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.
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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 team of 7 dimes.
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.
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?
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.