SOLUTION: how do you simplify 3/8*(16x-8)+2/3*(15y+12)

Algebra ->  Real-numbers -> SOLUTION: how do you simplify 3/8*(16x-8)+2/3*(15y+12)      Log On


   

Question 6722: how do you simplify 3/8*(16x-8)+2/3*(15y+12)
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
you use my simplifier...
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: 3%2F8%2A%2816x-8%29%2B2%2F3%2A%2815y%2B12%29 simplifies to 6%2Ax%2B10%2Ay%2B5
  • Text form: 3/8*(16x-8)+2/3*(15y+12) simplifies to 6*x+10*y+5
  • Cartoon (animation) form: simplify_cartoon%28+3%2F8%2A%2816x-8%29%2B2%2F3%2A%2815y%2B12%29+%29
    For tutors: simplify_cartoon( 3/8*(16x-8)+2/3*(15y+12) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+3%2F8%2A%2816%2Ax-8%29+%29%2B2%2F3%2A%2815%2Ay%2B12%29.
Expanded term 3%2F8 by using associative property on %2816%2Ax-8%29
It becomes .
Look at .
Factors 16 and 8 have greatest common factor (GCF) of 8. Reducing fraction.
It becomes .
Look at .
Multiplied numerator integers
It becomes highlight_green%28+6+%29%2F1%2Ax-3%2F8%2A8%2B2%2F3%2A%2815%2Ay%2B12%29.
Look at 6%2F1%2Ax-3%2Fhighlight_red%28+8+%29%2Ahighlight_red%28+8+%29%2B2%2F3%2A%2815%2Ay%2B12%29.
Factors 8 and 8 have greatest common factor (GCF) of 8. Reducing fraction.
It becomes .
Look at 6%2F1%2Ax-highlight_red%28+3+%29%2F1%2Ahighlight_red%28+1+%29%2B2%2F3%2A%2815%2Ay%2B12%29.
Multiplied numerator integers
It becomes 6%2F1%2Ax-highlight_green%28+3+%29%2F1%2B2%2F3%2A%2815%2Ay%2B12%29.
Look at 6%2F1%2Ax-highlight_red%28+3%2F1+%29%2B2%2F3%2A%2815%2Ay%2B12%29.
Moved -3%2F1 to the right of expression
It becomes 6%2F1%2Ax%2B2%2F3%2A%2815%2Ay%2B12%29-highlight_green%28+3%2F1+%29.
Look at 6%2Fhighlight_red%28+1+%29%2Ax%2B2%2F3%2A%2815%2Ay%2B12%29-3%2F1.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes 6%2Ax%2B2%2F3%2A%2815%2Ay%2B12%29-3%2F1.
Look at 6%2Ax%2B2%2F3%2A%2815%2Ay%2B12%29-3%2Fhighlight_red%28+1+%29.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes 6%2Ax%2B2%2F3%2A%2815%2Ay%2B12%29-3.
Look at 6%2Ax%2Bhighlight_red%28+2%2F3%2A%2815%2Ay%2B12%29+%29-3.
Expanded term 2%2F3 by using associative property on %2815%2Ay%2B12%29
It becomes 6%2Ax%2Bhighlight_green%28+2%2F3%2A15%2Ay+%29%2Bhighlight_green%28+2%2F3%2A12+%29-3.
Look at 6%2Ax%2B2%2Fhighlight_red%28+3+%29%2Ahighlight_red%28+15+%29%2Ay%2B2%2F3%2A12-3.
Factors 15 and 3 have greatest common factor (GCF) of 3. Reducing fraction.
It becomes 6%2Ax%2B2%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+5+%29%2Ay%2B2%2F3%2A12-3.
Look at 6%2Ax%2Bhighlight_red%28+2+%29%2F1%2Ahighlight_red%28+5+%29%2Ay%2B2%2F3%2A12-3.
Multiplied numerator integers
It becomes 6%2Ax%2Bhighlight_green%28+10+%29%2F1%2Ay%2B2%2F3%2A12-3.
Look at 6%2Ax%2B10%2F1%2Ay%2B2%2Fhighlight_red%28+3+%29%2Ahighlight_red%28+12+%29-3.
Factors 12 and 3 have greatest common factor (GCF) of 3. Reducing fraction.
It becomes 6%2Ax%2B10%2F1%2Ay%2B2%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+4+%29-3.
Look at 6%2Ax%2B10%2F1%2Ay%2Bhighlight_red%28+2+%29%2F1%2Ahighlight_red%28+4+%29-3.
Multiplied numerator integers
It becomes 6%2Ax%2B10%2F1%2Ay%2Bhighlight_green%28+8+%29%2F1-3.
Look at 6%2Ax%2B10%2F1%2Ay%2Bhighlight_red%28+8%2F1+%29-highlight_red%28+3+%29.
Added fractions or integers together
It becomes 6%2Ax%2B10%2F1%2Ay%2Bhighlight_green%28+5+%29.
Look at 6%2Ax%2B10%2Fhighlight_red%28+1+%29%2Ay%2B5.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes 6%2Ax%2B10%2Ay%2B5.
Result: 6%2Ax%2B10%2Ay%2B5

Universal Simplifier and Solver


Done!