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Q: Is it true that any real number has a multiplicative inverse?

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The statement is true only for non-zero fractions and it follows from the definition of a multiplicative inverse.

never a negative number * * * * * ... true if, by opposite, you mean the additive inverse. However, the multplicative inverse is also an opposite. And the multiplicative inverse of a negative number is always negative.

Zero does not have an opposite * * * * * While it is true that zero has no multiplicative opposite (or inverse), it certainly has an additive inverse, and that is also zero, since 0 + 0 = 0

The number that is its own "additive inverse" is zero. (x + 0 = x - 0)For the multiplicative inverse (1/x), the number 1 is its own inverse (also -1). (x times 1 = x/1)x = 1/x is only true where x = 1 or x = (-1)

First convert it into an improper fraction: 5 3/7 becomes 38/7. This is clear because "5" is simply "35/7" (do the math yourself) and 35/7 + 3/7 = 38/7. Additive inverse means "negative." Thus, the "additive inverse" of 38/7 is -38/7. This is true because 38/7 added to -38/7 is 0. That is the definition of an additive inverse. Multiplicative inverse means "reciprocal." Thus, the "multiplicative inverse" of 38/7 is 7/38. This is true because 38/7 multiplied by 7/38 is 266/266, or 1. That is the definition of multiplicative inverse.

False. Apart from the fact that there is no such thing as an opposite. If, by opposite, you mean negative (additive inverse), then start with a negative number. The negative of this will be positive, and so greater. If by opposite you mean the reciprocal (multiplicative inverse), start with a positive number less than one or a negative number less than -1.

zero has no opposite * * * * * While it is true that zero has no multiplicative opposite (or inverse), it certainly has an additive inverse, and that is also zero, since 0 + 0 = 0

No, not at all!I'll assume you mean the additive inverse, although the following examples can be adapted to the multiplicative inverse as well.The additive inverse of 5 is -5, and 5 is indeed greater than -5.However, the additive inverse of -5 is 5, and -5 is SMALLER than 5.

True

The answer depends on multiplicative WHAT!

The answer depends on whether you mean additive opposite (TRUE) or multiplicative opposite (FALSE).

Assuming that by "opposite" you mean the additive inverse, that is true for positive numbers.

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