Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            1
 Simplify   —
            4

Equation at the end of step  1  :

       7      5   1
  ((0-——)+(0-——))-—
      10     12   4

Step  2  :

             5
 Simplify   ——
            12

Equation at the end of step  2  :

          7            5      1
  ((0 -  ——) +  (0 -  ——)) -  —
         10           12      4

Step  3  :

             7
 Simplify   ——
            10

Equation at the end of step  3  :

          7     -5     1
  ((0 -  ——) +  ——) -  —
         10     12     4

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       12 

      Least Common Multiple:
      60 

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 = 6

   Right_M = L.C.M / R_Deno = 5

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.      -7 • 6
   ——————————————————  =   ——————
         L.C.M               60  

   R. Mult. • R. Num.      -5 • 5
   ——————————————————  =   ——————
         L.C.M               60  

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:

 -7 • 6 + -5 • 5     -67
 ———————————————  =  ———
       60            60 

Equation at the end of step  4  :

  -67    1
  ——— -  —
  60     4

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       60 

      The right denominator is :       4 

      Least Common Multiple:
      60 

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 = 1

   Right_M = L.C.M / R_Deno = 15

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      -67
   ——————————————————  =   ———
         L.C.M             60 

   R. Mult. • R. Num.      15
   ——————————————————  =   ——
         L.C.M             60

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 -67 - (15)     -41
 ——————————  =  ———
     60         30 

Final result :

  -41            
  ——— = -1.36667 
  30