Numbers with the same absolute value and opposite signs. Two numbers whose sum is 0.
Opposites, also called additive inverses, are pairs of numbers that are the same distance from zero on the number line but sit on opposite sides. When added together, they always cancel each other out and sum to zero.
For example:
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6 and –6 are opposites: 6 + (–6) = 0
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12 and –12 are opposites: 12 + (–12) = 0
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0.5 and –0.5 are opposites: 0.5 + (–0.5) = 0
The term "additive inverse" comes from the inverse property of addition: for every number, there is another number that brings the sum back to zero, the identity element for addition. That partner is the additive inverse.
Opposites always share the same absolute value. The absolute value of 6 is 6, and the absolute value of –6 is also 6. What differs is the sign: one is positive, the other is negative.
This entry connects closely to opposite (of) and the inverse property, both of which describe related ideas from slightly different angles. Together, they give students a complete picture of how numbers and their partners behave under addition.
When Do Students Learn About Opposites and Additive Inverses?
Students encounter opposites as soon as they begin working with negative numbers.
Grades 3–5 – Opposites on the Number Line
Students identify opposite numbers as mirror images of each other across zero, building intuition for the additive inverse relationship.
Grades 6–8 – Additive Inverses in Integer Operations
Students apply the additive inverse formally when adding and subtracting integers, and connect it to the inverse property of addition.
Grades 9+ – Additive Inverses in Algebra and Beyond
Students use additive inverses when solving equations, simplifying expressions, and working with vectors and advanced algebraic structures.
