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Fraction

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. Screenshot_49

* Value of proper fraction is greater than 1.

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

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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).

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

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

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Example: Find the LCM and HCF of the fractions

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Solution: Given that,

We know that,    LCM of the given fraction is

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

and HCF of 5,5 and 6 is 1

∴  LCM of the given fraction is

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=60 Ans:

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

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

and LCM of 5,5 and 6 is 30.

∴HCF of the given fraction

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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 Screenshot_61 - Copy

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

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Now,

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We know that,    LCM of the given fraction is

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Now, LCM of 36,72 and 144 is 144

and HCF of 5 ,25 and 25 is 5

∴  LCM of the given fraction is

Screenshot_71

∴ The least fraction is

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