What is Multiplicative Inverse?

The word meaning of ‘inverse’ is something the contrary in effect. So, the multiplicative inverse of a number is a number the nullifies the influence of the number to identification 1. Hence the multiplicative train station of a number is a number through which the multiplication results in 1.

You are watching: What is the multiplicative inverse of 7

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

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

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To make them into teams of 1 each, we have to divide the by 7. The department is the reverse procedure of multiplication. Dividing by a number is identical 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 inverse of 13 is1⁄13.

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

Multiplicative train station of a natural number

In the given image to make the unit groups of 8 stars, we have to divide the by 8.

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8 ÷8=8 × 18=1

Thus, the multiplicative station of 8 is1⁄8.

In general, if a is a organic number, the multiplicative inverse 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 station or mutual of unit fraction1⁄xis x.

Multiplicative inverse of a fraction

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

3⁄4× ?=1

By the properties of equality, if we multiply or division both sides of one equation by the same number the equation remains true. So, by multiply the equation by 4 and dividing that by 3 top top 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 inverse of3⁄4is4⁄3.

The multiplicative train station or reciprocal of a fractiona⁄bisb⁄a.

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Fun facts:

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