Question

help math

Answer 1

:/

Answer 2

The given expression, \( -\left(\dfrac{9}{5} \right) \) is interpreted as "the opposite of \( \dfrac{9}{5} \).

Just like -2 is the opposite of 2, and 5 is the opposite of -5, the opposite of \( \dfrac{9}{5} \) is \( -\dfrac{9}{5} \).

As you can see, \( -\dfrac{9}{5} \) is a negative number.
A negative divided by a positive is positive, so if you have a negative numerator and a negative denominator, you'd get a positive number. Also, -9/5 is not 5/9.

Do you have an idea of what the answer is now?

Answer 3

mathstudent55: I'm uncomfortable with the use of the word "opposite" in this context. Would you be comfortable substituting the word "negative" and thus explaining that
\[-\left( 9/5 \right)\] could be interpreted as the negative of \[\left(9/5 \right)\]

Given \[-\left( 9/5 \right),\] we could distribute that (-) sign in either of two different ways:
\[\frac{ -9 }{ 5 }\] or \[\frac{ 9 }{ -5 }.\]

Answer C must be crossed out because it has the wrong denominator (9 instead of 5).
Answer D must be rejected because it has the wrong sign.

So, TC, which of the four answer choices do you think is the correct one?

Answer 4

@mathmale I don't know what makes you uncomfortable with that usage of the word opposite. Consult any math dictionary or glossary of math terms, and you will see that the term opposite is well established having the meaning I used. Opposites, opposite numbers, and additive inverses are expressions that mean the same.

Answer 5

I'm surprised you objected to my use of the word opposite, but you didn't notice my glaring error above.

I wrote "A negative divided by a positive is positive" when I meant to write
"A negative divided by a negative is positive"

Answer 6

mathstudent55: Yes, I overlooked your "glaring error." My apologies. As regards your use of the word "opposite," I'd be fine if you were to use it as an adjective, as in "opposite sign." You're using it as a noun. Disagree if you wish, but I still believe "negative" is a better descriptor here than is "opposite." For example, you and I seem to be "opposites." I would not describe you as "my negative."

Answer 7

Still friends? I hope so.