Opposite of a Negative Number
The opposite of a negative number is positive — double negation cancels out — a key integer concept in Grade 8 math (Yoshiwara Core Math). The opposite of any number n is −n; the opposite of −5 is −(−5) = 5. On a number line, a number and its opposite are equidistant from zero on opposite sides. The notation −(−x) = x is fundamental for simplifying expressions, subtracting negatives, and understanding the involutory property of negation.
Key Concepts
Property The opposite of a negative number is a positive number. We write the opposite of $ 6$ as $ ( 6)$, so $$ ( 6) = 6$$.
Examples The opposite of $ 25$ is written as $ ( 25)$, which simplifies to $25$. If you cancel a debt of 30 dollars, your financial change is $ ( 30)$ dollars, which is a gain of $30$ dollars. On a number line, the opposite of $ 8.2$ is found by reflecting it over zero, resulting in $8.2$.
Explanation Taking the 'opposite' of a number flips it across zero on the number line. If you flip a negative number, it lands on the positive side. So, a double negative like $ ( 6)$ becomes a positive $6$.
Common Questions
What is the opposite of a negative number?
A positive number. The opposite of −7 is 7, because −(−7) = 7.
How do you show the opposite of −4 on a number line?
Find −4; its opposite is at the same distance on the other side: +4.
Why does −(−x) = x?
Negation reverses direction. Negating a negative reverses it back to positive.
What is the absolute value of a negative number?
Always positive: |−8| = 8. Absolute value gives magnitude; opposite gives sign change.
How does this connect to subtracting negatives?
a − (−b) = a + b. So 5 − (−3) = 5 + 3 = 8.