Simplify using disterbutive property of mutiplication
(3/8 × -4/5) + (7/9 × 3/8) - (3/8 × -8/10)

me fast

 7            

 —— = 0.29167  

 24          

Step-by-step explanation:

Step  1  :

           -4

Simplify   ——

           5

Equation at the end of step  1  :

   3 -4   7 3    3 -4

 ((—•——)+(—•—))-(—•——)

   8 5    9 8    8 5

Step  2  :

           3

Simplify   —

           8

Equation at the end of step  2  :

   3 -4   7 3    3 -4

 ((—•——)+(—•—))-(—•——)

   8 5    9 8    8 5  

Step  3  :

           3

Simplify   —

           8

Equation at the end of step  3  :

   3 -4   7 3   -3

 ((—•——)+(—•—))-——

   8 5    9 8   10

Step  4  :

           7

Simplify   —

           9

Equation at the end of step  4  :

   3 -4   7 3   -3

 ((—•——)+(—•—))-——

   8 5    9 8   10

Step  5  :

           -4

Simplify   ——

           5  

Equation at the end of step  5  :

   3   -4      7     -3

 ((— • ——) +  ——) -  ——

   8   5      24     10

Step  6  :

           3

Simplify   —

           8

Equation at the end of step  6  :

   3   -4      7     -3

 ((— • ——) +  ——) -  ——

   8   5      24     10

Step  7  :

Calculating the Least Common Multiple :

7.1    Find the Least Common Multiple

     The left denominator is :       10  

     The right denominator is :       24  

       Number of times each prime factor

       appears in the factorization of:

Prime  

Factor   Left  

Denominator   Right  

Denominator   L.C.M = Max  

{Left,Right}  

2133

5101

3011

Product of all  

Prime Factors  1024120

     Least Common Multiple:

     120  

Calculating Multipliers :

7.2    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 = 12

  Right_M = L.C.M / R_Deno = 5

Making Equivalent Fractions :

7.3      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 • 12

  ——————————————————  =   ———————

        L.C.M               120  

  R. Mult. • R. Num.      7 • 5

  ——————————————————  =   —————

        L.C.M              120  

Adding fractions that have a common denominator :

7.4       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 • 12 + 7 • 5      -1

———————————————  =  ———

      120           120

Equation at the end of step  7  :

  -1    -3

 ——— -  ——

 120    10

Step  8  :

Calculating the Least Common Multiple :

8.1    Find the Least Common Multiple

     The left denominator is :       120  

     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}  

2313

3101

5111

Product of all  

Prime Factors  12010120

     Least Common Multiple:

     120  

Calculating Multipliers :

8.2    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 = 12

Making Equivalent Fractions :

8.3      Rewrite the two fractions into equivalent fractions

  L. Mult. • L. Num.       -1

  ——————————————————  =   ———

        L.C.M             120

  R. Mult. • R. Num.      -3 • 12

  ——————————————————  =   ———————

        L.C.M               120  

Adding fractions that have a common denominator :

8.4       Adding up the two equivalent fractions

-1 - (-3 • 12)      7

——————————————  =  ——

     120           24