Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.2" was replaced by "(2/10)". 2 more similar replacement(s)

Step  1  :

            1
 Simplify   —
            5

Equation at the end of step  1  :

         8   287  1
  ((52)+—— ÷ ———)-—
        43   100  5

Step  2  :

            287
 Simplify   ———
            100

Equation at the end of step  2  :

            8   287    1
  ((52) +  —— ÷ ———) - —
           43   100    5

Step  3  :

             8
 Simplify   ——
            43

Equation at the end of step  3  :

            8   287     1
  ((52) +  —— ÷ ———) -  —
           43   100     5

Step  4  :

          8      287
 Divide  ——  by  ———
         43      100

 4.1    Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

 8     287        8     100
——  ÷  ———   =   ——  •  ———
43     100       43     287

Equation at the end of step  4  :

            800      1
  ((52) +  —————) -  —
           12341     5

Step  5  :

Equation at the end of step  5  :

          800      1
  (52 +  —————) -  —
         12341     5

Step  6  :

Rewriting the whole as an Equivalent Fraction :

 6.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  12341  as the denominator :

           52     52 • 12341
     52 =  ——  =  ——————————
           1        12341   

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 :

 6.2       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:

 52 • 12341 + 800     309325
 ————————————————  =  ——————
      12341           12341 

Equation at the end of step  6  :

  309325    1
  —————— -  —
  12341     5

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       12341 

      The right denominator is :       5 

      Least Common Multiple:
      61705 

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 = 5

   Right_M = L.C.M / R_Deno = 12341

Making Equivalent Fractions :

 7.3      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.      309325 • 5
   ——————————————————  =   ——————————
         L.C.M               61705   

   R. Mult. • R. Num.      12341
   ——————————————————  =   —————
         L.C.M             61705

Adding fractions that have a common denominator :

 7.4       Adding up the two equivalent fractions

 309325 • 5 - (12341)     1534284
 ————————————————————  =  ———————
        61705              61705 

Final result :

  1534284            
  ——————— = 24.86482 
   61705