So in general we find the opposite of a number by adding a '-' sign.
We're able to add the '-' sign to negative numbers as well, but I was wondering if this is correct:
Say we'd want to find the opposite of -7;
$$-(-7)$$
Is it true that one finds the opposite by calculating:
$$-1*-7=7$$
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$\begingroup$Yes it's true. If you want to find the opposite just add (or subtract) the number you need to reach 0, in this case +7, and then add (or subtract) +7 again... the result is the opposite. Adding (or subtracting) 2 times itself passing from negative to positive and viceversa is the same of multiplying for -1, where 1 is the neutral number in multiplication.
$\endgroup$ $\begingroup$Yes, that's true. The absolute value of a number is its distance from $0$. With your example, we see that $-7$ is $7$ away from $0$. If we choose to think that $-7$ is to the left of $0$, then the opposite of $-7$ is $7$ to the right of $0$. That would be $+7$.
The multiplicative identity is $1$. The opposite of the multiplicative identity is $-1$. Ergo multiplying by $-1$ gives the opposite of a number.
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