Opposite Numbers: Definition, Examples, Properties, and Problems

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.

Examples: As 1+(-1)=0 we can say that -1 is the opposite number of 1. Similarly, 1 is called the opposite number of -1.

Examples of Opposite Numbers

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

Opposites of Integers:

IntegerOpposite IntegerReason
000+0=0
2-22+(-2)=0
-33-3+3=0
5-55+(-5)=0
7-77+(-7)=0
-77-7+7=0
10-1010+(-10)=0

Opposites of Fractions:

FractionOpposite FractionReason
$\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:

DecimalOpposite DecimalReason
0.1-0.10.1+(-0.1)=0
1.1-1.11.1+(-1.1)=0
-3.23.2-3.2+3.2=0
10.5-10.510.5+(-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.
  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 ad its opposite have the same absolute value. For example, -5 is the opposite of 5. Note that both 5 and -5 have the same absolue value 5 as |5|=|-5|=5.

Also Read:

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

Q1. what are opposite numbers?

Ans: The sum of opposite numbers is 0. So the opposite numbers are those numbers having the same distance from 0 on the number line. For example, -10 is the opposite number of 10 as both 10 and -10 have the same distance from 0.

Q2. What is the opposite number of 15?

Ans: The opposite number of 15 is -15.

Q3. What is the opposite of 0?

Ans: As 0+0=0, the number 0 itself is the opposite number of 0.

Q4. What is the opposite of 2?

Ans: -2 is the opposite number of 2.