Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            25
 Simplify   ——
            8 

Equation at the end of step  1  :

   3    17     25
  (— +  ——) +  ——
   5    10     8 

Step  2  :

            17
 Simplify   ——
            10

Equation at the end of step  2  :

   3    17     25
  (— +  ——) +  ——
   5    10     8 

Step  3  :

            3
 Simplify   —
            5

Equation at the end of step  3  :

   3    17     25
  (— +  ——) +  ——
   5    10     8 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       10 

      Least Common Multiple:
      10 

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 = 2

   Right_M = L.C.M / R_Deno = 1

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.      3 • 2
   ——————————————————  =   —————
         L.C.M              10  

   R. Mult. • R. Num.      17
   ——————————————————  =   ——
         L.C.M             10

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:

 3 • 2 + 17     23
 ——————————  =  ——
     10         10

Equation at the end of step  4  :

  23    25
  —— +  ——
  10    8 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       8 

      Least Common Multiple:
      40 

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 = 4

   Right_M = L.C.M / R_Deno = 5

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      23 • 4
   ——————————————————  =   ——————
         L.C.M               40  

   R. Mult. • R. Num.      25 • 5
   ——————————————————  =   ——————
         L.C.M               40  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 23 • 4 + 25 • 5     217
 ———————————————  =  ———
       40            40 

Final result :

  217           
  ——— = 5.42500 
  40