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Here is one example of a practical use of multiplicative inverses. If you want to convert from feet to meters, you multiply by 0.3048. If you want to convert the other way round, you either DIVIDE by the same number, or you MULTIPLY by its multiplicative inverse. The same applies to many similar conversions.
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Why doesn't every real number have a multiplicative inverse?
The only real (or complex) number which does not have a multiplicative inverse is 0. There is nothing you can multiply by 0 to get 1.
What an multiplicative inverse property and real number?
For every real number, x, which is not zero, there exists a real number x' such that x * x' = x' * x = 1, the multiplicative identity.
Is the product of a fraction and its multiplicative inverse 1?
Yes. That's basically the definition of a multiplicative inverse.Also, this doesn't only apply to fractions - it applies to any real numbers.
Why can't you divide 100 by zero?
Because zero has no multiplicative inverse (no real number multiplied by 0 produces 1).
How do you prove the multiplicative inverse of a real number is unique?
Suppose p and q are inverses of a number x. where x is non-zero. Then, by definition, xp = 1 = xq therefore xp - xq = 0 and, by the distributive property of multiplication over subtraction, x*(p - q) = 0 Then, since x is non-zero, (p - q) = 0. That is, p = q. [If x = 0 then it does not have a multiplicative inverse.]
