The correct answer is: [C]: " [tex] \frac{21}{11} [/tex] " .
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Explanation:
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Let us begin by converting the:
"0.42 (with the "repeating bar on the digits, "42") " ;
into a fraction, as follows:
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Let x = 0.42424242424242424242424242424242....
100x = 42.42424242424242424242424242424242....
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100x = 42.42424242424242424242424242424242....
– x = 0.42424242424242424242424242424242...
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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" ;
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→ 99x / 99 = 42/99 = (42 ÷ 3) / (99 ÷ 3) = 14/ 33;
→ x = "[tex] \frac{14}{33} [/tex]" .
So; "0.42 (with a repeating bar over the digits, "42" ;
is equal to: "[tex] \frac{14}{33} [/tex]"
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So, rewrite the question/problem being asked:
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"Find the quotient:
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[tex] \frac{14}{33} [/tex] ÷ [tex] \frac{2}{9} [/tex] ;
= [tex] \frac{14}{33} [/tex] * [tex] \frac{9}{2} [/tex] ;
Note: The "14" cancels to a "7" ; and 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:
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" [tex] \frac{7}{11} [/tex] * [tex] \frac{3}{1} [/tex] " ;
= [tex] \frac{(7*3)}{(11*1} [/tex] = [tex] \frac{21}{11} [/tex] ;
→ which is: Answer choice: [C]: " [tex] \frac{21}{11} [/tex] " .
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