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Which statement about rational and irrational numbers is always true?
Any irrational number added to any rational number is equal to a rational number.
Any irrational number added to any irrational number is equal to a rational number.
Any irrational number multiplied by any non-zero rational number is equal to a rational number.
Any irrational number multiplied by any non-zero rational number is equal to an irrational number.

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Answer:

  (d)  Any irrational number multiplied by any non-zero rational number is equal to an irrational number.

Step-by-step explanation:

If a number cannot be represented by a fraction, multiplying it by a fraction will not change that fact.

  Any irrational number multiplied by any non-zero rational number is equal to an irrational number.

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Counterexamples

(a) 3+π is irrational

(b) π + π is irrational

(c) 3π is irrational

(d) true