Question

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?

Answer 1

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

_________________________________________________
→ Write "2 ⅔ " as an improper fraction;

→ 2 ⅔ = [(3*2) + 2 ] / 3 = (6+2) / 3 = 8/3 ;
________________________________________
→ Rewrite the problem, substituting "8/3" for "2 ⅔" ;
_______________________________________________
→
`(5)/(6)` *
`(8)/(3)` ;

→ 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") ;
_______________________________________________
→ and rewrite the equation as:
_____________________________________
→
`(5)/(3)` *
`(4)/(3)` ;
______________________________________________
→
`(5)/(3)` *
`(4)/(3)` =


`((5*4))/((3*3))` =
___________________________________________
→
`(20)/(9)` gallons =

→ 20 ÷ 9 =
_________________________________________

→ 2 2/9 gal ; or, write as: 2.222 gal
_______________________________________________