A/B + B/A

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Adding Fractions In The Form:  a/b + b/a

A.  This method is very easy since from algebra we know:

                        a +  b = 2 + (b – a)2     *Note: Since you are squaring (b – a) it does

                        b     a             ab                not matter if you use (b – a)2 or (a – b)2. 

B.  Use the following steps:

              1.  Find the difference between the two numbers, b and a.

              2.  Square the result of step 1.  This is the numerator.

              3.  Multiply the two numbers, b and a.  This is the denominator.

  1.  If the fraction is proper, write down 2.  This is the whole number.

  2.  If the fraction is improper, “fix” it to be a mixed number and add it to 2 for the answer (see Ex [2] below).

                 Ex [1]   3  +  5  =

                            5      3                         (mixed number).

               a)      (5 – 3)2 = 4.  This is the numerator.

               b)      5 x 3 = 15.  This is the denominator.

               c)      Since 4/15 is a proper fraction, write 2 for the whole number.

               d)      The answer is 2 4/15.

                 Ex [2]   2  +  7  =

                            7      2                         (mixed number).

               a) (7 – 2)2 = 25.  This is the numerator.

               b) 7 x 2 = 14.  This is the denominator.

               c) Since 25/14 is an improper fraction, we need to "fix" it to be 1 11/14. 

               d) Now we add this to 2 to get 3 11/14.

                  e) The answer is 3 11/14.

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