Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             3
 Simplify   ——
            25

Equation at the end of step  1  :

   1    3      3
  (— +  —) +  ——
   3    5     25

Step  2  :

            3
 Simplify   —
            5

Equation at the end of step  2  :

   1    3      3
  (— +  —) +  ——
   3    5     25

Step  3  :

            1
 Simplify   —
            3

Equation at the end of step  3  :

   1    3      3
  (— +  —) +  ——
   3    5     25

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       3 

      The right denominator is :       5 

      Least Common Multiple:
      15 

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 = 5

   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.       5
   ——————————————————  =   ——
         L.C.M             15

   R. Mult. • R. Num.      3 • 3
   ——————————————————  =   —————
         L.C.M              15  

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 • 3     14
 —————————  =  ——
    15         15

Equation at the end of step  4  :

  14     3
  —— +  ——
  15    25

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       15 

      The right denominator is :       25 

      Least Common Multiple:
      75 

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 = 3

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      14 • 5
   ——————————————————  =   ——————
         L.C.M               75  

   R. Mult. • R. Num.      3 • 3
   ——————————————————  =   —————
         L.C.M              75  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 14 • 5 + 3 • 3     79
 ——————————————  =  ——
       75           75

Final result :

  79           
  —— = 1.05333 
  75