Question

3

3
7
Which expression is equivalent to
7
-2
:
.?
4.
A
.
1 7
2 -2
27
1 2
2 7
B
1
-2
-1
D
2
-2

Answer 1

Answer: The correct answer is:

______________

→ Choice: [C]: "
`(2)/(1) * (7)/(-2)` " .

______________

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:

______________

"
`(-3)/(4) * (7)/(-2)` ÷
`(3)/(-8)` " ;

Is treated as:

______________

"
`((-3)/(4) * (7)/(-2))` ÷
`(3)/(-8)` " ;

______________

So, we start with:

______________

"
`(-3)/(4) * (7)/(-2)` " ;

______________

→
`(-3)/(4) * (7)/(-2) = ((-3*7))/([4*(-2) ]) = (-21)/(-8)` ;

______________

Simplify:

______________

"
`(-21)/(-8) = ((-1)*21)/((-1) *8)` " ;

______________

→ The "(-1)'s " cancel out:

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

→ And we have: "
`(21)/(8)` " ;

______________

Now, continue with the problem, and divide this value by: "
`(3)/(-8)` " ;

______________

"
`(21)/(8)` ÷
`(3)/(-8)` " ;

______________

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

______________

The reciprocal of "
`(3)/(-8)` " ; is: "
`(-8)/(3)` : l

As such:

"
`(21)/(8)` ÷
`(3)/(-8)` " ;

______________

= "
`(21)/(8) * (-8)/(3)` "

______________

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:

______________

→ "
`(7)/(1) * (-1)/(1)` " ;

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]: "
`(1)/(2) * (7)/(2)` " ; which equals: "
`((1*7))/((2*2)) = (7)/(4) = 1(3)/(4)` " ;

"
`1(3)/(4) \\eq -7` ."

Rule out: "Choice [A]."

______________

Consider Choice: [B]: "
`(2)/(1) * (7)/(2)` " ; which equals: "
`((2*7))/((1*2)) = (14)/(2) = 7` ; "
`7\\eq -7` ."

Rule out: "Choice: [B]."

______________

Consider Choice: [C]: "
`(2)/(1) * (7)/(-2)` " ; which equals: "
`-7` ; "
`-7 = -7` ".

Choice [C]: seems correct!

______________

Consider Choice: [D]: "
`(-1)/(2) * (7)/(-2)` " ; which equals:

"
`((-1*7))/((2*-2)) = (-7)/(-4) = ((-1)*7)/((-1)*4)` ;

→ cancel out the "(-1)'s" ;

→ {since: "(-1) / (-1) = 1 " ;

to get:

→ "
`(7)/(4)` " ; which equals:

→ "
`1(3)/(4)` " ; "
`1(3)/(4) \\eq -7` . "

Rule out: "Choice: [D]."

______________

The correct answer is:

______________

Choice: [C]: "
`(2)/(1) * (7)/(-2)` " .

______________

Hope this is helpful to you!

Wishing you the best!

______________