Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            7
 Simplify   —
            5

Equation at the end of step  1  :

   5    7     
  (— +  —) -  3
   2    5     

Step  2  :

            5
 Simplify   —
            2

Equation at the end of step  2  :

   5    7     
  (— +  —) -  3
   2    5     

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       5 

      Least Common Multiple:
      10 

Calculating Multipliers :

 3.2    Calculate multipliers for the two fractions


    Denote the Least Common Multiple by  L.C.M 
    Denote the Left Multiplier by  Left_M 
    Denote the Right Multiplier by  Right_M 
    Denote the Left Deniminator by  L_Deno 
    Denote the Right Multiplier by  R_Deno 

   Left_M = L.C.M / L_Deno = 5

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 3.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)²   and  (y²+y)/(y+1)³  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

   L. Mult. • L. Num.      5 • 5
   ——————————————————  =   —————
         L.C.M              10  

   R. Mult. • R. Num.      7 • 2
   ——————————————————  =   —————
         L.C.M              10  

Adding fractions that have a common denominator :

 3.4       Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 5 • 5 + 7 • 2     39
 —————————————  =  ——
      10           10

Equation at the end of step  3  :

  39    
  —— -  3
  10    

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  10  as the denominator :

         3     3 • 10
    3 =  —  =  ——————
         1       10  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 39 - (3 • 10)      9
 —————————————  =  ——
      10           10

Final result :

   9           
  —— = 0.90000 
  10