Answer: The correct answer is:
______________
→ Choice: [C]: " [tex]\frac{2}{1} * \frac{7}{-2}[/tex] " .
______________
Step-by-step explanation:
______________
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:
______________
The given problem:
______________
" [tex]\frac{-3}{4} * \frac{7}{-2}[/tex] ÷ [tex]\frac{3}{-8}[/tex] " ;
Is treated as:
______________
" [tex](\frac{-3}{4} * \frac{7}{-2})[/tex] ÷ [tex]\frac{3}{-8}[/tex] " ;
______________
So, we start with:
______________
" [tex]\frac{-3}{4} * \frac{7}{-2}[/tex] " ;
______________
→ [tex]\frac{-3}{4} * \frac{7}{-2} = \frac{(-3*7)}{[4*(-2) ]} = \frac{-21}{-8}[/tex] ;
______________
Simplify:
______________
" [tex]\frac{-21}{-8} = \frac{(-1)*21}{(-1) *8}[/tex] " ;
______________
→ The "(-1)'s " cancel out:
{since: "(-1)/(-1) = 1 "} ;
→ And we have: " [tex]\frac{21}{8}[/tex] " ;
______________
Now, continue with the problem, and divide this value by: " [tex]\frac{3}{-8}[/tex] " ;
______________
" [tex]\frac{21}{8}[/tex] ÷ [tex]\frac{3}{-8}[/tex] " ;
______________
Note that dividing by a number is the same as multiplying by the reciprocal of that said number:
______________
The reciprocal of " [tex]\frac{3}{-8}[/tex] " ; is: " [tex]\frac{-8}{3}[/tex] : l
As such:
" [tex]\frac{21}{8}[/tex] ÷ [tex]\frac{3}{-8}[/tex] " ;
______________
= " [tex]\frac{21}{8} * \frac{-8}{3}[/tex] "
______________
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 " ;
______________
And we can we rewrite the expression:
______________
→ " [tex]\frac{7}{1} * \frac{-1}{1}[/tex] " ;
which equals: " 7 * -1 " ; which equals " - 7 ".
______________
Now, the problem has 4 (four) answer choices. Which expression [i.e. which answer choice] is equal to: " -7 " ??
______________
Consider Choice [A]: " [tex]\frac{1}{2} * \frac{7}{2}[/tex] " ; which equals: " [tex]\frac{(1*7)}{(2*2)} = \frac{7}{4} = 1\frac{3}{4}[/tex] " ;
" [tex]1\frac{3}{4} \neq -7[/tex] ."
Rule out: "Choice [A]."
______________
Consider Choice: [B]: " [tex]\frac{2}{1} * \frac{7}{2}[/tex] " ; which equals: " [tex]\frac{(2*7)}{(1*2)} = \frac{14}{2} = 7[/tex] ; " [tex]7\neq -7[/tex] ."
Rule out: "Choice: [B]."
______________
Consider Choice: [C]: " [tex]\frac{2}{1} * \frac{7}{-2}[/tex] " ; which equals: " [tex]-7[/tex] ; " [tex]-7 = -7[/tex] ".
Choice [C]: seems correct!
______________
Consider Choice: [D]: " [tex]\frac{-1}{2} * \frac{7}{-2}[/tex] " ; which equals:
" [tex]\frac{(-1*7)}{(2*-2)} = \frac{-7}{-4} = \frac{(-1)*7}{(-1)*4}[/tex] ;
→ cancel out the "(-1)'s" ;
→ {since: "(-1) / (-1) = 1 " ;
to get:
→ " [tex]\frac{7}{4}[/tex] " ; which equals:
→ " [tex]1\frac{3}{4}[/tex] " ; " [tex]1\frac{3}{4} \neq -7[/tex] . "
Rule out: "Choice: [D]."
______________
The correct answer is:
______________
Choice: [C]: " [tex]\frac{2}{1} * \frac{7}{-2}[/tex] " .
______________
Hope this is helpful to you!
Wishing you the best!
______________
