ADD FRACTIONS,  SUBTRACT FRACTIONS
PROBLEMS
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11.  Calculate the following.
       
      				|   11.  a)   | 
      				 3 sevenths + 2 sevenths = 5 sevenths | 
      				
      				  | 
      				b)   | 
						3 7 | 
						 +  | 
						2 7 | 
						 =  | 
           			5 7 | 
      				
           
           
           
           
           		
						|   11. c)   | 
           			3 7 | 
           			 −  | 
           			2 7 | 
           			 =  | 
			1 7 | 
           			  | 
      		d)   | 
           15 16 | 
            −  | 
            5  16 | 
            =  | 
		   10 16 | 
            =  | 
		   5 8 | 
           
        
       
       
      		|   11.  e)   | 
           3 5 | 
            +  | 
           1 5 | 
            +  | 
           4 5 | 
            =  | 
           1 | 
		   3 5 | 
             | 
           
           
      		  f)   | 
           2 4 | 
            +  | 
           1 4 | 
            +  | 
           3 4 | 
            = 1½ | 
           
             | 
      		  g)   | 
           10 15 | 
            +  | 
            8  15 | 
             | 
            4  15 | 
            =  | 
		   14 15 | 
        
        
12.  Choose the LCM of denominators to calculate the following.
       
       
      		|   12.   a)   | 
           2 3 | 
            +  | 
           1 6 | 
            =  | 
		   5 6 | 
             | 
      		b)   | 
      		 5  12 | 
            +  | 
           1 4 | 
            =  | 
		   2 3 | 
           
			  | 
      		c)   | 
           1 2 | 
            +  | 
            5  32 | 
            =  | 
		   21 32 | 
        
        
        
       
       
      		|   12.   d)   | 
           3 5 | 
             | 
            2  15 | 
            =  | 
		    7  15 | 
             | 
           
      		e)   | 
      		3 8 | 
             | 
            7  32 | 
           
           =  | 
		    5  32 | 
             | 
      		f)   | 
           15 16 | 
             | 
           3 4 | 
          =  | 
		    3  16 |            
        
        
13.  Choose the LCM of denominators to calculate the following.
       
       
      		|   13.   a)   | 
           5 6 | 
            +  | 
           5 9 | 
            = 1 | 
		    7  18 | 
             | 
           
      		b)   | 
      		3 4 | 
            +  | 
           5 6 | 
            = 1 | 
		    7  12 | 
             |            
      		c)   | 
           5 6 | 
            +  | 
           3 8 | 
           
             = 1 | 
		    5  24 |           
        
        
        
       
       
      		|   13.   d)   | 
           11 15 | 
             | 
            7  10 | 
            =  | 
		    1  30 | 
           
             | 
      		e)   | 
      		7 8 | 
             | 
            5  12 | 
            =  | 
		   11 24 | 
             | 
      		f)   | 
           8 9 | 
             | 
            5  12 | 
            =  | 
		   17 36 | 
        
        
14.  Calculate the following.
       
       
      		|   14.   a)   | 
           1 2 | 
            +  | 
           1 3 | 
            =  | 
		   5 6 | 
             | 
      		b)   | 
      		3 8 | 
            +  | 
           2 5 | 
            =  | 
		   31 40 | 
             | 
      		c)   | 
           7 9 | 
            +  | 
            7  10 | 
            = = 1 | 
		   43 90 | 
        
        
       
       
      		|   14.   d)   | 
           2 7 | 
             | 
           1 5 | 
            =  | 
		    3  35 | 
           
             | 
      		e)   | 
      		3 4 | 
             | 
           2 3 | 
             =  | 
		    1  12 | 
           
             |           
      		f)   | 
           7 8 | 
             | 
           5 9 | 
            =  | 
		   23 72 | 
        
        
15.   Add.
       
       
      		|   15.   a)   | 
           1 2 | 
            +  | 
           1 3 | 
            +  | 
           1 4 | 
            = 1 | 
		    1  12 | 
             | 
           
      		  b)   | 
           1 2 | 
            +  | 
           3 4 | 
            +  | 
           4 5 | 
          = 2 | 
		    1  20 | 
             | 
           
      		  c)   | 
           1 2 | 
            +  | 
           5 6 | 
             | 
           3 4 | 
            =  | 
		    7  12 | 
        
