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. Thus the multiplicative 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 inverse of the number a, if a × b = 1.

For example: right here is a group of 7 dimes.


To do them into teams of 1 each, we must divide the by 7. The department is the reverse procedure of multiplication. Splitting by a number is tantamount to multiply by the mutual of the number.

Thus, 7 ÷7=7 × 1⁄7=1.

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

Another word because that multiplicative inverse is ‘reciprocal’. It comes from the Latin word ‘reciprocus’ which means returning.

Multiplicative train station of a organic number

In the given image to do the unit groups of 8 stars, we need to divide the by 8.


8 ÷8=8 × 18=1

Thus, the multiplicative inverse of 8 is1⁄8.

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

Multiplicative inverse of a unit fraction

To make a unit fraction, say1⁄4to 1, we require 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 should we multiply the fraction3⁄4to gain 1?

3⁄4× ?=1

By the properties of equality, if we multiply or division both sides of one equation through the exact same number the equation remains true. So, by multiply the equation by 4 and also dividing the by 3 on both sides provides us

3⁄4× ? × 4 ÷3 =1×4 ÷3

3⁄4× ? ×4⁄3=4⁄3

Canceling the typical terms:

1× ? =4⁄3

Thus, the multiplicative inverse 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.