ALL ABOUT FRACTIONS

Fractions represent parts of a whole.

fractions

For example, if an apple is divided into three equal parts, each part is called one third and is denoted  by 1/3. We call 1/3 a fraction. Similalry, 1/4 , 2/5 , 3/7 , and 5/4 are also fractions.

      

In any fraction a/b, the dividend a is called the numerator and dividend b is called the denominator. For example, in the fraction 5/9, the numerator is 5 and the denominator is 9.

Classification of Fractions

           

Common, simple or vulgar fraction

The numerator and the denominator are integers in a common fraction, also known as a simple fraction or vulgar fraction.

Example 3/5 , 7/9 , 11/7 , 3/2 are some simple fractions.

Complex fraction

A fraction in which the numerator or the denominator or the both of them also contain fractions, is called a complex fractions.

For example: (4/5)/(7/9), (3/5)/(8/7), etc.

Proper fraction

A vulgar fraction in which the numerator is less than the denominator.

For example: 3/5, 4/9, etc.

Improper fraction

A vulgar fraction in which the numerator is greater than the denominator.

For example: 4/3, 8/5, etc.

Mixed fraction

An integer together with a proper fraction, is called a mixed fraction.

From example: 67/5, etc.

         A mixed fraction can easily be converted into an improper fraction as follows.

 Mixed fraction = [ (integral part) × (denominator of the proper fraction) + (numerator of the proper fraction)] / denominator.

OR

    Mixed fraction = quotient in (numerator ÷ denominator) + remainder/ denominator

Equivalent or equal fractions

If the numerator and denominator of a fraction are multiplied or divided by the same non-zero number, then we get an equivalent or equal fraction.

For example: 2/5 = 6/15, 7/9 = 42/54, etc.

This brings us to conclusion that the value of a fraction remains same of both its numerator and denominator are multiplied or divided by the same number.

• Two fractions a/b and c/d   are equivalent fractions if ad = BC.

Simplest form of fraction: A fraction is said to be in the simplest form of if its numerator and denominator have no factor in common except 1.

For example: 2/3, 7/9, 11/51, etc.

Like and unlike fractions: Two or more fractions are called like fractions of they have the same denominator. Fractions that do not have the same denominator are called unlike fractions.

For example: 2/9, 5/9, 7/9 are like fractions where as 2/5, 3/7,6/11 are unlike fractions.