What is Multiplicative Inverse?
The word an interpretation of ‘inverse’ is something opposite in effect. So, the multiplicative train station of a number is a number that nullifies the affect of the number to identification 1. For this reason the multiplicative train station of a number is a number whereby the multiplication results in 1.
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That is, number b is the multiplicative station 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 that by 7. The division is the reverse procedure of multiplication. Separating by a number is equivalent to multiplying by the mutual of the number.
Thus, 7 ÷7=7 × 1⁄7=1.
Here,1⁄7is referred to as the multiplicative station of 7. Similarly, the multiplicative inverse of 13 is1⁄13.
Another word for multiplicative inverse is ‘reciprocal’. It comes from the Latin word ‘reciprocus’ which means returning.
Multiplicative inverse of a organic number
In the provided 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 herbal number, the multiplicative station or mutual of a is1⁄a.
Multiplicative station of a unit fraction
To make a unit fraction, say1⁄4to 1, we need to include it 4 times. Or in various other words, multiply1⁄4by 4. Thus, the multiplicative inverse of1⁄4is 4.
In general, the multiplicative train station or mutual of unit fraction1⁄xis x.
Multiplicative inverse of a fraction
By what number need to we main point the fraction3⁄4to obtain 1?
By the properties of equality, if we multiply or divide both political parties of one equation by the exact same number the equation remains true. So, by multiplying the equation by 4 and dividing it by 3 top top both sides gives us
3⁄4× ? × 4 ÷3 =1×4 ÷3
3⁄4× ? ×4⁄3=4⁄3
Canceling the usual terms:
1× ? =4⁄3
Thus, the multiplicative station of3⁄4is4⁄3.
The multiplicative inverse or reciprocal of a fractiona⁄bisb⁄a.
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Fun facts:The multiplicative station of zero is not defined.The multiplicative station of 1 is 1 itself.