Additive Inverse
In short: The additive inverse of a number is its opposite, the one value that sits the same distance from zero on the other side and adds with it to give exactly zero.
7th GradeNumbers and Operations7.NS.A.1a
What is Additive Inverse?
Every number has a mirror partner across zero, and that partner is its additive inverse. The partner of \(9\) is \(-9\), and the partner of \(-2.4\) is \(2.4\).
Formally, the additive inverse of \(a\) is the number \(-a\) for which \(a + (-a) = 0\). Zero is its own partner. The idea explains why subtracting a number is the same as adding its opposite: \(a – b = a + (-b)\).
How to spot it
- A problem asks for the opposite of a number, or for what must be added to reach zero.
- A temperature, elevation or bank balance returns to its starting level after two equal and opposite changes.
- Two points on a number line are equally far from zero but lie on different sides.
- You must rewrite a subtraction as an addition to combine signed numbers more easily.
The method
- Look at the sign of the given number and its distance from zero on the number line.
- Keep the same distance but flip the side: change a positive sign to negative, or negative to positive.
- Check by adding the original number and your answer; the sum must be \(0\).
- Use it to subtract: replace \(a – b\) by \(a + (-b)\), then add.
Additive Inverse: solved example
Problem
A scuba diver is at an elevation of \(-35\) feet. By how many feet must she rise to be back at the surface, and what is the additive inverse of \(-35\)?
Solution
The surface is at \(0\). The needed change \(x\) satisfies \(-35 + x = 0\), so \(x = 35\).
The opposite of \(-35\) is \(35\), and the check is \(-35 + 35 = 0\).
Try it
Question 1
Find the additive inverse of \(-\frac{7}{12}\).
Show the answer
It is \(\frac{7}{12}\), because \(-\frac{7}{12} + \frac{7}{12} = 0\).
Question 2
Rewrite \(14 – (-6)\) as an addition and evaluate it.
Show the answer
Subtracting \(-6\) means adding its opposite: \(14 + 6 = 20\).
Additive Inverse vs. Integer Rules
The additive inverse is one specific partner number whose sum with the original is zero. The integer rules are the full set of sign patterns for adding, subtracting, multiplying and dividing. Do not mix it up with the reciprocal, which is the multiplicative partner: the opposite of 4 is -4, while the reciprocal of 4 is one fourth.
Keep going
Lessons
Worksheets and quizzes
- Adding and Subtracting Rational Numbers – Worksheet
- Adding and Subtracting Rational Numbers – Quiz
- Integers and Rational Numbers on the Number Line – Worksheet
- Integers and Rational Numbers on the Number Line – Quiz
Related words
Whole dictionary: A–Z · 7th Grade · Numbers and Operations