Opposite Numbers

Sommaire

In short: Opposite numbers are mirror partners across zero, each the same size but with a different sign, like 9 and -9, and every such pair has a sum of 0.

6th GradeNumbers and Operations6.NS.C.6a

What is Opposite Numbers?

Every number except zero has a mirror partner across zero, and together the two make opposite numbers. They have the same size but carry different signs: 9 sits nine steps right of zero while its partner sits nine steps left.

Precisely, the opposite of $a$ is $-a$, and $a + (-a) = 0$. Flipping twice returns the starting value, $-(-a) = a$. Zero is its own opposite.

How to spot it

A story pairs a gain with a loss of the same amount, like earning $25 and then spending $25.
A question asks for the partner of a number, or for a value that adds with it to give 0, which is the job of opposite numbers.
Two marked points lie equally far from the origin of a line, one left and one right.
A double minus appears, as in $-(-12)$, and you must decide the sign of the result.

The method

Locate the number on a line and measure how far it sits from 0.
Jump the identical distance to the opposite side of 0.
Write the new number with the opposite sign: positive becomes negative and negative becomes positive.
Check that the sum of the pair is 0; if it is not, the two values are not opposite numbers.

Each pair is a mirror image across the point 0.

Opposite Numbers: solved example

Problem

A diver in a Florida quarry is at $-18$ feet. A drone hovers at the opposite number of that value above the surface. How high is the drone, and what do the two positions sum to?

Solution

The opposite of $-18$ is $-(-18) = 18$, so the drone is 18 feet above the surface.

Check the sum: $-18 + 18 = 0$.

Try it

Question 1

Find the opposite of $-4.6$.

Show the answer

4.6, because $-4.6 + 4.6 = 0$.

Question 2

Simplify $-(-(-5))$.

Show the answer

$-(-5) = 5$, then $-5$ again, so the result is $-5$.

Opposite Numbers vs. Reciprocal

Opposites add to 0 and flip the sign: 5 and $-5$. Reciprocals multiply to 1 and flip the fraction: 5 and $\frac{1}{5}$. Only the first kind share a distance from zero.

Reciprocal

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Whole dictionary: A–Z · 6th Grade · Numbers and Operations

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