Final answer:
The statement is true; an irrational number multiplied by its reciprocal always equals the rational number 1. This is because multiplying any number by its reciprocal (which is the inverse of the number) results in 1, which is a rational number.
Step-by-step explanation:
Regarding the statement that an irrational number multiplied by its reciprocal equals a rational number, the answer is A) True. A reciprocal is defined as the inverse of a number, such that when a number is multiplied by its reciprocal, the result is 1. This is because the reciprocal of a number a is 1/a, and when a is multiplied by 1/a, the result is (a * 1/a), which simplifies to 1.
The fact that we are dealing with an irrational number does not change this basic property. No matter if the number is irrational or rational, as long as it is not zero, its reciprocal will give a product of 1 when multiplied together. Since 1 is a rational number (it can be expressed as a ratio of two integers, for example, 1/1), multiplying an irrational number by its reciprocal always results in the rational number 1.
Remember, algebra dictates that as long as we perform the same operation on both sides of the equals sign, the expression remains an equality. As such, both the quantity in the numerator and the denominator cancel each other out, leaving us with 1, which is a rational number.