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# What is the Multiplicative Inverse of a Negative Rational Number?

## Understanding the Basics

A rational number is defined as a number that can be written as a fraction, with an integer numerator and an integer denominator. A negative rational number is a rational number with a negative sign. A multiplicative inverse of a number is defined as the number that when multiplied with the original number yields a result of one. In other words, it is the reciprocal of a number. So, the multiplicative inverse of a negative rational number is the reciprocal of the number with a negative sign.

## Calculating the Multiplicative Inverse

To calculate the multiplicative inverse of a negative rational number, you must first take the reciprocal of the number. This is done by flipping the numerator and denominator of the fraction. After taking the reciprocal, the sign of the number should be changed to its opposite. For instance, the multiplicative inverse of -5/7 is 7/-5.

## Examples of Multiplicative Inverse of Negative Rational Numbers

To further understand the concept of the multiplicative inverse of a negative rational number, here are some examples:

- The multiplicative inverse of -15/4 is 4/-15.
- The multiplicative inverse of -2/5 is 5/-2.
- The multiplicative inverse of -7/9 is 9/-7.

## Uses of Multiplicative Inverse of Negative Rational Numbers

The multiplicative inverse of a negative rational number can be used in a variety of ways. It can be used in mathematical operations such as division and multiplication. It can also be used to solve equations and simplify fractions. Additionally, it can be used in scientific calculations and in finance.

## Conclusion

In summary, the multiplicative inverse of a negative rational number is the reciprocal of the number with a negative sign. It can be used in a variety of ways, from solving equations to simplifying fractions. Understanding this concept is essential for anyone dealing with rational numbers.