The multiplicative station of a number is a number which once multiplied v the initial number equates to to one. Here, the original number have to never be same to 0. The multiplicative inverse of a number X is stood for as X-1 or 1/X. The multiplicative train station of a number is also referred to together its reciprocal.

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Multiplicative train station Example

Multiplicative station of One: The multiplicative station of one is one only due to the fact that 1x1=1.

Multiplicative station of Zero: The multiplicative inverse of zero does not exist. This is due to the fact that 0xN=0 and also 1/0 is undefined.

Multiplicative inverse of a organic Number: The multiplicative train station of a natural number X is X-1 or 1/X. For example, the multiplicative station of 256 is 1/256 since 256x1/256=1.

Multiplicative inverse of a an unfavorable Number: The multiplicative train station of a natural number -Y is -Y-1 or 1/-X. For example, the multiplicative train station of -8 is 1/-8 since -8x1/-8=1.

Multiplicative station of A Fraction: The multiplicative inverse of a fraction x/y is y/x. In situation the fraction is a unit fraction, climate its multiplicative inverse will be the value present in the denominator. Because that example, the multiplicative train station of 5/6 is 6/5 and also the multiplicative station of 1/9 is 9.

4 x 7 = 1 2 x 3 = 1

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Multiplicative inverse Property

The multiplicative inverse residential property states the a number P, once multiplied v its multiplicative inverse, give the an outcome as one.




3/4x 4/3=1

How to uncover Multiplicative Inverse?

The easiest trick come finding the multiplicative of any rational number (except zero) is just flipping the numerator and denominator.

We can likewise find the multiplicative station by using a linear equation as follows. In the below equation y is the unknown multiplicative inverse.

8/9 * y = 1

y= 1/ (8/9)



Multiplicative train station Of A complex Number

The multiplicative inverse of any complicated number x+yi is 1/(x+yi). In this multiplicative inverse, x and also y space rational numbers and i is a radical.

In this case, we must always remember come rationalise the multiplicative inverse. Our final answer should not contain any kind of radicals in the denominator.


To rationalise multiply the numerator and denominator of 1/(x+yi) through (x-yi). This will provide you (x-yi)/(x2-(yi)2).

When we execute this procedure using numbers instead of variables, us will gain a continuous whole number in the denominator and radicals in the numerator. In ~ this step, our multiplicative train station is rationalised.

Problems: find the Multiplicative Inverse

Problem 1: What is the reciprocal of 105/7.

Solution: The reciprocal of 105/7 is 7/105.

If we further simplify. Us get,

7/105 = 1/15

So, the mutual of 15 is 1/15, because, 15 × 1/15 = 1.

Hence it satisfies the reciprocal property.

Problem 2: find the reciprocal of y2

Solution: The reciprocal of y2 is 1/y2 or y-2

Verification: y2 × y-2 = 1

1 = 1

Did friend know?

If X-1 or 1/X is the multiplicative inverse of X, then X is the multiplicative station of X-1 or 1/X. This is because of the commutative home of multiplication, which states that the an outcome does not change if the order of numbers is changed.

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One is called the multiplicative identity because when multiplied by itself, it provides itself together the result. In various other words, 1 is the reciprocal of itself. This deserve to be created as 1x1=1.