Adding and Subtracting Unlike Fractions Add and Simplify 9/44 + 17/36 = I know the answer is 67/99 but how do i get it?

9/44   + 17/36       we  need to find a common denominator between 44 and 36

Note that 44 factors as 4 X 11

And 36 factors as 4 X 9     

So.....taking each different factor found in both numbers and multiplying them together, we get  4 x 9 x 11  = 36 x 11 = 396....and this is the common denominator

So  9/44  =  [9 x 9]/[11 x 4 x 9] =  81/396

And   17/36  =  [17 x 11]/ [11 x 4 x 9]  =  187/396

So we have ........     81/396 + 187/396  =  268/396    .... and  since both numerator and denominator are even, we can divide them by 2 ....and we get....

134/198     and we can divde both by 2, again....and we get

67/99

And that's it!!!!

Thanks Chris - I am going to put my 2c worth in now  

$$\\\frac{9}{44} + \frac{17}{36} \\\\ =\frac{9}{11*4} + \frac{17}{9*4} \\\\ =\frac{9*9}{11*4*9} + \frac{17*11}{9*4*11} \\\\ =\frac{9*9+17*11}{11*4*9} \\\\ =\frac{81+187}{11*4*9} \\\\ =\frac{268}{11*4*9} \\\\ =\frac{268\div 4}{11*4*9\div 4} \\\\ =\frac{67}{11*9} \\\\ =\frac{67}{99} \\\\$$