Fractions
 
Decimals
 
Take offs
 
Offsets
 
Rolling Offsets
 
 
 
 
 
 

 

Adding Fractions

 

 

 

 

 

 

 

 

 

 

 

 

 
           All fractions consist of two numbers. The top number is called the numerator. The bottom number
 is called the denominator..  		  1   (numerator)
  2   (denominator) or 1/2
 
          Adding Fractions With the Same Denominator.  If all the fractions you are adding have the same (common) denominator you will just need to add the top numbers (numerators)..
 

Example #1
 1   +  3  +  5  =  9    (numerator) 
16     16    16     16   (denominator)
9/16 is the lowest denominator. No reduction is necessary.

Example #2  Reducing the fraction to the  lowest denominator
 1   +  3   =   4     (numerator) 
 8       8         8     (denominator)
Reduce to lowest denominator.
  To find the lowest denominator divide both the numerator and denominator by the largest possible number with no remainder. In this example the numerator and denominator is divided by 4.

An improper fraction has a numerator equal to or greater than the denominator.

Example #3  Convert between an improper fraction and a mixed number.
 3   +  6   =   9     (numerator) 
 8       8         8     (denominator)
Convert improper fraction to a mixed number.
9/8 = 1 1/8   To convert the improper fraction divide the numerator by the denominator.  In this example divide 9 (numerator) by 8  (denominator) equals 1 with a remainder of 1 or 1 1/8

 
 
Adding Fractions With Different Denominators.   You will need to find a common denominator  when adding fractions with different denominators.

Example #1 Finding a common denominator.
 3   +  7   =    9     (numerator) 
18      16       16    (denominator)
To find the common denominator multiply the denominators together . This will give you the greatest common factor (GCF) ( ). Divide the GCF by one of the original denominators (). Multiply the answer (16) by the numerator (3).  This will give you the new numerator (). Divide the GCF by the next denominators (). Multiply the answer (18) by the numerator (7).  This will give you the new numerator ().

  and   Now add the new numerators (48 + 126 = 174.).   Reduce  to the  lowest denominator