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Chapter 1 | Review of Basic Arithmetic  23



                1.3   Fractions



                                 Definition of Fractions and Types of Fractions


                             A fraction is a rational number written as one integer divided by another non-zero integer. It is usually
        If the denominator of a   written as a pair of numbers, with the top number being called the numerator and the bottom number
        fraction is zero, then the   the denominator. A fraction bar (horizontal bar indicating division) separates the numerator and the
        fraction is undefined.
                             denominator. The use of fractions is another method of representing numbers.
                                                                     3       numerator
                                                    fraction bar
                                                                     8       denominator

                                        3
                             For example,    f  p is a fraction. It is read as "three divided by eight",  "three-eighths", or "three
                                        8
                             over eight", which all indicate that 3 is the numerator and 8 the denominator.

                             A proper fraction is a fraction in which the absolute value of the numerator is less than the absolute
                             value of the denominator; i.e. the absolute value of the entire fraction is less than 1.


                             For example,
        The absolute value of
        a number refers to the      3
        positive sign of            ■   f  p is a proper fraction.
        that number.                8
        For example, the
                                                      2
        absolute value of –2 is 2.    ■  –2  in absolute value is   f  p, which is a proper fraction. Therefore,  –2  is a proper fraction.
        i.e. |–2| = 2.              5                 5                                      5
                             An improper fraction is a fraction in which the absolute value of the numerator is greater than the
                             absolute value of the denominator; i.e. the absolute value of the entire fraction is more than 1.

                                        7                –3
                             For example,   f       p and    f        p are improper fractions.
                                        4                 2
                                           (seven quarters)  (negative three halves)

                             If the numerator and denominator are equal, then the fraction is equal to 1.
                                        7
                             For example,   = 1.
                                        7
                             If the absolute value of the numerator and denominator are equal but with opposite signs, then the
                             fraction is equal to –1.
                                        9        –8
                             For example,    = –1 or    = –1.
                                        –9        8

                             To reduce a fraction, divide the numerator and denominator by a number by which they are both
                             divisible.
                             A mixed number consists of both a whole number and a proper fraction, written side-by-side, which
                             implies that the whole number and proper fraction are added.

                                         5
                             For example, 3  implies 3 +  5                              Mixed Number
                                         8
                                                    8
                                                                                               5
                                                                 three     five-eighths       3 8    Fraction
                                                                                                     Whole Number
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