SOLUTION: {{{(5n+1)/6}}} + {{{(3n-2)/8}}}

Algebra ->  Expressions-with-variables -> SOLUTION: {{{(5n+1)/6}}} + {{{(3n-2)/8}}}      Log On


   



Question 616515: %285n%2B1%29%2F6 + %283n-2%29%2F8
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
%285n%2B1%29%2F6 + %283n-2%29%2F8

1. Put parentheses around the numerators:

%28%285n%2B1%29%29%2F6 + %28%283n-2%29%29%2F8

2. The denominators are 6 and 8

3. The smallest positive whole number which 6 and 8 will both 
   go into without leaving a remainder is 24.

4. 24 is the LCD, the least common denominator.

5. The denominator 6 needs to be multiplied by 4 to become 24.

6. We multiply the first fraction by the fraction 4%2F4, which
   will not change the value because multiplying by 4%2F4 is the
   same as multiplying by 1.

%28%285n%2B1%29%29%2F6·4%2F4 + %28%283n-2%29%29%2F8

7. The denominator 8 needs to be multiplied by 3 to become 24.

8. We multiply the second fraction by the fraction 3%2F3, which
   also will not change the value because multiplying by 3%2F3 is 
   the same as multiplying by 1.

%28%285n%2B1%29%29%2F6·4%2F4 + %28%283n-2%29%29%2F8·3%2F3

9. Multiply numerators and denominators:

 4%2A%285n%2B1%29%2F%284%2A6%29 + 3%2A%283n-2%29%2F%288%2A3%29

10.  Finish the multiplications:

%28%2820n%2B4%29%29%2F24 + %28%289n-6%29%29%2F24

11.  Now that the fractions have equal denominators, we add
    the two numerators and place it over the 24.

%28%2820n%2B4%29%2B%289n-6%29%29%2F24

12. Remove the parentheses in the numerator:

%2820n%2B4%2B9n-6%29%2F24

13. Combine like terms in the numerator:

%2829n-2%29%2F24  

Edwin