Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            1
 Simplify   —
            8

Equation at the end of step  1  :

           1      1     1
  ((17 +  ——) +  ——) +  —
          29     48     8

Step  2  :

             1
 Simplify   ——
            48

Equation at the end of step  2  :

           1      1     1
  ((17 +  ——) +  ——) +  —
          29     48     8

Step  3  :

             1
 Simplify   ——
            29

Equation at the end of step  3  :

           1      1     1
  ((17 +  ——) +  ——) +  —
          29     48     8

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  29  as the denominator :

           17     17 • 29
     17 =  ——  =  ———————
           1        29   

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 :

 4.2       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:

 17 • 29 + 1     494
 ———————————  =  ———
     29          29 

Equation at the end of step  4  :

   494     1     1
  (——— +  ——) +  —
   29     48     8

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       29 

      The right denominator is :       48 

      Least Common Multiple:
      1392 

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 = 48

   Right_M = L.C.M / R_Deno = 29

Making Equivalent Fractions :

 5.3      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.      494 • 48
   ——————————————————  =   ————————
         L.C.M               1392  

   R. Mult. • R. Num.       29 
   ——————————————————  =   ————
         L.C.M             1392

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 494 • 48 + 29     23741
 —————————————  =  —————
     1392          1392 

Equation at the end of step  5  :

  23741    1
  ————— +  —
  1392     8

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       1392 

      The right denominator is :       8 

      Least Common Multiple:
      1392 

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 = 1

   Right_M = L.C.M / R_Deno = 174

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      23741
   ——————————————————  =   —————
         L.C.M             1392 

   R. Mult. • R. Num.       174
   ——————————————————  =   ————
         L.C.M             1392

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 23741 + 174     23915
 ———————————  =  —————
    1392         1392 

Final result :

  23915            
  ————— = 17.18032 
  1392