document.write( "Question 212090: $\"1%2F4%2A%2813+y-3%29+%2B+1%2F8%2A%286y%2B9%29\"$ \r
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Algebra.Com's Answer #160211 by ichudov(507) $\"\"$ $\"About$

You can put this solution on YOUR website!
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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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.

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DETAILED EXPLANATION

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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 $\"%2813%2Ay-3%29%2F4%2B1%2F8%2A%286%2Ay%2B9%29\"$ .
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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 $\"%2813%2Ay-3%29%2F4%2B%286%2Ay%2B9%29%2F8\"$ .
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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 $\"highlight_green%28+1%2F4%2A13%2Ay+%29-highlight_green%28+1%2F4%2A3+%29%2B%286%2Ay%2B9%29%2F8\"$ .
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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 $\"highlight_green%28+13+%29%2F4%2Ay-1%2F4%2A3%2B%286%2Ay%2B9%29%2F8\"$ .
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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 $\"13%2F4%2Ay-highlight_green%28+3+%29%2F4%2B%286%2Ay%2B9%29%2F8\"$ .
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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 $\"13%2F4%2Ay%2B%286%2Ay%2B9%29%2F8-highlight_green%28+3%2F4+%29\"$ .
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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 $\"13%2F4%2Ay%2Bhighlight_green%28+1%2F8%2A6%2Ay+%29%2Bhighlight_green%28+1%2F8%2A9+%29-3%2F4\"$ .
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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 $\"13%2F4%2Ay%2B1%2Fhighlight_green%28+4+%29%2Ahighlight_green%28+3+%29%2Ay%2B1%2F8%2A9-3%2F4\"$ .
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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 $\"13%2F4%2Ay%2Bhighlight_green%28+3+%29%2F4%2Ay%2B1%2F8%2A9-3%2F4\"$ .
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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 $\"13%2F4%2Ay%2B3%2F4%2Ay%2Bhighlight_green%28+9+%29%2F8-3%2F4\"$ .
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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 $\"13%2F4%2Ay%2B3%2F4%2Ay%2Bhighlight_green%28+3%2F8+%29\"$ .
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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 $\"highlight_green%28+%2813%2A1%2F4%2B3%2A1%2F4%29%2Ay+%29%2B3%2F8\"$ .
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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 $\"%28highlight_green%28+13+%29%2F4%2B3%2A1%2F4%29%2Ay%2B3%2F8\"$ .
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Look at $\"%2813%2F4%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+1+%29%2F4%29%2Ay%2B3%2F8\"$ .
Multiplied numerator integers
It becomes $\"%2813%2F4%2Bhighlight_green%28+3+%29%2F4%29%2Ay%2B3%2F8\"$ .
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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 $\"%28highlight_green%28+16%2F4+%29%29%2Ay%2B3%2F8\"$ .
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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 $\"highlight_green%28+16+%29%2Fhighlight_green%28+4+%29%2Ay%2B3%2F8\"$ .
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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 $\"highlight_green%28+4+%29%2Fhighlight_green%28+1+%29%2Ay%2B3%2F8\"$ .
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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: $\"4%2Ay%2B3%2F8\"$
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Universal Simplifier and Solver

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Done!

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