Addition and Subtraction of Fractions

Addition of like fractions
Steps to add like fractions:
Step 1: Add the numerators of the fractions to get the numerator of the resultant fraction.
Step 2: Use the common denominator of the like fractions as the denominator of the resultant fraction.

e.g. Find the sum of  1 7 , 2 7 and 3 7

Sol: 1 7 + 2 7 + 3 7 = 1 + 2 + 3 7 = 6 7
                             
Subtraction of like fractions
Steps to subtract two like fractions:
Step 1: Subtract the numerators of the fractions to get the numerator of the resultant fraction.
Step 2: Use the common denominator of the like fractions as the denominator of the resultant fraction.

e.g. Find the difference between 3 7 and 1 7 .
Sol: 3 7 1 7 = 3 - 1 7 = 2 7
                      
Addition of unlike fractions
Steps to add unlike fractions:
Step 1: Find the equivalent fractions of the given unlike fractions with the same denominator.
Step 2: Add the numerators of the fractions to get the numerator of the resultant fraction.
Step 3: Use the common denominator of the obtained like fractions as the denominator of the resultant fraction.
e.g. Find the sum of 5 18 and 4 15 .
Sol: LCM of 18 and 15 = 90.

       18  = 5 x 5 18 x 5 = 25  90

       415  = 4 x 6 15 x 6 = 24  90
                                                        
        18  + 15 = 25  90 + 24  90
                      

                     = 25 + 24  90

                      = 49 90
          
Subtraction of unlike fractions
Steps to subtract two unlike fractions:
Step 1: Find the equivalent fractions of the given unlike fractions with the same denominator.
Step 2: Subtract the numerators of the fractions to get the numerator of the resultant fraction.
Step 3: Use the common denominator of the obtained like fractions as the denominator of the resultant fraction.
     e.g. Find the difference between 5 18 and 4 15 .

Sol: LCM of 18 and 15 = 90.

       18  = 5 x 5 18 x 5 = 25  90

       415  = 4 x 6 15 x 6 = 24  90
                                                        
       18  15 = 25  90 24  90
                      
                    = 25 - 24  90

                    = 1 90

Addition or subtraction of mixed fractions
Two mixed fractions can be added or subtracted by adding or subtracting the whole numbers of the two fractions, and then adding or subtracting the fractional parts together. Two mixed fractions can also be converted into improper fractions and then added or subtracted.

Summary

Addition of like fractions
Steps to add like fractions:
Step 1: Add the numerators of the fractions to get the numerator of the resultant fraction.
Step 2: Use the common denominator of the like fractions as the denominator of the resultant fraction.

e.g. Find the sum of  1 7 , 2 7 and 3 7

Sol: 1 7 + 2 7 + 3 7 = 1 + 2 + 3 7 = 6 7
                             
Subtraction of like fractions
Steps to subtract two like fractions:
Step 1: Subtract the numerators of the fractions to get the numerator of the resultant fraction.
Step 2: Use the common denominator of the like fractions as the denominator of the resultant fraction.

e.g. Find the difference between 3 7 and 1 7 .
Sol: 3 7 1 7 = 3 - 1 7 = 2 7
                      
Addition of unlike fractions
Steps to add unlike fractions:
Step 1: Find the equivalent fractions of the given unlike fractions with the same denominator.
Step 2: Add the numerators of the fractions to get the numerator of the resultant fraction.
Step 3: Use the common denominator of the obtained like fractions as the denominator of the resultant fraction.
e.g. Find the sum of 5 18 and 4 15 .
Sol: LCM of 18 and 15 = 90.

       18  = 5 x 5 18 x 5 = 25  90

       415  = 4 x 6 15 x 6 = 24  90
                                                        
        18  + 15 = 25  90 + 24  90
                      

                     = 25 + 24  90

                      = 49 90
          
Subtraction of unlike fractions
Steps to subtract two unlike fractions:
Step 1: Find the equivalent fractions of the given unlike fractions with the same denominator.
Step 2: Subtract the numerators of the fractions to get the numerator of the resultant fraction.
Step 3: Use the common denominator of the obtained like fractions as the denominator of the resultant fraction.
     e.g. Find the difference between 5 18 and 4 15 .

Sol: LCM of 18 and 15 = 90.

       18  = 5 x 5 18 x 5 = 25  90

       415  = 4 x 6 15 x 6 = 24  90
                                                        
       18  15 = 25  90 24  90
                      
                    = 25 - 24  90

                    = 1 90

Addition or subtraction of mixed fractions
Two mixed fractions can be added or subtracted by adding or subtracting the whole numbers of the two fractions, and then adding or subtracting the fractional parts together. Two mixed fractions can also be converted into improper fractions and then added or subtracted.

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