A multiplicative inverse, also known as a reciprocal, is a number that when multiplied by a given number, results in a product of 1. In other words, it is the number that "undoes" the effect of multiplication.
The multiplicative inverse of a number can be proved using the property of fractions that states: a/b = 1 if and only if b/a = 1. Therefore, to prove the multiplicative inverse of a number, we need to show that when multiplied together, the number and its inverse result in a product of 1.
Yes, the multiplicative inverse of a number is always unique. This is because if there were two different numbers that when multiplied together resulted in a product of 1, they would essentially be the same number, just written in different forms.
No, not every number has a multiplicative inverse. In order for a number to have a multiplicative inverse, it must not be equal to 0. This is because when a number is multiplied by 0, the result is always 0, not 1.
The multiplicative inverse is used in solving equations by "undoing" the effect of multiplication. For example, if a variable is being multiplied by a number, we can divide both sides of the equation by the same number (its multiplicative inverse) to isolate the variable and solve for its value.