Question

simplify 2/3 - 5/6 + 5/12

Answer 1

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "/-5" was replaced by "/(-5)".

Step by step solution :

Step  1  :

           5

Simplify   —

           6

Equation at the end of step  1  :

 2    5

 — +  — ÷ -5 ÷ 12

 3    6

Step  2  :

        5      

Divide  —  by  -5

        6      

Equation at the end of step  2  :

 2    -1

 — +  —— ÷ 12

 3    6

Step  3  :

        -1      

Divide  ——  by  12

        6      

Equation at the end of step  3  :

 2    -1

 — +  ——

 3    72

Step  4  :

           2

Simplify   —

           3

Equation at the end of step  4  :

 2    -1

 — +  ——

 3    72

Step  5  :

Calculating the Least Common Multiple :

5.1    Find the Least Common Multiple

     The left denominator is :       3

     The right denominator is :       72

       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 2 2

2 0 3 3

Product of all

Prime Factors  3 72 72

     Least Common Multiple:

     72

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 = 24

  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.      2 • 24

  ——————————————————  =   ——————

        L.C.M               72  

  R. Mult. • R. Num.      -1

  ——————————————————  =   ——

        L.C.M             72

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:

2 • 24 + -1     47

———————————  =  ——

    72          72

Final result :

 47          

 —— = 0.65278

 72          

Answer 2

Answer:

After simplication value of the given term is $\frac{1}{4}$

Step-by-step explanation:

Given,

$\frac{2}{3} - \frac{5}{6} + \frac{5}{12}$

This is a problem of fraction chapter of Algebra.

By fraction's addition and subtraction we can solve this problem easily.

$\frac{2}{3} - \frac{5}{6} \\ = \frac{2 \times 2 - 5}{6} \\ = \frac{4 - 5}{6} \\ = - \frac{1}{6}$

And

$\frac{2}{3} - \frac{5}{6} + \frac{5}{12} \\ = - \frac{1}{6} + \frac{5}{12} \\ = \frac{ - 2 + 5}{12} \\ = \frac{3}{12} \\ = \frac{1}{4}$

Required value after simplication is $\frac{1}{4}$

This is a problem of Algebra.

Some important formulas of Algebra,

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

${a}^{2} - {b}^{2} = (a + b)(a - b)\\{a}^{2} + {b}^{2} = {(a + b)}^{2} - 2ab\\{a}^{2} + {b}^{2} = {(a - b)}^{2} + 2ab\\{a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )\\{a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} )$