Question

Ashley uses 1/4 package of raisin for a fruit cake. She then uses 1/9 of the remainder for muffins. What fraction of the package of raisins dose she have left?

Answer 1

$\text {Fruit cake = } \dfrac{1}{4}$

$\text {Raisin left = } 1 - \dfrac{1}{4} = \dfrac{4}{4} - \dfrac{1}{4} = \dfrac{3}{4}$

$\text {Muffins = } \dfrac{1}{9} \times \dfrac{3}{4} = \dfrac{3}{36} = \dfrac{1}{12}$

$\text {Raisin left = } \dfrac{3}{4} - \dfrac{1}{12} =\dfrac{9}{12} - \dfrac{1}{12} = \dfrac{8}{12} -= \dfrac{2}{3}$

Answer: She has 2/3 of the package left.

Answer 2

Find a common denominator between 1/4 and 1/9. The common denominator is 36. Multiply 1/4, 1 and 4, by 9. You get 9/36. Multiply 1/9, 1 and 9, by 4. You get 4/36. Add the two answers together. 
9/36 + 4/36 = 13/36
Now subtract 36 by 13 to get 23. You get 23/36. This is the most simplified form.
Ashley has 23/36 package of raisin left.