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3 years ago

Find the quotient (line over 42 is repeating)

1 answer:

3 0

The correct answer is: [C]:  " $\frac{21}{11}$ " .
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<span>Explanation:
_____________________________________________________
</span>
Let us begin by converting the:
"0.42 (with the "repeating bar on the digits, "42") " ;

into a fraction, as follows:
______________________________________________________
Let x = 0.42424242424242424242424242424242....

100x = 42.42424242424242424242424242424242....
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100x = 42.42424242424242424242424242424242....
– x = 0.42424242424242424242424242424242...
______________________________________________________
99x = 42.000000000000000000000000000000.... ;

→ 99x = 42 ;

Divide each side of the equation by " 99 " ;
to isolate "x" on one side of the equation; & to solve for "x" ;
______________________________________________________
→ 99x / 99 = 42/99 = (42 ÷ 3) / (99 ÷ 3) = 14/ 33;

→ x = " $\frac{14}{33}$ " .

So; "0.42 (with a repeating bar over the digits, "42" ;

is equal to: " $\frac{14}{33}$ "
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So, rewrite the question/problem being asked:
________________________________________________
"Find the quotient:
________________________________________________
$\frac{14}{33}$ ÷ $\frac{2}{9}$ ;

=   $\frac{14}{33}$ * $\frac{9}{2}$ ;

Note: The "14" cancels to a "7" <span>; and</span> the "2" cancels to a "1" ;
→ {since: " 14 ÷ 2 = 7 " ; and since: " 2 ÷ 2 = 1 "} ;

Note : The "33" cancels to an "11" ; and the "9" cancels to a "3" ;
   → {since: " 33 ÷ 3 = 11 " ; and since: " 9 ÷ 3 = 3 "} ;

And we can rewrite the problem as:
____________________________________________________

" $\frac{7}{11}$ * $\frac{3}{1}$ " ;

= $\frac{(7*3)}{(11*1}$ = $\frac{21}{11}$ ;

→ which is: Answer choice: [C]: " $\frac{21}{11}$ " .
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