PRACTICE ADDING FRACTIONS
(least common denominators)
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Suggestions for this self exam:
[A] Study text section 4.3 , but then keep your book closed during this entire test
[B] Enter your answers in the boxes provided. Check them when you've finished.
[C]
Remember the general rules: a
b
 =  ac
bc
  and also   a
d
 +  b
d
 =  a + b
d
[D] The LCD ("least common denominator": "d" in the paragraph above), is the smallest number which is a multiple of all denominators in a sum. Typically, we find the LCD by factoring all denominators into prime (unfactorable) expressions. The LCD then includes any prime expression as a factor, and includes it as many times as that denominator which contains it most abundantly.
 
Thus, for       13
12
+ 11
18
=   13  
(22)(3)
+   11  
(2)(32)
  , the LCD is (22)(32) = 36.
 
Hence: 13
12
+ 11
18
= (13)(3)
(12)(3)
+ (11)(2)
(18)(2)
= (13)(3)+ (11)(2)
36
= 61
36

[1] Enter the correct numerator and denominator of the reduced sum:
17
48
 +  13
40
 = 

 
   

[2] Enter the correct numerator and denominator of the reduced difference:
11
6
 -    3  
10
 = 

 
   

[3] Enter the correct numerator and denominator of the reduced difference:
11
6x
 -    3  
10y
 = 

  
   
   

[4] First determine the LCD for the fractions to be added below. Then, in the answer box, enter the numerator of the correct reduced sum:
  6 - x  
x2 - 25
 +     3   
x + 5
 = 

LCD
  
   
 
Review
Factoring
Formulas ?
   

[5] First determine the LCD for the fractions to be subtracted below. Then, in the answer box, enter the numerator of the correct reduced difference:
(x + 1)2

x3 - 1
 -  x + 1

x2 + x + 1
 = 

LCD
  
   
 
Review
Factoring
Formulas ?
   

[6] First determine the LCD for the fractions to be added and subtracted below. Then, in the answer box, enter the numerator of the correct reduced sum (right side):
x2 +5x + 6

x2 - 9
 -  2x - 3

x + 3
 +  x + 1

x - 3
 = 

LCD
  
   
 
Review
Factoring
Formulas ?
   

[7] First determine the LCD for the fractions to be added below. Then, in the answer box, enter the numerator of the correct reduced sum:
2x2 + 3x - 3

8x3 + 27
 +  2 - x2

4x3 - 6x2 + 9x
 = 

LCD
  
   
 
Review
Factoring
Formulas ?
   

[8] First determine the LCD for the fractions to be subtracted below. Then, in the answer box, enter the numerator of the correct reduced difference:
x + 1

x2 + ax - 3x - 3a
 -  x - 3

x2 + ax + x + a
 = 

LCD
  
   
 
Review Factoring Formulas ?

[9] First determine the LCD for the fractions to be added below. Then, in the answer box, enter the numerator of the correct reduced sum:
x + 3

x2 + 3x + 2
 +  1 - x

x2 - 4
 = 

LCD
  
   
 
Review
Factoring
Formulas ?
   

[10] First determine the LCD for the fractions to be subtracted below. Then, in the answer box, enter the numerator of the correct reduced difference:
x + 1

x2 - x - 6
 -  x - 6

x2 - 8x + 15
 = 

LCD
  
   
 
Review
Factoring
Formulas ?
   

[11] First determine the LCD for the fractions to be added below. Then, in the answer box, enter the numerator of the correct reduced sum:
6 - x2

x4 - 16
 +  1

x2 + 4
 = 

LCD
  
   
 
Review
Factoring
Formulas ?
   
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This page last updated
31 May 2001