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

(18m-5)/90

See steps

Adding, subtracting and finding the least common multiple

Step by Step Solution

Step 1 :

            1
 Simplify   —
            6

Equation at the end of step 1 :

  m    1
  — -  — ÷ 1 ÷ 3
  5    6

Step 2 :

         1      
 Divide  —  by  1
         6

Equation at the end of step 2 :

  m    1
  — -  — ÷ 3
  5    6

Step 3 :

         1      
 Divide  —  by  3
         6

Equation at the end of step 3 :

  m     1
  — -  ——
  5    18

Step 4 :

            m
 Simplify   —
            5

Equation at the end of step 4 :

  m     1
  — -  ——
  5    18

Step 5 :

Calculating the Least Common Multiple :

5.1    Find the Least Common Multiple

      The left denominator is :       5

      The right denominator is :       18

Number of times each prime factor
appears in the factorization of:
Prime Factor	Left Denominator	Right Denominator	L.C.M = Max {Left,Right}
5	1	0	1
2	0	1	1
3	0	2	2
Product of all Prime Factors	5	18	90

Least Common Multiple:
90

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 = 18

   Right_M = L.C.M / R_Deno = 5

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.      m • 18
   ——————————————————  =   ——————
         L.C.M               90  

   R. Mult. • R. Num.       5
   ——————————————————  =   ——
         L.C.M             90

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:

 m • 18 - (5)     18m - 5
 ————————————  =  ———————
      90            90

Final result :

  18m - 5
  ———————
    90