Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            1
 Simplify   —
            2

Equation at the end of step  1  :

   5    1      1
  (—+(0-—))-(0-—)
   7    3      2

Step  2  :

            1
 Simplify   —
            3

Equation at the end of step  2  :

   5          1      -1
  (— +  (0 -  —)) -  ——
   7          3      2 

Step  3  :

            5
 Simplify   —
            7

Equation at the end of step  3  :

   5    -1     -1
  (— +  ——) -  ——
   7    3      2 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       7 

      The right denominator is :       3 

      Least Common Multiple:
      21 

Calculating Multipliers :

 4.2    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 = 3

   Right_M = L.C.M / R_Deno = 7

Making Equivalent Fractions :

 4.3      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 • 3
   ——————————————————  =   —————
         L.C.M              21  

   R. Mult. • R. Num.      -1 • 7
   ——————————————————  =   ——————
         L.C.M               21  

Adding fractions that have a common denominator :

 4.4       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 • 3 + -1 • 7      8
 ——————————————  =  ——
       21           21

Equation at the end of step  4  :

   8    -1
  —— -  ——
  21    2 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       21 

      The right denominator is :       2 

      Least Common Multiple:
      42 

Calculating Multipliers :

 5.2    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 = 2

   Right_M = L.C.M / R_Deno = 21

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      8 • 2
   ——————————————————  =   —————
         L.C.M              42  

   R. Mult. • R. Num.      -1 • 21
   ——————————————————  =   ———————
         L.C.M               42   

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 8 • 2 - (-1 • 21)     37
 —————————————————  =  ——
        42             42

Final result :

  37           
  —— = 0.88095 
  42