Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            1
 Simplify   —
            5

Equation at the end of step  1  :

   1    1     1
  (— -  —) -  —
   3    4     5

Step  2  :

            1
 Simplify   —
            4

Equation at the end of step  2  :

   1    1     1
  (— -  —) -  —
   3    4     5

Step  3  :

            1
 Simplify   —
            3

Equation at the end of step  3  :

   1    1     1
  (— -  —) -  —
   3    4     5

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       3 

      The right denominator is :       4 

      Least Common Multiple:
      12 

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 = 4

   Right_M = L.C.M / R_Deno = 3

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.       4
   ——————————————————  =   ——
         L.C.M             12

   R. Mult. • R. Num.       3
   ——————————————————  =   ——
         L.C.M             12

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:

 4 - (3)      1
 ———————  =  ——
   12        12

Equation at the end of step  4  :

   1    1
  —— -  —
  12    5

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       12 

      The right denominator is :       5 

      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 = 5

   Right_M = L.C.M / R_Deno = 12

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

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

   R. Mult. • R. Num.      12
   ——————————————————  =   ——
         L.C.M             60

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 5 - (12)     -7
 ————————  =  ——
    60        60

Final result :

  -7            
  —— = -0.11667 
  60