8) Find m 5x + 5 11x + 15

 15 • (4x + 11)

 ———————

         11      

Step-by-step explanation:

Step  1  :

            5

Simplify   ——

           11

Equation at the end of step  1  :

          5          

 (5x +  (—— • x)) +  15

         11          

Step  2  :

Rewriting the whole as an Equivalent Fraction :

2.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  11  as the denominator :

          5x     5x • 11

    5x =  ——  =  ———————

          1        11  

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 :

2.2       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:

5x • 11 + 5x     60x

————————————  =  ———

     11          11

Equation at the end of step  2  :

 60x    

 ——— +  15

 11    

Step  3  :

Rewriting the whole as an Equivalent Fraction :

3.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  11  as the denominator :

         15     15 • 11

   15 =  ——  =  ———————

         1        11  

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

60x + 15 • 11     60x + 165

—————————————  =  —————————

     11              11    

Step  4  :

Pulling out like terms :

4.1     Pull out like factors :

  60x + 165  =   15 • (4x + 11)

Final result :

 15 • (4x + 11)

 ——————————————

       11      

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