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ACT: Math Question #9

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Question:
 If  x  and  y  are positive numbers, 
x
4
 - 
3
y
 =   ? 


Choices:
A. -3 x - 4 y
B. 3 x 4 y
C. 3 x - 4 y 12 xy
D. xy - 3 4 y
E. xy - 12 4 y

 The correct answer is E. 
  
 To solve, you need a common denominator. The common 
 denominator is  4 y.
  
 To convert the first fraction, 
x
4
 , to a denominator of  4 y  , multiply 
 the top and bottom by  y  , like this: 
y
y
 × 
x
4
 = 
xy
4 y
  
 To give the second fraction a denominator of  4 y  , multiply its top 
 and bottom by 4, like this: 
4
4
 × 
3
y
 = 
12
4 y
  
 Since the denominators are now the same, you can now 
 subtract: 
xy
4 y
 - 
12
4 y
 = 
xy  -  12
4 y


 

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