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Solution - Adding, subtracting and finding the least common multiple

56

Other Ways to Solve:

Step by Step Solution

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.12" was replaced by "(212/100)". 2 more similar replacement(s)

Step 1 :

            53
 Simplify   ——
            25

Equation at the end of step 1 :

   49        313 53
  (——•5)+(4•(———+——))
   7         100 25

Step 2 :

            313
 Simplify   ———
            100

Equation at the end of step 2 :

   49               313    53
  (—— • 5) +  (4 • (——— +  ——))
   7                100    25

Step 3 :

Calculating the Least Common Multiple :

3.1    Find the Least Common Multiple

      The left denominator is :       100

      The right denominator is :       25

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
5	2	2	2
Product of all Prime Factors	100	25	100

Least Common Multiple:
100

Calculating Multipliers :

3.2    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 = 1

   Right_M = L.C.M / R_Deno = 4

Making Equivalent Fractions :

3.3 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.      313
   ——————————————————  =   ———
         L.C.M             100

   R. Mult. • R. Num.      53 • 4
   ——————————————————  =   ——————
         L.C.M              100

Adding fractions that have a common denominator :

3.4 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:

 313 + 53 • 4     21
 ————————————  =  ——
     100          4

Equation at the end of step 3 :

   49              21
  (—— • 5) +  (4 • ——)
   7               4

Step 4 :

            7
 Simplify   —
            1

Equation at the end of step 4 :

  (7 • 5) +  21