Concepts of Fractions

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Like and Unlike fractions

A part of a whole when it is divided into equal parts is a fraction.

Eg: The whole Pizza is divided into 5 equal parts,then one part of it is expressed as 1/5
 
A fraction has two parts,the top number is the numerator and the down number is the denominator.
 
In 1/5, 1 is the numerator and 5 is the denominator
 
Set of Fraction is a subset of the set of Rational Numbers
 
Like Fractions
 
Fractions with same denominators are called like Fractions
 1/3, 2/3, 5/3 , etc are like fractions.
 
Unlike Fractions
 
Frations with different denominators are called unlike fractions
 2/3 ,3/4 , 5/7 etc are unlike fractions

Types of Fraction

 

Proper fraction

In a fraction if the numerator is smaller than the denominator it is called a proper fraction
Eg. 1/3, 2/7,3/8 etc
 
Improper fraction
 
If the numerator is greater than denominator then the fraction is known as improper fraction
Eg: 12/7, 11/9, 5/2 etc
 
Mixed number
 
A whole number added with a fraction is a mixed number
12 and 2/3 1 and1/4 are all mixed numbers means these numbers are greater than 1
The improper fractions can be written as mixed fractions.
Mixed fractions can be written as improper fraction.
 
 

Equivalent fraction

When the numerator and denominator of any fraction are multiplied or divided by the same number except zero we get equivalent fraction

Let us find the equivalent fraction of 5/7

Step1: 5/7 = (5x2)/(7x2) =10/14

Step2: 5/7 = (5x3)/(7x3) =15/21

Step3: The equivalent fraction of 5/7 =10/14=15/21

For Example : 3/2 = 6/4 = 9/6 = 12/8

How to do Fractions

    The simple procedure to perform fraction.

To divide given whole object into specified number of equal parts is called as fraction.

Following example illustrate how to do fractions and basic operations involved during fractions.

Example : fraction of 12 objects into 7 equal parts = 12/7

              Verification - 1 object and 1/7th part of another objects when added 7 times gives apprximately 12 objects

                   fraction of 18 objects into 3 equal parts = 18/3

              Verification - 6 object added 3 times gives 18 object.

Decimal fractions

Fractions having 10 and powers of 10 as their denominators are called decimal fractions

Eg: 1/10, 2/10, 3/100, 4/100 etc 

Percentage :

Fractions having 100 as their denominators are also called as percentage.

Eg: 14/100 =14%

Complex Fractions

A complex fraction is a fraction where the numerator, denominator, or both contain a fraction.

 

  • Example 1: 
     5 
3/4
    is a complex fraction. The numerator is 3 and the denominator is 1/2.
  • Example 2: 
     4/6 
 10
    is a complex fraction. The numerator is 3/7 and the denominator is 9.
  • Example 3: 
    5/6 
8/10
    is a complex fraction. The numerator is 3/4 and the denominator is 9/10