**Definition:** If p,q are co-prime numbers; q≠0 and q≠1,numbers expressed in (p ⁄ q) form are called fractional number.

Kind of fraction: There are two types of fraction,

(i) General fraction,

(ii) Decimal fraction.

General fraction: There are three kinds of general fraction

(i) Proper fraction,

(ii) Improper fraction and

(iii) Mixed fraction.

**Proper fraction:** A fraction in which the denominator is greater than the numerator, is proper fraction.

Example:¼

* Value of proper fraction is less than 1.

**Improper fraction:** A fraction in which the numerator is greater than the denominator, is an Improper fraction.

* Value of proper fraction is greater than 1.

**Mixed fraction:** A fraction in which have an integer number and a proper fraction .

**Reciprocal fraction:** A fraction obtained by changing the numerator to denominator and denominator to numerator of a given fraction is called the reciprocal fraction of the given fraction.

Example:Reciprocal fraction 4 ⁄ 5of is 5 ⁄4 .

* The product of a fraction and its reciprocal fraction is always 1.

**Equivalent fraction:** The value of a fraction is not changed if it’s numerator and denominator are multiplied or divided by the same number except by 0(zero).

**Complex fraction:** A complex fraction is a fraction whose numerator or denominator or both are not integers.

**Simple fraction:** A simple fraction is a fraction whose numerator or denominator or both are integers.

Example: Find the LCM and HCF of the fractions

Solution: Given that,

We know that, LCM of the given fraction is

Now, LCM of 4,3 and 5 is 60.

and HCF of 5,5 and 6 is 1

∴ LCM of the given fraction is

=60 __Ans:__

Again, We know that, HCF of the given fraction is

Now, HCF of 4,3 and 5 is 1.

and LCM of 5,5 and 6 is 30.

∴HCF of the given fraction

## Note that: The product of any two fractions= The product of their LCM and HCF.

Exercise: What is the least fraction so that if (1 ⁄ 8) is subtracted from it, the result is exactly divisible by

Solution: The least fraction will be more than the LCM of

Now,

We know that, LCM of the given fraction is

Now, LCM of 36,72 and 144 is 144

and HCF of 5 ,25 and 25 is 5

∴ LCM of the given fraction is

∴ The least fraction is