Question

3

Answer 1

Answer:  The correct answer is:

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            →   Choice: [C]:  "  $\frac{2}{1} * \frac{7}{-2}$ " .

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Step-by-step explanation:

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Note that this problem contains multiplication and division.

 WIth multiplication and division;

the order of operations we perform is from "left side to right side" in the expression;  in the order in which the operation occurs:

As such:

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The given problem:

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"   $\frac{-3}{4} * \frac{7}{-2}$ ÷ $\frac{3}{-8}$ " ;

Is treated as:

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" $(\frac{-3}{4} * \frac{7}{-2})$ ÷ $\frac{3}{-8}$ " ;

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So, we start with:

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" $\frac{-3}{4} * \frac{7}{-2}$ " ;

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→ $\frac{-3}{4} * \frac{7}{-2} = \frac{(-3*7)}{[4*(-2) ]} = \frac{-21}{-8}$ ;  

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Simplify:

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"  $\frac{-21}{-8} = \frac{(-1)*21}{(-1) *8}$ " ;

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          →  The "(-1)'s " cancel out:

              {since: "(-1)/(-1) = 1 "} ;

→ And we have:  " $\frac{21}{8}$ " ;

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Now, continue with the problem, and divide this value by: " $\frac{3}{-8}$ " ;

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 " $\frac{21}{8}$ ÷ $\frac{3}{-8}$ " ;

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Note that dividing by a number is the same as multiplying by the reciprocal of that said number:

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The reciprocal of " $\frac{3}{-8}$ " ; is:  " $\frac{-8}{3}$ : l

As such:

" $\frac{21}{8}$ ÷ $\frac{3}{-8}$ " ;

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     =   "  $\frac{21}{8} * \frac{-8}{3}$  "

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Now, let us simplify:

 Note:  The "8" and the "-8" ;

    The "8" can be changed to "1" ; and the "-8" can be changed to "-1" ;

since: "-8 ÷ 8 = 1 " ;  and since:  "8 ÷ 8 = 1 " ;

Note:  The "3" and the "21" ;

    The "3" can be changed to "1";  and the "21" can be changed to "7" ;

since: "21 ÷ 3 = 7 " ; and since:  "3 ÷ 3 = 1 " ;

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And we can we rewrite the expression:

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 → " $\frac{7}{1} * \frac{-1}{1}$ " ;

which equals:  " 7 * -1 " ;  which equals " - 7 ".

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Now, the problem has 4 (four) answer choices.  Which expression [i.e. which answer choice] is equal to:  " -7 " ??

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Consider Choice [A]: " $\frac{1}{2} * \frac{7}{2}$ " ; which equals: " $\frac{(1*7)}{(2*2)} = \frac{7}{4} = 1\frac{3}{4}$ " ;

" $1\frac{3}{4} \neq -7$ ."

Rule out: "Choice [A]."

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Consider Choice: [B]: " $\frac{2}{1} * \frac{7}{2}$ " ; which equals: " $\frac{(2*7)}{(1*2)} = \frac{14}{2} = 7$ ; " $7\neq -7$ ."

Rule out: "Choice: [B]."

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Consider Choice: [C]: " $\frac{2}{1} * \frac{7}{-2}$ " ; which equals: " $-7$ ;  " $-7 = -7$ ".  

 Choice [C]: seems correct!

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Consider Choice: [D]: " $\frac{-1}{2} * \frac{7}{-2}$ " ; which equals:

                           " $\frac{(-1*7)}{(2*-2)} = \frac{-7}{-4} = \frac{(-1)*7}{(-1)*4}$ ;

                                              → cancel out the "(-1)'s" ;

                                              → {since: "(-1) / (-1) = 1 " ;  

                                         to get:

                                              → " $\frac{7}{4}$ " ; which equals:

                                              → " $1\frac{3}{4}$ " ;  " $1\frac{3}{4} \neq -7$ . "

 Rule out: "Choice: [D]."

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The correct answer is:

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Choice: [C]:  "  $\frac{2}{1} * \frac{7}{-2}$ " .

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Hope this is helpful to you!

Wishing you the best!

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