21w - 379
 ——————
  21 Â
Step-by-step explanation:
Step  1  :
      52
Simplify  ——
      3
Equation at the end of step  1  :
    5   52
 (w -  —) -  ——
    7   3
Step  2  :
      5
Simplify  —
      7
Equation at the end of step  2  :
    5   52
 (w -  —) -  ——
    7   3
Step  3  :
Rewriting the whole as an Equivalent Fraction :
3.1 Â Subtracting a fraction from a whole
Rewrite the whole as a fraction using  7  as the denominator :
     w   w • 7
  w =  —  =  —————
     1    7 Â
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 :
3.2 Â Â Â 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:
w • 7 - (5)   7w - 5
———————————  =  ——————
   7       7 Â
Equation at the end of step  3  :
 (7w - 5)   52
 ———————— -  ——
  7     3
Step  4  :
Calculating the Least Common Multiple :
4.1 Â Â Find the Least Common Multiple
   The left denominator is :    7
   The right denominator is :    3
    Number of times each prime factor
    appears in the factorization of:
Prime
Factor  Left
Denominator  Right
Denominator  L.C.M = Max
{Left,Right}
7101
3011
Product of all
Prime Factors  7321
   Least Common Multiple:
   21
Calculating Multipliers :
4.2 Â Â 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 = 3
 Right_M = L.C.M / R_Deno = 7
Making Equivalent Fractions :
4.3 Â Â Â 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.    (7w-5) • 3
 ——————————————————  =  ——————————
    L.C.M         21  Â
 R. Mult. • R. Num.    52 • 7
 ——————————————————  =  ——————
    L.C.M        21 Â
Adding fractions that have a common denominator :
4.4 Â Â Â Adding up the two equivalent fractions
(7w-5) • 3 - (52 • 7)   21w - 379
—————————————————————  =  —————————
     21          21  Â
Final result :
 21w - 379
 —————————
  21  Â
Processing ends successfully
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