Question

#17-1: Simplify this complex fraction. 1/3 / 6/9

Answer 1

Answer:  The correct answer is:  " $\frac{1}{2}$ " .

________________________________________________

                                                  or;  in decimal form:  " 0.5 " .

________________________________________________

Step-by-step explanation:

________________________________________________

Given:  " (1/3) / (6/9) " ;  

Rewrite as:  " $\frac{1}{3}$  ÷  $\frac{6}{9}$ " ;  

Note that:  " $\frac{6}{9}$ " ;

             

                     =  (6 ÷ 3) / (9÷ 3} ;  

               

                     = $\frac{2}{3}$ ;

Rewrite the original expression:

           

            " $\frac{1}{3}$  ÷  " $\frac{2}{3}$ " ;  

 Now,  "dividing by a fraction" results in the same value as:  

           "multiplying by the inverse—or reciprocal" value:

_________________________________________________

  " $\frac{1}{3}$  ÷  $\frac{2}{3}$ " ;

 

         =  " $\frac{1}{3}$  *   $\frac{3}{2}$ " ;

________________________________________________

The " 3 's "  both cancel out to "1's" ;  

       

        →    {since:  "$\frac{3}{3} = 1$" ;  

________________________________________________

And we have:

       →    " $\frac{1}{1}$  *   $\frac{1}{2}$ " ;

            =    1    *   $\frac{1}{2}$  ;  

            =    " $\frac{1}{2}$  " .

________________________________________________

The correct answer is:  " $\frac{1}{2}$ " .

  or; in decimal form:  " 0.5 " .

________________________________________________

Hope this answer is helpful to you!

        Best wishes to you in your academic pursuits

                — and within the "Brainly" community!

________________________________________________

Answer 2

$\huge{\boxed{\frac{1}{2}}}$

To divide by a fraction, you multiply by its reciprocal, which you find by flipping the numerator and the denominator. $\frac{1}{3} \div \frac{6}{9} = \frac{1}{3} * \frac{9}{6}$

Multiply the numerators and the denominators separately. $\frac{1}{3} * \frac{9}{6} = \frac{1*9}{3*6} = \frac{9}{18}$

Simplify by dividing both sides of the equation by $9$. $\frac{9 \div 9}{18 \div 9} = \boxed{\frac{1}{2}}$