Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            4
 Simplify   —
            7

Equation at the end of step  1  :

  5    1   4
  — -  — ÷ —
  8    4   7

Step  2  :

            1
 Simplify   —
            4

Equation at the end of step  2  :

  5    1   4
  — -  — ÷ —
  8    4   7

Step  3  :

         1      4
 Divide  —  by  —
         4      7

 3.1    Dividing fractions

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

1     4       1     7
—  ÷  —   =   —  •  —
4     7       4     4

Equation at the end of step  3  :

  5     7
  — -  ——
  8    16

Step  4  :

            5
 Simplify   —
            8

Equation at the end of step  4  :

  5     7
  — -  ——
  8    16

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       8 

      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 = 2

   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.      5 • 2
   ——————————————————  =   —————
         L.C.M              16  

   R. Mult. • R. Num.       7
   ——————————————————  =   ——
         L.C.M             16

Adding fractions that have a common denominator :

 5.4       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 • 2 - (7)      3
 ———————————  =  ——
     16          16

Final result :

   3           
  —— = 0.18750 
  16