Adding, subtracting and finding the least common multiple

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This solution deals with adding, subtracting and finding the least common multiple.

Solution found

89/108=0.82407

See steps

Adding, subtracting and finding the least common multiple

Step by Step Solution

Step 1 :

            8
 Simplify   —
            9

Equation at the end of step 1 :

  3    8
  — +  — ÷ 4 ÷ 3
  4    9

Step 2 :

         8      
 Divide  —  by  4
         9

Equation at the end of step 2 :

  3    2
  — +  — ÷ 3
  4    9

Step 3 :

         2      
 Divide  —  by  3
         9

Equation at the end of step 3 :

  3     2
  — +  ——
  4    27

Step 4 :

            3
 Simplify   —
            4

Equation at the end of step 4 :

  3     2
  — +  ——
  4    27

Step 5 :

Calculating the Least Common Multiple :

5.1    Find the Least Common Multiple

      The left denominator is :       4

      The right denominator is :       27

Number of times each prime factor
appears in the factorization of:
Prime Factor	Left Denominator	Right Denominator	L.C.M = Max {Left,Right}
2	2	0	2
3	0	3	3
Product of all Prime Factors	4	27	108

Least Common Multiple:
108

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 = 27

   Right_M = L.C.M / R_Deno = 4

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.      3 • 27
   ——————————————————  =   ——————
         L.C.M              108  

   R. Mult. • R. Num.      2 • 4
   ——————————————————  =   —————
         L.C.M              108

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:

 3 • 27 + 2 • 4      89
 ——————————————  =  ———
      108           108

Final result :

   89           
  ——— = 0.82407 
  108