Question

Racheal used a total of 5 1/6 gallons of gas while driving her car. Each hour she was driving, she used 5/9 gallons of gas. What was the total number of hours she was driving ?

Answer 1

Answer:  The correct answer is:  " 9.3 hours " .

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Step-by-step explanation:

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To calculate:

Let "gal" represent "gallons (of gas)" ;

Let "h" represent "hour(s)" ;

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 5 $\frac{1}{6}$  gal  * (   1 h      )     =  ?  h   ;

                ( 5/9 gal  ) ;

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Note: On the "left-hand side" of the equation;

           The units of "gal" ["gallons"] — "cancel out" ;

         →  {since:  "gal/ gal = 1"} ;

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and we can rewrite our equation as:

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 ( 5 $\frac{1}{6}$  )      

________   hours  ;

 ( 5/9 )    

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To solve:

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5  1/6  ÷ (5/9)  =

   5  1/6 * (9/5) ;

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Note:  Dividing by a fraction is the same as multiplying by that very fraction's reciprocal form.

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Now, let us convert "5 1/6" ; which is a "mixed fraction" ; into an

"Improper fraction" ;

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To do this, we can use the "MAD" method:

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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" ;

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Then:

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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:

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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:  " $\frac{31}{6}$ " .

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Now, substitute this "improper fraction" into our original problem; and rewrite:

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 " $\frac{31}{6} * \frac{9}{5}$ " hours;

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We can reduce the "9" to "3" ; and the "6" to "2" ;

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{Since "9/6 = 3/2" };

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And rewrite as:

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" $\frac{31}{2} * \frac{3}{5}$ " hours ;

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Note:  " \frac{31}{2} * \frac{3}{5} " ;

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 = " $\frac{(31*3)}{(2*5)} = \frac{93}{10}$  " ;

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 =  93 ÷ 10 ;  

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  =  9.3 hours.

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The answer is:  " 9.3 hours " .

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Hope this explanation is helpful!

Best of luck to you in your academic pursuits!

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