What is multiplicative inverse?

Question

Answer

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. ... Multiplicative inverses can be defined over many mathematical domains as well as numbers.

Answer

In simple language multiplicative inverse is reciprocal of a number
eg reciprocal of 1/2 is 2/1

Answer

Multiplicative Inverse:

The multiplicative inverse, also known as the reciprocal, of a number is a value that, when multiplied by the original number, gives a product of 1. In other words, it is the number that 'undoes' the effect of multiplication.

Definition:
The multiplicative inverse of a non-zero number 'a' is denoted as 'a⁻¹' and is calculated as 1/a.

Properties:
The multiplicative inverse possesses several important properties:

1. Reciprocal Property: The product of a number and its multiplicative inverse is always equal to 1. Mathematically, a * a⁻¹ = 1.

2. Existence: Every non-zero number has a multiplicative inverse, except for zero itself. If a number 'a' has a multiplicative inverse 'a⁻¹', then 'a⁻¹' also has 'a' as its multiplicative inverse.

3. Unique: The multiplicative inverse of a number is unique. There is only one number that, when multiplied by the original number, gives a product of 1.

4. Multiplication: Multiplying a number by its multiplicative inverse results in the cancellation of the two operations, leaving only the identity element, 1. This property is useful in simplifying expressions and solving equations.

Examples:

1. The multiplicative inverse of 2 is 1/2, as 2 * (1/2) = 1.
2. The multiplicative inverse of -5 is -1/5, as -5 * (-1/5) = 1.
3. The multiplicative inverse of 1/3 is 3, as 1/3 * 3 = 1.

Importance:

The concept of multiplicative inverses is fundamental in various mathematical areas, including algebra, calculus, and number theory. It allows for the division of numbers and the solving of equations involving multiplication. It is particularly useful in solving equations with fractions or variables by isolating the variable term.

Conclusion:

The multiplicative inverse of a number is its reciprocal, which, when multiplied by the original number, yields a product of 1. It possesses properties such as the reciprocal property, existence, uniqueness, and cancellation under multiplication. Understanding the concept of multiplicative inverses is crucial for various mathematical operations and problem-solving.

Answer

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the number.

Answer

Reciprocal of a number is called it's multiplicative inverse

Answer

In easy language we can say that reciprocal

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