Question

Jamie says that the value of -1 • x is always equal to the value of × ÷ (-1), knowing that the x is the same value in both problems. Explain whether Jamie is correct or incorrect.

Answer 1

Jamie is correct

The two expressions
`- 1 \cdot x` and
`(x)/(-1)` are equivalent

Explanation:

We are asked to find if the two expressions
`- 1 \cdot x` and
`(x)/(-1)` are equivalent

Let's take the expression

`- 1 \cdot x`

`-1\cdot \:x = -x`

Take the second expression

`(x)/(-1)`

`\mathrm{Apply\:the\:fraction\:rule}:\:(a)/(-b)=-(a)/(b)`

`(x)/(-1) = - (x)/(1) = - x`

And we get both expresions as

`-1\cdot \:x = -x` and
`(x)/(-1) = -x`

-x = -x for all x

So the two expressions are equivalent i.e the resultant values are same for any value of x