Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            27
 Simplify   ——
            10

Equation at the end of step  1  :

   7    35     27
  (— +  ——) +  ——
   3    18     10

Step  2  :

            35
 Simplify   ——
            18

Equation at the end of step  2  :

   7    35     27
  (— +  ——) +  ——
   3    18     10

Step  3  :

            7
 Simplify   —
            3

Equation at the end of step  3  :

   7    35     27
  (— +  ——) +  ——
   3    18     10

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       3 

      The right denominator is :       18 

      Least Common Multiple:
      18 

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 = 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.      7 • 6
   ——————————————————  =   —————
         L.C.M              18  

   R. Mult. • R. Num.      35
   ——————————————————  =   ——
         L.C.M             18

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 + 35     77
 ——————————  =  ——
     18         18

Equation at the end of step  4  :

  77    27
  —— +  ——
  18    10

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       18 

      The right denominator is :       10 

      Least Common Multiple:
      90 

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 = 9

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      77 • 5
   ——————————————————  =   ——————
         L.C.M               90  

   R. Mult. • R. Num.      27 • 9
   ——————————————————  =   ——————
         L.C.M               90  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 77 • 5 + 27 • 9     314
 ———————————————  =  ———
       90            45 

Final result :

  314           
  ——— = 6.97778 
  45