Working with Fractions, Step-by-Step

ADDING FRACTIONS

1.   WRITE THE NUMBERS VERTICALLY

Go to the NEXT step...  



2.   DO YOU HAVE A COMMON DENOMINATOR?
(same bottom number = same size pieces)
NO:   Continue below...
 
YES:   Skip to the NEXT STEP.

Change to equivalent fractions with a common denominator:
  • Find a number divisible by BOTH denominators (such as the LCM: Least Common Multiple).
  • Multiply both the numerator AND denominator of one fraction by the SAME NUMBER to get an equivalent fraction with the common denominator.
  • Repeat with the other fraction.

Go to the NEXT step...  



3.   DO the Addition:
  • Add the numerators   (to find the total number of pieces).  
    Keep the same denominator.

  • Add the whole numbers (if any).

Go to the NEXT step...  



4.   IS THE FRACTION IN LOWEST TERMS?
NO:   Continue below...
 
YES:   Skip to the NEXT STEP.

Improper fraction:   (Top number is greater than the bottom number.)
  • Divide the top BY the BOTTOM;
  • Write any remainder as the numerator of a fraction using the same denominator.

Reduce the fraction:
  • Divide both the numerator and the denominator by the same number.
  • Repeat until the only common factor is one.

Go to the NEXT step...  



5.   Check your answer.

 







SAMPLE PROBLEM #1:
  2/7 + 4/7 =  
 
Look at the set-up.

 
 
See the solution.





SAMPLE PROBLEM #2:
  2/3 + 1/4 =
 
Look at the set-up:   Step 1   Step 2

 
 
See the solution.







SAMPLE PROBLEM #3:
  5/6 + 3/4 =  
 
Look at the set-up:   Step 1   Step 2

 
 
See the solution.





SAMPLE PROBLEM #4:
  5 1/2 + 6 3/8 =
 
Look at the set-up:   Step 1   Step 2

 
 
See the solution.







SAMPLE PROBLEM #5:
  1 2/3 + 7 5/6 + 9 3/4 =
 
Look at the set-up:   Step 1   Step 2

 
 
See the solution.





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