Opposite Numbers: Definition, Examples, and Properties

We will learn about opposite numbers in this post. The two operations addition and subtraction are involved in the concept behind opposite numbers.

Let’s learn what are opposite numbers.

Definition of Opposite Numbers

A number is called the opposite number of a given number if their sum is zero. More precisely, m is called the opposite number of n if m+n=0. Note that m=-n.

Sometimes opposite numbers are called additive inverses.

From the definition, it is clear that -n is the opposite number (or additive inverse) of n and vice-versa. For example, as 1+(-1)=0 we say that -1 is the opposite number of 1. Similarly, 1 is called the opposite number of -1.

Opposite integers definition

Let n be an integer. Then the number -n is called the opposite integer of n as the sum n+(-n)=0. For example, -20 is the opposite integer of 20.

From the definition of opposite integer, we observe that the opposite of a positive integer is a negative integer and the opposite of a negative integer is a positive integer.

Examples of opposite integers: The opposite integer of 10 is -10 and the opposite integer of -10 is 10 as 10+(-10)=0.

Examples of Opposite Numbers

Opposite numbers examples: In the tables below we have provided numbers with their opposites.

Opposites of Integers:

Integer	Opposite Integer	Reason
0	0	0+0=0
2	-2	2+(-2)=0
-3	3	-3+3=0
5	-5	5+(-5)=0
7	-7	7+(-7)=0
-7	7	-7+7=0
10	-10	10+(-10)=0

Opposites of Fractions:

Fraction	Opposite Fraction	Reason
$\frac{1}{2}$	$-\frac{1}{2}$	$\frac{1}{2}+(-\frac{1}{2})=0$
$\frac{3}{4}$	$-\frac{3}{4}$	$\frac{3}{4}+(-\frac{3}{4})=0$
$\frac{1}{10}$	$-\frac{1}{10}$	$\frac{1}{10}+(-\frac{1}{10})=0$
$-\frac{2}{15}$	$\frac{2}{15}$	$-\frac{2}{15}+\frac{2}{15}=0$

Opposites of Decimals:

Decimal	Opposite Decimal	Reason
0.1	-0.1	0.1+(-0.1)=0
1.1	-1.1	1.1+(-1.1)=0
-3.2	3.2	-3.2+3.2=0
10.5	-10.5	10.5+(-10.5)=0

Properties of Opposite Numbers

1. The sum of a number and its opposite is zero.
2. Numbers and their opposites have the same distance from 0 but they are located in the opposite direction on the number line. In other words, opposite numbers are symmetric about the origin on the number line.
3. The opposite of a positive number is the negative of that number. Similarly, the opposite of a negative number is the positive of that number.
4. A number and its opposite have the same absolute value. For example, -5 is the opposite of 5. Note that both 5 and -5 have the same absolute value 5 as |5|=|-5|=5.
5. Every real number has a unique opposite number.
6. The product of an integer (except 0) and its opposite is the negative of a perfect square. For example, 3×(-3)=-9 where 9 is a perfect square. The product of zero and its opposite number is equal to 0 itself.
7. The division of a number (except 0) and its opposite is always -1. For example, 7/ (-7) = -1.

Have You Read These:

Factors of a Number: A number is called a factor of a number M if that number completely divides M.

Even and Odd Numbers: If a number is divisible by 2, then it is called an even number. Otherwise, we call it an odd number.

Divisors of Numbers: Divisors of a number N are those numbers that completely divide N without a remainder.

Square Root: The square root of x=a² is √a.

FAQs of Opposite Numbers