A x A/B

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Multiplying Fractions In The Form:  a x a/b

A.  From algebra we learn: 

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

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

B.  Use the following steps:

1.      The denominator is always b.

2.      Subtract the values b and a and square it.  This is the numerator.

3.  If the resulting fraction is proper, write it down, otherwise "fix" it and carry.

4.      If a/b is proper: subtract the difference of b and a from a to get the whole number.

5.  If a/b is improper: add the difference of b and a to a to get the whole number.

            Ex [1]  13  x  13  =

                               15                         (mixed number). 

a)      (15 – 13)2 = 4.  This is the numerator.

b)      Since 4/15 is a proper fraction we write it down.

c)      Since the fraction 13/15 is proper, we subtract the difference, 2, from 13, which equals 11.  This is the whole number.

d)      The answer is 11 4/15.

                               Ex [2]  8  x 8  =

                                                5                           (mixed number). 

a)  (8 – 5)2 = 9.

b)      Since 9/5 is an improper fraction, rewrite it as 1 4/5.  Write 4/5 and carry the 1.

c)      Since 8/5 is improper, add the difference, 3, to 8, which equals 11.  Adding the carried number the whole number becomes 12.

d)      The answer is 12 4/5.

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