Simple order of operations question: G(2)=2/1-2

[Jwmx9]

This came up in my class today
G(2)=2/1-2

 

[HallsofIvy]

What???? I would think the value of "G(2)" would depend strongly on what "G" is! And do you mean G(2)= (1/2)- 1= -1/2 or G(2)= 1/(2- 1)= 1/2?

 

[Otis]

Simple order of operations question ...

G(2) = 2/(1-2)

Note the grouping symbols shown in red above. They're required, when using a keyboard, to show that the denominator is 1-2 instead of just 1.

When using mathematical formatting, the right-hand side of the equation looks like \(\displaystyle \dfrac{2}{1-2}\).

The horizontal "fraction bar" acts like a grouping symbol; it groups the expression on top as numerator, and it groups the expression on bottom as denominator.

You know that the Order of Operations tells us to evaluate expressions within groups first. Therefore, we first evaluate the numerator, then we evaluate the denominator, and we finish by dividing what we got on top by what we got on bottom.

The numerator is 2.

The denominator 1-2 evaluates to -1.

We finish by dividing 2 by -1.

G(2) = -2


Here's another example:

\(\displaystyle \dfrac{5^2 - 1}{2(7) - 6}\)

Using a keyboard, we can type this as (5^2 - 1)/(2*7 - 6)

The fraction bar separates the numerator and the denominator into separate groups.

The numerator evaluates to 24.

The denominator evaluates to 8.

24/8 evaluates to 3.

\(\displaystyle \dfrac{5^2 - 1}{2(7) - 6} = 3\)

 

[Otis]

I would think the value of "G(2)" would depend strongly on what "G" is!

We're given an expression for what G(2) equals, so we don't need the definition for G(x) to answer the question.

... do you mean G(2)= (1/2)- 1= -1/2 or G(2)= 1/(2- 1)= 1/2?

Halls, I think that you misread the given expression. The numerator is 2.