Let x=the amount of water in the bucket. a bucket holds 2 2/3 gallons of water. the bucket is 5/6 full. how much water is in the bucket?

The answer is:  2  2/9 gal  ; or, write as: 2.222 gal
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Explanation: 
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(5/6) * (2  ⅔ ) = x ; Solve for "x"; which is our answer (in "gallons", or "gal").

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→ Write "2 ⅔ " as an improper fraction;

→ 2  ⅔  = [(3*2) + 2 ] / 3 = (6+2) / 3 =  8/3  ;
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→ Rewrite the problem, substituting "8/3" for "2  ⅔" ; 
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→    *   ;

→  The "6" and the "8" can be reduced; since both the "6" and the "8" can be divided by "2";    →  So change the  "6" to a "3" ; (since "6÷2 = 3"); 
                                    →  and change the "8" to a "4"; (since "8÷2 = 4") ;
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→ and rewrite the equation as:
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→    *   ; 
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     →    *    = 
  
                = 
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      →    gallons =

             → 20 ÷ 9 =
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                →    2  2/9 gal  ; or, write as: 2.222 gal
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