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