document.write( "Question 6722: how do you simplify 3/8*(16x-8)+2/3*(15y+12) \n" ); document.write( "

Algebra.Com's Answer #3700 by ichudov(507) $\"\"$ $\"About$

You can put this solution on YOUR website!
you use my simplifier...\r
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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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.

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DETAILED EXPLANATION

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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

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Look at

.
Factors 16 and 8 have greatest common factor (GCF) of 8. Reducing fraction.
It becomes

.
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Look at

.
Multiplied numerator integers
It becomes $\"highlight_green%28+6+%29%2F1%2Ax-3%2F8%2A8%2B2%2F3%2A%2815%2Ay%2B12%29\"$ .
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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

.
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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 $\"6%2F1%2Ax-highlight_green%28+3+%29%2F1%2B2%2F3%2A%2815%2Ay%2B12%29\"$ .
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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 $\"6%2F1%2Ax%2B2%2F3%2A%2815%2Ay%2B12%29-highlight_green%28+3%2F1+%29\"$ .
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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 $\"6%2Ax%2B2%2F3%2A%2815%2Ay%2B12%29-3%2F1\"$ .
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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 $\"6%2Ax%2B2%2F3%2A%2815%2Ay%2B12%29-3\"$ .
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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 $\"6%2Ax%2Bhighlight_green%28+2%2F3%2A15%2Ay+%29%2Bhighlight_green%28+2%2F3%2A12+%29-3\"$ .
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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 $\"6%2Ax%2B2%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+5+%29%2Ay%2B2%2F3%2A12-3\"$ .
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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 $\"6%2Ax%2Bhighlight_green%28+10+%29%2F1%2Ay%2B2%2F3%2A12-3\"$ .
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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 $\"6%2Ax%2B10%2F1%2Ay%2B2%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+4+%29-3\"$ .
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Look at $\"6%2Ax%2B10%2F1%2Ay%2Bhighlight_red%28+2+%29%2F1%2Ahighlight_red%28+4+%29-3\"$ .
Multiplied numerator integers
It becomes $\"6%2Ax%2B10%2F1%2Ay%2Bhighlight_green%28+8+%29%2F1-3\"$ .
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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 $\"6%2Ax%2B10%2F1%2Ay%2Bhighlight_green%28+5+%29\"$ .
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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: $\"6%2Ax%2B10%2Ay%2B5\"$
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Universal Simplifier and Solver

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Done!

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