Which expression shows the product of a number and its multiplicative inverse equals 1?

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Multiple Choice

Which expression shows the product of a number and its multiplicative inverse equals 1?

Explanation:
The key idea here is the multiplicative inverse: a number times its reciprocal equals 1. For any nonzero a, the reciprocal is 1/a, and multiplying them gives a * (1/a) = 1. This is the defining relationship that shows why this expression is the correct one. The other expressions don’t produce 1 in general: multiplying a by itself gives a^2, not 1; adding a and its reciprocal is not guaranteed to equal 1; and a*(1/a) = 1 only when a is not zero (since 1/0 is undefined).

The key idea here is the multiplicative inverse: a number times its reciprocal equals 1. For any nonzero a, the reciprocal is 1/a, and multiplying them gives a * (1/a) = 1. This is the defining relationship that shows why this expression is the correct one. The other expressions don’t produce 1 in general: multiplying a by itself gives a^2, not 1; adding a and its reciprocal is not guaranteed to equal 1; and a*(1/a) = 1 only when a is not zero (since 1/0 is undefined).

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