What is Multiplicative Inverse?

The word meaning of ‘inverse’ is something opposite in effect. So, the multiplicative station of a number is a number the nullifies the impact of the number to identification 1. For this reason the multiplicative station of a number is a number through which the multiplication outcomes in 1.

You are watching: What is the definition of multiplicative inverse

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

For example: here is a team of 7 dimes.

*

To make them into teams of 1 each, we have to divide the by 7. The division is the reverse process of multiplication. Splitting by a number is indistinguishable to multiply by the mutual of the number.

Thus, 7 ÷7=7 × 1⁄7=1.

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

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

Multiplicative train station of a natural number

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

*

8 ÷8=8 × 18=1

Thus, the multiplicative train station of 8 is1⁄8.

In general, if a is a natural number, the multiplicative train station or reciprocal 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 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 station of a fraction

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

3⁄4× ?=1

By the nature of equality, if us multiply or division both sides of one equation by the very same number the equation remains true. So, by multiply the equation through 4 and dividing it by 3 on both sides offers us

3⁄4× ? × 4 ÷3 =1×4 ÷3

3⁄4× ? ×4⁄3=4⁄3

Canceling the common terms:

1× ? =4⁄3

Thus, the multiplicative inverse of3⁄4is4⁄3.

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

See more: How Do You Set The Time And Date On The Armitron Wr 165 Ft Watch Instructions

Fun facts:

The multiplicative inverse of zero is no defined.The multiplicative inverse of 1 is 1 itself.