The additive inverse of a number is its . When you add a number to its additive inverse, the result is always zero . Core Concept
Do not confuse the with the multiplicative inverse (reciprocal). Additive Inverse Multiplicative Inverse Goal Product of Action Change the sign Flip the fraction Example (for 5) -5negative 5 15one-fifth Additive Inverse 127-3.3
: Used to "zero out" constants to isolate variables (e.g., subtracting from both sides of additive inverse
Finding an additive inverse is a simple 1-step procedure: . For Fractions
: Subtraction can be rewritten as adding the opposite (e.g., Balancing Accounts : In finance, if you owe -50negative 50 ), a payment of +50positive 50 ) is the additive inverse that brings your balance to Common Mistake: Inverse vs. Reciprocal The additive inverse of a number is its
The numerical values of the numerator and denominator do not change. Only the sign of the entire fraction flips. The inverse of 23two-thirds −23negative two-thirds The inverse of −59negative five-nineths 59five-nineths For Algebraic Expressions
To find the inverse of an expression, multiply the entire thing by -1negative 1 or flip the sign of every term. : Inverse : Practical Applications Only the sign of the entire fraction flips
The states that for any real number , there exists a number −anegative a such that: a+(−a)=0a plus open paren negative a close paren equals 0 Positive numbers : The inverse is negative (e.g., 8→-88 right arrow negative 8 Negative numbers : The inverse is positive (e.g., -12→12negative 12 right arrow 12 Zero : The only number that is its own additive inverse ( How to Find It