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

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

• A. a*(1/a)=0
• B. a+(1/a)=1
• C. (a)(a)=a^2
• D. a*(1/a)=1

Answer: (D)

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).