Additive inverse of a number

Elementary SchoolMiddle School

Definition

The opposite sign of a number. Flipping the sign of a number from positive (+) to negative (-) or vice versa. For example, the additive inverse of 10 and -5 is -10 and 5 respectively. When adding a number with its additive inverse, it will always result in a zero. A double additive inverse is the rule applied twice, and would have no effect as it cancels out each other.

Worked examples

\(10 + (-10) = 0\)

The additive inverse of 10 is -10; together they sum to zero.

\(-5 + 5 = 0\)

The additive inverse of -5 is 5; adding them cancels to zero.

\(-(-8) = 8\)

A double additive inverse returns the original number.

Common mistakes

\(7 + (-7) = -14\) → \(7 + (-7) = 0\) Adding a number and its additive inverse always equals zero, not the sum of their absolute values.
The additive inverse of \(3\) is \(\frac{1}{3}\) → The additive inverse of \(3\) is \(-3\) Additive inverse flips the sign; reciprocal (multiplicative inverse) flips the fraction.
\(-(-x) = -x\) → \(-(-x) = x\) Two negatives cancel, returning the original value.

Where you'll use it next

You'll use additive inverses to solve equations by isolating variables, simplify expressions, understand subtraction as adding the inverse, and work with negative numbers in algebra, coordinate geometry, and beyond.

Found in 1 StudyPug lesson

Adding Integers: Mastering the Fundamentals with Examples

Grade 7 Math

Discover effective strategies for adding integers, from basic rules to advanced techniques. Enhance your problem-solving skills with our comprehensive lessons and practice examples.

7th Grade7th