What is Multiplicative Inverse?

The word definition of ‘inverse’ is something the contrary in effect. So, the multiplicative train station of a number is a number the nullifies the impact of the number to identity 1. For this reason the multiplicative train station of a number is a number through which the multiplication results in 1.

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That is, number b is the multiplicative train station of the number a, if a × b = 1.

For example: below is a group of 7 dimes.


To make them into groups of 1 each, we must divide it by 7. The department is the reverse process of multiplication. Separating by a number is tantamount to multiply by the mutual of the number.

Thus, 7 ÷7=7 × 1⁄7=1.

Here,1⁄7is called the multiplicative inverse of 7. Similarly, the multiplicative station of 13 is1⁄13.

Another word for multiplicative station is ‘reciprocal’. It comes from the Latin native ‘reciprocus’ which way returning.

Multiplicative train station of a natural number

In the provided image to make the unit groups of 8 stars, we must divide it by 8.


8 ÷8=8 × 18=1

Thus, the multiplicative station of 8 is1⁄8.

In general, if a is a natural number, the multiplicative train station or mutual of a is1⁄a.

Multiplicative station of a unit fraction

To make a unit fraction, say1⁄4to 1, we need to add it 4 times. Or in various other words, multiply1⁄4by 4. Thus, the multiplicative station of1⁄4is 4.

In general, the multiplicative inverse or mutual of unit fraction1⁄xis x.

Multiplicative train station of a fraction

By what number need to we multiply the fraction3⁄4to get 1?

3⁄4× ?=1

By the nature of equality, if us multiply or divide both political parties of an equation by the same number the equation continues to be true. So, by multiply the equation by 4 and also dividing it by 3 ~ above both sides offers us

3⁄4× ? × 4 ÷3 =1×4 ÷3

3⁄4× ? ×4⁄3=4⁄3

Canceling the typical terms:

1× ? =4⁄3

Thus, the multiplicative train station of3⁄4is4⁄3.

The multiplicative station or mutual of a fractiona⁄bisb⁄a.

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Fun facts:

The multiplicative train station of zero is no defined.The multiplicative station of 1 is 1 itself.