Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             3
 Simplify   ——
            10

Equation at the end of step  1  :

   3    2       5   3
  (—•(0-—))+((0-—)•——)
   5    7       7  10

Step  2  :

            5
 Simplify   —
            7

Equation at the end of step  2  :

   3    2       5   3
  (—•(0-—))+((0-—)•——)
   5    7       7  10

Step  3  :

            2
 Simplify   —
            7

Equation at the end of step  3  :

   3         2      -3
  (— • (0 -  —)) +  ——
   5         7      14

Step  4  :

            3
 Simplify   —
            5

Equation at the end of step  4  :

   3   -2     -3
  (— • ——) +  ——
   5   7      14

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       35 

      The right denominator is :       14 

      Least Common Multiple:
      70 

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 = 5

Making Equivalent Fractions :

 5.3      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.      -6 • 2
   ——————————————————  =   ——————
         L.C.M               70  

   R. Mult. • R. Num.      -3 • 5
   ——————————————————  =   ——————
         L.C.M               70  

Adding fractions that have a common denominator :

 5.4       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:

 -6 • 2 + -3 • 5     -27
 ———————————————  =  ———
       70            70 

Final result :

  -27            
  ——— = -0.38571 
  70