Question

The multiplicative inverse of -8/7​

Answer 1

Answer:

The multiplicative inverse of a number is defined as a number which when multiplied by the original number gives the product as 1. The multiplicative inverse of 'a' is denoted by  a-1 or 1/a. In other words, when the product of two numbers is 1, they are said to be multiplicative inverses of each other. 

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Answer 2

Answer:The multiplicative inverse of a number say, N is represented by 1/N or N-1. It is also called reciprocal, derived from a Latin word ‘reciprocus‘. The meaning of inverse is something which is opposite. The reciprocal of a number obtained is such that when it is multiplied with the original number the value equals to identity 1. In other words, it is a method of dividing a number by its own to generate identity 1, such as N/N = 1.

Fact: When a number is multiplied by its own multiplicative inverse the resultant value is equal to 1.

Consider the examples, the multiplicative inverse of 3 is 1/3, of -1/3 is -3, of 8 is 1/8 and of 4/7 is -7/4. But the multiplicative inverse of 0 is infinite, because of 1/0 = infinity. So, there is no reciprocal for a number ‘0’. Whereas the multiplication inverse of 1 is 1 only

Definition

The multiplicative inverse of a number for any n is simply 1/n. It is denoted as:

1 / x  or  x-1 (Inverse of x)

It is also called as the reciprocal of a number and 1 is called the multiplicative identity.

Finding the multiplicative inverse of natural numbers is easy, but it is difficult for complex and real numbers.

For example, the multiplicative inverse of 3 is 1/3, of 47 is 1/47, of 13 is 1/13, of 8 is 1/8, etc, whereas the reciprocal of 0 will give an infinite value or 1/0 = ∞. Now to check whether the inverse of a number is correct or not, we can perform the multiplication operation, such that;

3 x 1/3 = 1

47 x 1/47 = 1

13 x 1/13 = 1

8 x 1/8 = 1

Hence, you can see in all the above four cases, we get the identity number 1. So it is proved.

Multiplicative Inverse of Natural Number

If x is any natural number (0,1,2,3,4,5,6,7,…), then the multiplicative inverse of x will be 1/x. For example, the multiplicative inverse of 5 is 1/5.

Step-by-step explanation:

The product of a number and its multiplicative inverse is 1.

x. x-1 = 1

For example, consider the number 13.

The multiplicative inverse of 13 is 1/13.

According to the property,

13. (1/13) = 1

Hence Proved.