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Kinds  of  Fractions

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Kinds  of  Fractions

Fractions :- If p\in I, q\in N and   (p, q)  =  1,  then  only \frac{p}{q} is called a fraction.

Proper  Fraction  :   A proper fraction is one whose numerator is less than its denominator.

example \frac{5}{8} is  a  proper fraction.   As  5  <  8

Improper  Fraction  :   A improper fraction is one whose numerator is equal to or greater   than its denominator.

e.g. (i) \frac{7}{4} is  an improper fraction.  As  7  >  4.

(ii) \frac{5}{5} is  an improper fraction.  As  5  =  5.

Mixed  Fraction  :   A mixed fraction is one which consists of  two parts, an integer and a fraction.

e.g. 3\frac{1}{4} is a mixed fraction.        ( Where, 3\frac{1}{4} = \frac{12+1}{4}=\frac{13}{4} )

Vulgar  Fraction  :   The fraction of  the form mixed fraction or proper faction is called vulgar fraction.

e.g. \frac{1}{4},\frac{5}{8},5\frac{2}{3},etc

Decimal  Fraction  :   A fraction with denominator 10n (n  N.  i.e. 10, 100, 1000, … ) is called a decimal fraction.

e.g. \frac{3}{100},\frac{4}{100},\frac{1723}{1000},etc.

Compounded  Fraction  :   Fraction of  type  \frac{\frac{2}{3}}{\frac{5}{7}}  or  \frac{\frac{2}{3}}{5}  or  \frac{2}{\frac{3}{5}}  or  \frac{5\frac{7}{8}}{3} are called compound fractions.

\frac{\frac{a}{b}}{\frac{c}{d}}  =  \frac{a}{b} \times \frac{d}{c},                    \frac{\frac{a}{b}}{c}  = \frac{a}{b} \times \frac{1}{c},            \frac{a}{\frac{b}{c}}  = a \times \frac{c}{b}

 

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