Answer: The correct answer is: " 9.3 hours " .
_________________________________
Step-by-step explanation:
_________________________________
To calculate:
Let "gal" represent "gallons (of gas)" ;
Let "h" represent "hour(s)" ;
________________________________
5 gal * ( <u> 1 h </u> ) = ? h ;
( 5/9 gal ) ;
________________________________
<u> Note</u>: On the "left-hand side" of the equation;
The units of "gal" ["gallons"] — "cancel out" ;
→ {since: "gal/ gal = 1"} ;
____________________________
and we can rewrite our equation as:
_____________________________
( 5 )
________ hours ;
( 5/9 )
______________________________ ;
To solve:
_____________________________
5 1/6 ÷ (5/9) =
5 1/6 * (9/5) ;
____________________________
<u>Note</u>: Dividing by a fraction is the same as multiplying by that very fraction's reciprocal form.
__________________________
Now, let us convert "5 1/6" ; which is a "mixed fraction" ; into an
"Improper fraction" ;
__________________________
To do this, we can use the "MAD" method:
__________________________
M: Multiply the "denominator number" of the "fraction portion" [within the "mixed fraction"]—by the "whole number" [within the "mixed fraction" ; In this case: "6" , multiplied by "5" ; to get "30" ;
_________________
Then:
_________________
A: Add this obtained value; to the "numerator number" of the
"fraction portion" [within the "mixed fraction"] ;
In this case: "30" ; added to "1" ; to get 31:
__________________
Then:
D: Divide this number by the "denominator number" of the "fraction portion" [within the "mixed fraction"] ; but instead of solving for the quotient—write in the format of a fraction:
In this case: " " .
_________________________
Now, substitute this "improper fraction" into our original problem; and rewrite:
_________________________
" " hours;
_________________________
We can reduce the "9" to "3" ; and the "6" to "2" ;
_________________________
{Since "9/6 = 3/2" };
_________________________
And rewrite as:
_________________________
" " hours ;
_________________________
Note: " \frac{31}{2} * \frac{3}{5} " ;
_________________________
= " " ;
_________________________
= 93 ÷ 10 ;
_________________________
= 9.3 hours.
_________________________
The answer is: " 9.3 hours " .
_________________________
Hope this explanation is helpful!
Best of luck to you in your academic pursuits!
_________________________