Sara says "−n" is always a negative number, because it has a minus sign in front
Sara says "−n" is always a negative number, because it has a minus sign in front. Her brother says if n is itself negative, then −n becomes positive. Who is right?
Who do you think is right? Pick one.
The answer: Her brother is right, if n = −4 then −n = 4 (positive)
Why
Sara is reading the minus sign in front of 'n' as 'this is a negative number', but that is not what it means. The minus sign there means 'the opposite of' — flip it to the other side of zero. If n is a positive number, its opposite is negative; but if n is already negative, its opposite is positive. Test it: let n = −4. Then −n means 'the opposite of −4', and the opposite of −4 is +4. So −n = 4, a positive number, even though it is written with a minus sign in front of the letter. Her brother is right: −n is positive whenever n is negative — the minus sign in front means 'opposite of', not 'make it negative'.
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