Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.5" was replaced by "(45/10)". 4 more similar replacement(s)

Step  1  :

            9
 Simplify   —
            2

Equation at the end of step  1  :

     45     7  93  9
  (((——+5)+——)+——)+—
     10    10  10  2

Step  2  :

            93
 Simplify   ——
            10

Equation at the end of step  2  :

     45     7  93  9
  (((——+5)+——)+——)+—
     10    10  10  2

Step  3  :

             7
 Simplify   ——
            10

Equation at the end of step  3  :

     45           7     93     9
  (((—— +  5) +  ——) +  ——) +  —
     10          10     10     2

Step  4  :

            9
 Simplify   —
            2

Equation at the end of step  4  :

     9           7     93     9
  (((— +  5) +  ——) +  ——) +  —
     2          10     10     2

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  2  as the denominator :

         5     5 • 2
    5 =  —  =  —————
         1       2  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 5.2       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:

 9 + 5 • 2     19
 —————————  =  ——
     2         2 

Equation at the end of step  5  :

    19     7     93     9
  ((—— +  ——) +  ——) +  —
    2     10     10     2

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       10 

      Least Common Multiple:
      10 

Calculating Multipliers :

 6.2    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 = 1

Making Equivalent Fractions :

 6.3      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.      19 • 5
   ——————————————————  =   ——————
         L.C.M               10  

   R. Mult. • R. Num.       7
   ——————————————————  =   ——
         L.C.M             10

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 19 • 5 + 7     51
 ——————————  =  ——
     10         5 

Equation at the end of step  6  :

   51    93     9
  (—— +  ——) +  —
   5     10     2

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       10 

      Least Common Multiple:
      10 

Calculating Multipliers :

 7.2    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 :

 7.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      51 • 2
   ——————————————————  =   ——————
         L.C.M               10  

   R. Mult. • R. Num.      93
   ——————————————————  =   ——
         L.C.M             10

Adding fractions that have a common denominator :

 7.4       Adding up the two equivalent fractions

 51 • 2 + 93     39
 ———————————  =  ——
     10          2 

Equation at the end of step  7  :

  39    9
  —— +  —
  2     2

Step  8  :

Adding fractions which have a common denominator :

 8.1       Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 39 + 9     24
 ——————  =  ——
   2        1 

Final result :

  24