Table of Contents

## Does every rational number has a multiplicative inverse?

1 and -1 are the only rational numbers which are their own reciprocals. No other rational number is its own reciprocal. We know that there is no rational number which when multiplied with 0, gives 1. Therefore, rational number 0 has no reciprocal or multiplicative inverse.

## How do you find the multiplicative inverse of a rational number?

Reciprocal or Multiplicative inverse: Dividing a number by 1 is the multiplicative inverse for Rational, natural, whole numbers and integers, since multiplying it to the original number always results in 1. Hence, ax 1/a = 1/a x a = 1, where a can be rational number or natural number or integer.

## Can you find a rational number whose multiplicative inverse is 1?

No, we cannot find a rational number whose multiplicative inverse is –1.

## What is the product of a rational number and its multiplicative inverse?

Product of a Rational Number and its Multiplicative inverse is 1.

## Which is the only rational number with a multiplicative inverse?

1 and -1 are the only rational numbers which are their own reciprocals. No other rational number is its own reciprocal…. We know that there is no rational number which when multiplied with 0, gives 1. Therefore, rational number 0 has no reciprocal or multiplicative inverse.

## Is the property of multiplicative inverse really that simple?

Yes, it is. The multiplicative inverse and multiplicative inverse property are really that simple. A multiplicative inverse is a reciprocal. A reciprocal is one of a pair of numbers that when multiplied with another number equals the number 1.

## Which is the only rational number which is its own reciprocal?

1 and – 1 are the only rational numbers which are their own reciprocals. Let us see some example problems based on the above concept. Hence multiplicative inverse of 9/11 is 11/9. Hence multiplicative inverse of -5 is -1/5. What is the multiplicative inverse of the mixed number 00 2 5/7

## Which is the multiplicative inverse of x + yi?

The multiplicative inverse of any complex number x+yi is 1/ (x+yi). In this multiplicative inverse, x and y are rational numbers and i is a radical. In this case, we must always remember to rationalise the multiplicative inverse. Our final answer should not contain any radicals in the denominator.