Adding, subtracting and finding the least common multiple

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

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(a-1)/6

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Adding, subtracting and finding the least common multiple

Step by Step Solution

Step 1 :

            1
 Simplify   —
            6

Equation at the end of step 1 :

       2      5     1
  ((0-(—•a))+(—•a))-—
       3      6     6

Step 2 :

            5
 Simplify   —
            6

Equation at the end of step 2 :

       2      5     1
  ((0-(—•a))+(—•a))-—
       3      6     6

Step 3 :

            2
 Simplify   —
            3

Equation at the end of step 3 :

          2          5a     1
  ((0 -  (— • a)) +  ——) -  —
          3          6      6

Step 4 :

Calculating the Least Common Multiple :

4.1    Find the Least Common Multiple

      The left denominator is :       3

      The right denominator is :       6

Number of times each prime factor
appears in the factorization of:
Prime Factor	Left Denominator	Right Denominator	L.C.M = Max {Left,Right}
3	1	1	1
2	0	1	1
Product of all Prime Factors	3	6	6

Least Common Multiple:
6

Calculating Multipliers :

4.2    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 :

4.3 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.      -2a • 2
   ——————————————————  =   ———————
         L.C.M                6   

   R. Mult. • R. Num.      5a
   ——————————————————  =   ——
         L.C.M             6

Adding fractions that have a common denominator :

4.4 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:

 -2a • 2 + 5a     a
 ————————————  =  —
      6           6

Equation at the end of step 4 :

  a    1
  — -  —
  6    6

Step 5 :

Adding fractions which have a common denominator :

5.1 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:

 a - (1)     a - 1
 ———————  =  —————
    6          6

Final result :

  a - 1
  —————
    6