTIONS

A fraction is a number in the form of a/b where a and b are whole numbers and b is not equal to 0. Example of fractions are ½, 2/4 and 7/3.

## Types of Fractions

Fractions can be classified into many classes.

### Proper Fraction

If the numerator of the fraction is less than the denominator of the fraction then fraction is called proper fraction. Numerically if numerator<denominator then fraction is proper. Examples are ½, 5/9, 10/37 and 11/23.

### Improper Fraction

If the numerator is greater than or equal to denominator then fraction is called improper fraction.Examples of improper fractions are 2/2, 3/2, 11/9 and 66/33.

### Mixed fraction

A fraction mixed fraction consists of a whole number and a proper fraction.

### Simple Fraction

A fraction in which both numerator and denominator are whole numbers then the fraction is called simple fraction. Simple fraction is also called vulgar fraction. Examples of simple fraction are 0/1, 6/8, 13/17 and 111/173.

### Complex Fraction

If numerator or denominator or both have a fraction then that fraction is called complex fraction. Examples of complex fractions are as follows:

(1/2)/5 is a complex fraction because it contains a fraction is numerator.

3/(4/5) is also a complex fraction because it had a fraction in denominator.

And (2/5)/(2/7) is complex fraction because it has fraction at numerator as well as at denominator.

### Decimal Fraction

If the denominator if a fraction is a multiple of 10 then the fraction is called decimal fraction. 1/10, 9/1000,  321/100 are decimal fractions.

### Like Fractions

Two or more fractions are said to be like fractions if they have same number in denominator. Examples of like fractions are 3/5, 6/5 and 9/5.

### Unlike Fractions

If two or more fraction have no common denominator then they are called unlike fractions. 3/2, 7/4 and 5/9 are unlike fractions.

### Equivalent Fractions

Two or more fractions are said to be equivalent fractions if their simplest forms are same. 2/4 and 4/8 are equivalent fractions because the simplest format of each fraction is 1/2.

## Converting Unlike Fractions to Like Fractions

To convert unlike fractions into like fraction first find the LCM (Least Common Multiple) of denominators of each fraction. Let 3/4 and 7/5 are two unlike fractions we want to convert them into like fractions. Here denominators are 4 and 5 and LCM of 4 and 5 is 20.

Then Chose a number for which the product of denominator and the chosen number is equal to LCM of denominators. In the above example the denominator of first fraction is 4 so we have to multiply 4 by 5 to get 20. Thus the chosen number for first fraction is 5. Similarly do the same thing with other fractions. The second fraction of above example of 7/5 and the denominator is 5. Now we have to multiply 5 by 4 to get 20. Thus the chosen number for second fraction is 4.

Now multiply with the chosen number with both numerator and denominator of the fraction. The chosen number for first fraction is 5 so after multiplying by 5 with numerator and denominator the first fraction becomes (5 x 3)/(5 x 4) = 15/20. Similarly the second fraction becomes (4 x 7)/(4 x 5) = 28/20. Thus the like fractions are 15/20 and 28/20.

### Arranging Fractions in Ascending and Descending Order

If the denominator of the fractions are same then sort the numerator in increasing order. For example arrange 2/9, 8/9, 6/9 and 7/9 in ascending orders. Since the denominator are same thus we start writing order with 2, 6, 8 and 9. Hence the ascending order is as follows: 2/9 < 6/9 < 7/9 < 8/9.

Similarly to arrange fractions in descending order we will have to arrange the numerators in decreasing order. for example arrange 6/7, 5/7, 15/7 and 4/7 in descending order. The numerators are 6, 5, 15, and 4. Now the decreasing order of numerator is 15, 6, 5, 4. Hence Descending order is as follows: 15/7 > 6/7 > 5/7 > 4/7.

If numerator of the fractions are same then to sort the them in ascending order we have to sort the denominator in decreasing order. For example sort 15/13, 15/19, 15/17 and 15/21 in ascending order. Decreasing order of denominators is as 21, 19, 17 and 13. Hence Ascending order of 15/13, 15/19, 15/17 and 15/21 is as follows: 15/21 < 15/19 < 15/17 < 15/13.

Similarly to sort them in descending order we will have to sort the denominator in increasing order. For example sort 5/12, 5/11, 5/9, 5/13 and 5/10 in descending order. The increasing order of denominators is as follows: 9, 10, 11, 12 and 13. Hence descending order of 5/12, 5/11, 5/9, 5/13 and 5/10 is as follows: 5/9 > 5/10 > 5/11 > 5/12 > 5/13.

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