SOLUTION: {{{1/4*(13 y-3) + 1/8*(6y+9)}}}

Algebra ->  Expressions-with-variables -> SOLUTION: {{{1/4*(13 y-3) + 1/8*(6y+9)}}}       Log On


   

Question 212090: 1%2F4%2A%2813+y-3%29+%2B+1%2F8%2A%286y%2B9%29




Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: 1%2F4%2A%2813y-3%29%2B1%2F8%2A%286y%2B9%29 simplifies to 4%2Ay%2B3%2F8
  • Text form: 1/4*(13y-3)+1/8*(6y+9) simplifies to 4*y+3/8
  • Cartoon (animation) form: simplify_cartoon%28+1%2F4%2A%2813y-3%29%2B1%2F8%2A%286y%2B9%29+%29
    For tutors: simplify_cartoon( 1/4*(13y-3)+1/8*(6y+9) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+1+%29%2F4%2A%2813%2Ay-3%29%2B1%2F8%2A%286%2Ay%2B9%29.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes %2813%2Ay-3%29%2F4%2B1%2F8%2A%286%2Ay%2B9%29.
Look at %2813%2Ay-3%29%2F4%2Bhighlight_red%28+1+%29%2F8%2A%286%2Ay%2B9%29.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes %2813%2Ay-3%29%2F4%2B%286%2Ay%2B9%29%2F8.
Look at highlight_red%28+%2813%2Ay-3%29%2F4+%29%2B%286%2Ay%2B9%29%2F8.
Expanded term 1%2F4 by using associative property on %2813%2Ay-3%29
It becomes highlight_green%28+1%2F4%2A13%2Ay+%29-highlight_green%28+1%2F4%2A3+%29%2B%286%2Ay%2B9%29%2F8.
Look at highlight_red%28+1+%29%2F4%2Ahighlight_red%28+13+%29%2Ay-1%2F4%2A3%2B%286%2Ay%2B9%29%2F8.
Multiplied numerator integers
It becomes highlight_green%28+13+%29%2F4%2Ay-1%2F4%2A3%2B%286%2Ay%2B9%29%2F8.
Look at 13%2F4%2Ay-highlight_red%28+1+%29%2F4%2Ahighlight_red%28+3+%29%2B%286%2Ay%2B9%29%2F8.
Multiplied numerator integers
It becomes 13%2F4%2Ay-highlight_green%28+3+%29%2F4%2B%286%2Ay%2B9%29%2F8.
Look at 13%2F4%2Ay-highlight_red%28+3%2F4+%29%2B%286%2Ay%2B9%29%2F8.
Moved -3%2F4 to the right of expression
It becomes 13%2F4%2Ay%2B%286%2Ay%2B9%29%2F8-highlight_green%28+3%2F4+%29.
Look at 13%2F4%2Ay%2Bhighlight_red%28+%286%2Ay%2B9%29%2F8+%29-3%2F4.
Expanded term 1%2F8 by using associative property on %286%2Ay%2B9%29
It becomes 13%2F4%2Ay%2Bhighlight_green%28+1%2F8%2A6%2Ay+%29%2Bhighlight_green%28+1%2F8%2A9+%29-3%2F4.
Look at 13%2F4%2Ay%2B1%2Fhighlight_red%28+8+%29%2Ahighlight_red%28+6+%29%2Ay%2B1%2F8%2A9-3%2F4.
Factors 6 and 8 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes 13%2F4%2Ay%2B1%2Fhighlight_green%28+4+%29%2Ahighlight_green%28+3+%29%2Ay%2B1%2F8%2A9-3%2F4.
Look at 13%2F4%2Ay%2Bhighlight_red%28+1+%29%2F4%2Ahighlight_red%28+3+%29%2Ay%2B1%2F8%2A9-3%2F4.
Multiplied numerator integers
It becomes 13%2F4%2Ay%2Bhighlight_green%28+3+%29%2F4%2Ay%2B1%2F8%2A9-3%2F4.
Look at 13%2F4%2Ay%2B3%2F4%2Ay%2Bhighlight_red%28+1+%29%2F8%2Ahighlight_red%28+9+%29-3%2F4.
Multiplied numerator integers
It becomes 13%2F4%2Ay%2B3%2F4%2Ay%2Bhighlight_green%28+9+%29%2F8-3%2F4.
Look at 13%2F4%2Ay%2B3%2F4%2Ay%2Bhighlight_red%28+9%2F8+%29-highlight_red%28+3%2F4+%29.
Added fractions or integers together
It becomes 13%2F4%2Ay%2B3%2F4%2Ay%2Bhighlight_green%28+3%2F8+%29.
Look at highlight_red%28+13%2F4%2Ay+%29%2Bhighlight_red%28+3%2F4%2Ay+%29%2B3%2F8.
Eliminated similar terms highlight_red%28+13%2F4%2Ay+%29,highlight_red%28+3%2F4%2Ay+%29 replacing them with highlight_green%28+%2813%2A1%2F4%2B3%2A1%2F4%29%2Ay+%29
It becomes highlight_green%28+%2813%2A1%2F4%2B3%2A1%2F4%29%2Ay+%29%2B3%2F8.
Look at %28highlight_red%28+13+%29%2Ahighlight_red%28+1+%29%2F4%2B3%2A1%2F4%29%2Ay%2B3%2F8.
Multiplied numerator integers
It becomes %28highlight_green%28+13+%29%2F4%2B3%2A1%2F4%29%2Ay%2B3%2F8.
Look at %2813%2F4%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+1+%29%2F4%29%2Ay%2B3%2F8.
Multiplied numerator integers
It becomes %2813%2F4%2Bhighlight_green%28+3+%29%2F4%29%2Ay%2B3%2F8.
Look at %28highlight_red%28+13%2F4+%29%2Bhighlight_red%28+3%2F4+%29%29%2Ay%2B3%2F8.
Added fractions or integers together
It becomes %28highlight_green%28+16%2F4+%29%29%2Ay%2B3%2F8.
Look at highlight_red%28+%28highlight_red%28+16%2F4+%29%29%2Ay+%29%2B3%2F8.
Remove unneeded parentheses around factor highlight_red%28+16+%29,highlight_red%28+1%2F4+%29
It becomes highlight_green%28+16+%29%2Fhighlight_green%28+4+%29%2Ay%2B3%2F8.
Look at highlight_red%28+16+%29%2Fhighlight_red%28+4+%29%2Ay%2B3%2F8.
Factors 16 and 4 have greatest common factor (GCF) of 4. Reducing fraction.
It becomes highlight_green%28+4+%29%2Fhighlight_green%28+1+%29%2Ay%2B3%2F8.
Look at 4%2Fhighlight_red%28+1+%29%2Ay%2B3%2F8.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes 4%2Ay%2B3%2F8.
Result: 4%2Ay%2B3%2F8

Universal Simplifier and Solver


Done!