Question

Find the quotient (line over 42 is repeating)

_
(0.42. Divided by 2/9)
A)84/891
B)189/100
C)21/11
D)21

Answer 1

The correct answer is: [C]: "
`(21)/(11)` " .
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Step-by-step 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 = "
`(14)/(33)`" .

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

is equal to: "
`(14)/(33)`"
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So, rewrite the question/problem being asked:
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"Find the quotient:
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`(14)/(33)` ÷
`(2)/(9)` ;

=
`(14)/(33)` *
`(9)/(2)` ;

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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"
`(7)/(11)` *
`(3)/(1)` " ;

=
`((7*3))/((11*1)` =
`(21)/(11)` ;

→ which is: Answer choice: [C]: "
`(21)/(11)` " .
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