        
 16.  Mental calculation.
       
       
      		|   16.   a)   | 
           1 2 | 
            +  | 
           1 4 | 
            =  | 
		   3 4 | 
             | 
      		b)   | 
      		1 2 | 
            +  | 
           1 8 | 
          =  | 
		   5 8 | 
             |            
      		c)   | 
           1 2 | 
            +  | 
            2  10 | 
            =  | 
		    7  10 | 
        
        
       
       
      		|   16.   d)   | 
           1 2 | 
            +  | 
           3 4 | 
            = 1¼ | 
             | 
           
           
      		e)   | 
      		1 2 | 
            +  | 
            1  16 | 
            =  | 
		    9  16 | 
             | 
      		f)   | 
           1 2 | 
            +  | 
            5  12 | 
            =  | 
		   11 12 | 
        
        
 17.  Mental calculation.
       
       
      		|   17.   a)   | 
           1 2 | 
            +  | 
           1 4 | 
            +  | 
           1 8 | 
            =  | 
		   7 8 | 
             | 
           
           
      		  b)   | 
           1 2 | 
            +  | 
           3 8 | 
            +  | 
            5  16 | 
            = 1
		    |  3  16 | 
              | 
      		  c)   | 
           1 4 | 
            +  | 
           5 8 | 
            +  | 
            3  16 | 
            = 1
		    |  1  16 | 
        
        
                
  18.  What number must you add to each of the following to make 1?
  
         
  
             
   
           
       
       19.   Three candidates were running for office.  One of them got half the
10.   vote.  Another got two fifths of the vote.  What fraction did the
       
       
	   
	    	
	   		| third candidate get?    | 
	       		 1  10 | 
	       		. | 
	          
	   
 
       
10.   Add these mixed numbers.
       
       
      		|   18.   a)  3 | 
           1 5 | 
            + 4 | 
           2 5 | 
            = 7
		    | 3 5 | 
		  | 
          
      		  10.  
      		b)  8 | 
           2 9 | 
            + 7 | 
           3 9 | 
           
            = 15
		    | 5 9 | 
		  |            
      		  10.  
      		c)  3 | 
           2 4 | 
            + 4 | 
           3 4 | 
           
              = 8
		    | 1 4 |          
        
        
       
       
      		|   18.   d)  6 | 
           5 8 | 
            + 2 | 
           7 8 | 
            = 9½ | 
             | 
      		e)  4 | 
           5 6 | 
            + 3 | 
           5 6 | 
            = 8
		    | 2 3 | 
             | 
           
      		f)  1 | 
           2 3 | 
            + 8 | 
           1 3 | 
            =  | 
           10 | 
        
        
11.  Add.
       
       
      		|   19.   a)  3 | 
           1 4 | 
            + 2 | 
           5 8 | 
            = 5
		    | 7 8 | 
             | 
      		b)  2 | 
           5 6 | 
            + 7 | 
            5  18 | 
            = 10
		    | 1 9 | 
             | 
      		c)  7 | 
           3 4 | 
            + 1 | 
            5  16 | 
            = 9
		    |  1  16 |            
        
        
       
       
      		|   11.   d)  6 | 
           4 5 | 
            + 9 | 
           1 2 | 
            = 16
		    |  3  10 | 
             | 
      		e)  4 | 
           3 4 | 
            + 1 | 
           5 6 | 
          = 6
		    |  7  12 | 
             |            
      		f)  3 | 
           2 9 | 
            + 2 | 
           5 6 | 
           = 6
		    |  1  18 |           
        
        
12.   Subtract.
       
       
      		| 10.     a)  5 | 
           3 4 | 
            2 | 
           1 4 | 
            =  | 
           3½ | 
           
      		  | 
      		b)  4 | 
           4 5 | 
            1 | 
           1 5 | 
            = 3
		    | 3 5 | 
             | 
      		c)  3 | 
           5 8 | 
            3 | 
           3 8 | 
            =  | 
		   1 4 | 
        
        
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