> Fractions

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  • A Fraction is a number   , of the form where a  and  b  are integers and b ≠ 0. The integer a is called the numerator of the fraction, and b is called the denominator. For e.g.  is a fraction in which -7 is the numerator and 5 is the denominator. Such numbers are called rational numbers.
  • If both the numerator  a  and denominator  b are multiplied by the same nonzero integer, the resulting fraction will be equivalent to  . For e.g. 
  • If both the numerator and denominator have a common factor, then the numerator and denominator can be factored and reduced to an equivalent fraction. For e.g.
  • To add two fractions with the same denominator, you add the numerators and keep the same denominator. For e.g.
  • To add two fractions with different denominators, first find a  common denominator, which is a common multiple of the tow denominators. Then convert both fractions to equivalent fractions with the same denominator. Finally, add the numerators and keep the common denominator. For e.g. to add the fractions  and  , use the common denominator 15:

  • The same method applies to subtraction of fractions.
  • To multiply two fractions, multiply the two numerators and multiply the two denominators. For e.g. 
  • To divide one fraction by another, first invert the second fraction, that is, find its reciprocal, and then multiply the first fraction by the inverted fraction. For e.g.
  • An expression such as  is called mixed number. It consists of an integer part and a fraction part; the mixed number   means    .  To convert a mixed number to an ordinary fraction, convert the integer part to an equivalent fraction and add it to the fraction part. For e.g.
  • Note that numbers of the form  , where either a or b is not an integer and b , are fractional expressions that can be manipulated just like fractions. For e.g. the numbers    can be added together as follows.


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