Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             7
 Simplify   ——
            10

Equation at the end of step  1  :

   3        7
  —— ÷ 5 - ——
  44       10

Step  2  :

             3
 Simplify   ——
            44

Equation at the end of step  2  :

   3         7
  —— ÷ 5 -  ——
  44        10

Step  3  :

          3      
 Divide  ——  by  5
         44      

Equation at the end of step  3  :

   3      7
  ——— -  ——
  220    10

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       220 

      The right denominator is :       10 

      Least Common Multiple:
      220 

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 = 1

   Right_M = L.C.M / R_Deno = 22

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 
   ——————————————————  =   ———
         L.C.M             220

   R. Mult. • R. Num.      7 • 22
   ——————————————————  =   ——————
         L.C.M              220  

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 - (7 • 22)     -151
 ————————————  =  ————
     220          220 

Final result :

  -151            
  ———— = -0.68636 
  220