Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            7
 Simplify   —
            9

Equation at the end of step  1  :

   5         7      
  (— +  (1 • —)) +  3
   8         9      

Step  2  :

            5
 Simplify   —
            8

Equation at the end of step  2  :

   5    7     
  (— +  —) +  3
   8    9     

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       8 

      The right denominator is :       9 

      Least Common Multiple:
      72 

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 = 9

   Right_M = L.C.M / R_Deno = 8

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 • 9
   ——————————————————  =   —————
         L.C.M              72  

   R. Mult. • R. Num.      7 • 8
   ——————————————————  =   —————
         L.C.M              72  

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 • 9 + 7 • 8     101
 —————————————  =  ———
      72           72 

Equation at the end of step  3  :

  101    
  ——— +  3
  72     

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  72  as the denominator :

         3     3 • 72
    3 =  —  =  ——————
         1       72  

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

 101 + 3 • 72     317
 ————————————  =  ———
      72          72 

Final result :

  317           
  ——— = 4.40278 
  72