FRACTIONS

FRACTON :-  If any unit be divided into any number of equal parts, one or more of those parts is called a fraction of the unit. The fraction one-fourths, three-fourths are written as  $\frac{1}{4}$, $\frac{3}{4}$.
    Here, the upper number of fraction is called numerator of fraction and the lower number of fraction is called denominator of fraction.

PROPERTIES OF FRACTIONS :- 

•  A fraction is also called a rational number.
• A fraction is equal to zero when its numerator is zero, and the denominator of the fraction is always not equal to zero.
• A fraction is unity when its numerator and denominator are equal.
• The fraction is said to be in its lowest terms,if the numerator and denominator of the fraction have no common factor.

PROPER FRACTION :-  A proper fraction is a fraction whose numerator is less then the denominator.

                For eg.  $\frac{2}{3}, \frac{4}{7}$.

IMPROPER FRACTION :-  An improper fraction is a fraction whose numerator is more than the denominator.

                For eg.  $\frac{7}{3}, \frac{21}{6}$.

MIXED FRACTION :-   A mixed fraction is an improper fraction when expressed as a combination of a whole number and a proper fraction.

                For eg.  $2\frac{5}{7}, 3\frac{3}{5}$.

EQUIVALENT FRACTIONS :-  Equivalent fractions are those two or more fractions which can be reduced to the same lowest terms.

                For eg.  $\frac{20}{8} and \frac{25}{10}$ are equivalent fractions

          $\because$ when both reduced to lowest  term answer is $\frac{5}{2}$.

LIKE FRACTIONS :-  Fractions in which denominators are same are called like fractions.

                For eg.  $\frac{4}{15}, \frac{7}{15}$, etc.

                NOTE :-  In this case, the fraction having the greatest numerator is the greatest.

UNLIKE FRACTIONS :-  Fractions in which the denominator are different are called unlike fractions.

                For eg.  $\frac{4}{15}, \frac{20}{7}$.

DECIMAL FRACTIONS :- 

                For eg.  $\frac{3}{10}, \frac{7}{100}$, etc.   are decimal fractions.

COMPOUND FRACTIONS :-  A fraction of a fraction is called s compound fraction.

                For eg.  $\frac{1}{2} of  \frac{3}{7}$ is a compound fraction.

                            

                             $\frac{1}{2} of \frac{3}{7} = \frac{1}{2} \times \frac{3}{7}= \frac{3}{14}$

COMPLEX FRACTIONS :-  A comlpex fraction is a fraction in which the numerator or denominator or both are fractions.

                Foe eg.  $\frac{\boldsymbol{\frac{5}7}}{8}$, $\mathbf{\frac{\boldsymbol{\frac{1}2}+\frac{2}{3}}{\frac{3}4-\frac{2}{5}}}$.


CONTINUED FRACTIONS :-  Fractions that contain an additional fraction in the numerator or the denominator are called continued fraction.
                For eg.  $3\div \frac{1}{1+\frac{1}{3+\frac{2}{3}}}$.