What big equation equals -3.8

 4-2*6+189/2-37*5+102.3

Step-by-step explanation:

Step by step solution :

Step  1  :

           1023

Simplify   ————

            10  

Equation at the end of step  1  :

         189             1023

 ((-8 +  ———) -  185) +  ————

          2               10  

Step  2  :

           189

Simplify   ———

            2  

Equation at the end of step  2  :

         189             1023

 ((-8 +  ———) -  185) +  ————

          2               10  

Step  3  :

Rewriting the whole as an Equivalent Fraction :

3.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  2  as the denominator :

          -8     -8 • 2

    -8 =  ——  =  ——————

          1        2    

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2       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:

-8 • 2 + 189     173

————————————  =  ———

     2            2  

Equation at the end of step  3  :

  173            1023

 (——— -  185) +  ————

   2              10  

Step  4  :

Rewriting the whole as an Equivalent Fraction :

4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  2  as the denominator :

          185     185 • 2

   185 =  ———  =  ———————

           1         2    

Adding fractions that have a common denominator :

4.2       Adding up the two equivalent fractions

173 - (185 • 2)     -197

———————————————  =  ————

       2             2  

Equation at the end of step  4  :

 -197    1023

 ———— +  ————

  2       10  

Step  5  :

Calculating the Least Common Multiple :

5.1    Find the Least Common Multiple

     The left denominator is :       2  

     The right denominator is :       10  

       Number of times each prime factor

       appears in the factorization of:

Prime  

Factor   Left  

Denominator   Right  

Denominator   L.C.M = Max  

{Left,Right}  

2111

5011

Product of all  

Prime Factors  21010

     Least Common Multiple:

     10  

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 = 5

  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.      -197 • 5

  ——————————————————  =   ————————

        L.C.M                10    

  R. Mult. • R. Num.      1023

  ——————————————————  =   ————

        L.C.M              10  

Adding fractions that have a common denominator :

5.4       Adding up the two equivalent fractions

-197 • 5 + 1023     19

———————————————  =  ——

      10            5  

Final result :

 19            

 —— = 3.80000  

 5            

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