Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             9
 Simplify   ——
            16

Equation at the end of step  1  :

       5       1      9
  (10+——)-(((5+—)+2)+——)
      16       4     16

Step  2  :

            1
 Simplify   —
            4

Equation at the end of step  2  :

       5       1      9
  (10+——)-(((5+—)+2)+——)
      16       4     16

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  4  as the denominator :

          5     5 • 4
     5 =  —  =  —————
          1       4  

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       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:

 5 • 4 + 1     21
 —————————  =  ——
     4         4 

Equation at the end of step  3  :

          5       21           9
  (10 +  ——) -  ((—— +  2) +  ——)
         16       4           16

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  4  as the denominator :

         2     2 • 4
    2 =  —  =  —————
         1       4  

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 21 + 2 • 4     29
 ——————————  =  ——
     4          4 

Equation at the end of step  4  :

          5      29     9
  (10 +  ——) -  (—— +  ——)
         16      4     16

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       16 

      Least Common Multiple:
      16 

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 = 4

   Right_M = L.C.M / R_Deno = 1

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.      29 • 4
   ——————————————————  =   ——————
         L.C.M               16  

   R. Mult. • R. Num.       9
   ——————————————————  =   ——
         L.C.M             16

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 29 • 4 + 9     125
 ——————————  =  ———
     16         16 

Equation at the end of step  5  :

          5     125
  (10 +  ——) -  ———
         16     16 

Step  6  :

             5
 Simplify   ——
            16

Equation at the end of step  6  :

          5     125
  (10 +  ——) -  ———
         16     16 

Step  7  :

Rewriting the whole as an Equivalent Fraction :

 7.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  16  as the denominator :

           10     10 • 16
     10 =  ——  =  ———————
           1        16   

Adding fractions that have a common denominator :

 7.2       Adding up the two equivalent fractions

 10 • 16 + 5     165
 ———————————  =  ———
     16          16 

Equation at the end of step  7  :

  165    125
  ——— -  ———
  16     16 

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:

 165 - (125)     5
 ———————————  =  —
     16          2

Final result :

  5           
  — = 2.50000 
  2