The term inverse is used alternatively in place of inverted, contrary, reverse, etc many times in our everyday life. Inverse in mathematics means a reciprocal quantity or mathematical expression which is the result of inversion. These are four types of inverse operations, namely additive inverse property, additive property, multiplicative inverse property, and multiplicative property. In this article, we will discuss in detail about the additive inverse and the multiplicative inverse. We will also solve some examples related to both the properties so that this topic becomes clearer to you.
What Do You Mean by Additive Inverse?
When any number is added to a given number and their sum becomes zero, both the numbers become the additive inverse of each other. Additive inverse is very useful in solving questions of algebra. You went to a gym and exercised daily to gain 5kgs. You were successful in doing so. However, because of viral fever, you lost 5kgs. This nullifies the effect of the gain. This is how additive inverse works. Examples of additive inverse are: 17 is the additive inverse of -17, -35 is the additive inverse of 35, etc.
Additive Inverse In Case of Different Scenarios
- In the case of Real Numbers: Whole numbers, natural numbers, integers, decimals, and fractions are part of real numbers. Any number that falls within the set of real numbers has the additive inverse as the negative of the number in consideration. Example: 0.5678 is the additive inverse of -0.5678.
- In the case of Complex Numbers: Complex numbers are imaginary numbers. Complex numbers also have the property of additive inverse. The additive inverse of the complex number Z = a + ib is -Z = -a – ib. Example: i + 5 is the additive inverse of -i – 5.
What Do You Mean by Multiplicative Inverse?
In simple language, multiplicative inverse is a number which when multiplied with the number in consideration results in the product becoming 1. We can also say that when the product of any two given numbers results in 1, both numbers are multiplicative inverse of each other. Let us understand the multiplicative inverse with the help of an example. 5 is the multiplicative inverse of 1/5 because the product of 5 and 1/5 is 1.
Multiplicative Inverse In Case of Different Scenarios
- In the case of a Natural Number: All the numbers ranging from 1 to infinity come under the umbrella of natural numbers. 1/x is the multiplicative inverse of a natural number x. Example: The multiplicative inverse of 27 is 1/27.
- In the case of a Unit Fraction: A fraction with the value of numerator as one is called a unit fraction. Example: 1/77. 1/x is the multiplicative inverse of a unit fraction x. Example: 55 is the multiplicative inverse of 1/55.
- In the case of a Fraction: A fraction is a quantity that is the part of a whole. y/x is the multiplicative inverse of x/y. Here, the value of the denominator of the number in consideration should not be equal to 0. Example: 13/17 is the multiplicative inverse of 17/13. One important thing to note about the multiplicative inverse of fractions is that its value can be obtained by flipping the position of the value of the numerator and the denominator of the fraction in consideration.
- In the case of Negative Integers: As we did in case of natural numbers, in negative integers also, the multiplicative inverse of the negative number -x is -1/x. Example: -16 is the multiplicative inverse of -1/16.
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