The number with the same absolute value and different sign.
The opposite of a number is the value that is the same distance from zero on the number line, but on the other side. It has the same absolute value but the opposite sign.
For example:
-
The opposite of 5 is –5
-
The opposite of –3 is 3
-
The opposite of 0 is 0 (zero is its own opposite)
Every number and its opposite are mirror images of each other across zero. Add them together and they always cancel out: 5 + (–5) = 0. This is why opposites are also called additive inverses — they are the inverse pair for addition, always summing to zero, the identity element for addition.
The concept of opposites is closely related to absolute value. Two numbers are opposites if they share the same absolute value but carry different signs. For instance, |5| = |–5| = 5, confirming that 5 and –5 are opposites.
When Do Students Learn About Opposites of Numbers?
Students encounter opposites as soon as they begin working with negative numbers and the number line.
Grades 3–5 – Opposites on the Number Line
Students identify opposite numbers by locating values that are equidistant from zero on either side of the number line.
Grades 6–8 – Opposites, Absolute Value, and Additive Inverses
Students connect opposites to absolute value and the additive inverse property, applying the concept when adding and subtracting integers.
Grades 9+ – Opposites in Algebra and Advanced Contexts
Students work with opposites in algebraic expressions, equation solving, and functions, including recognizing opposite transformations in graphs.
