Question

Silvie states that the sum of a rational number and an irrational number is sometimes rational and sometimes irrational. Which statement correctly describes whether Silvie is correct or incorrect?
A) Silvie is incorrect; the sum of a rational number and an irrational number is always irrational

B) Silvie is correct; the sum of a rational number and an irrational number may be rational or irrational

C) Silvie is incorrect; the sum of a rational number and an irrational number is always rational

Answer 1

Answer:

A) Silvie is incorrect; the sum of a rational number and an irrational number is always irrational

Step-by-step explanation:

The concept of adding rational and irrational numbers states that the result will always be irrational.

Take for instance the addition of 4.5 and 3.142857

4.5 is a rational number because it can easily be expressed in fractions while 3.142857 is irrational because it can't be expressed as a simple fraction.

The addition of these two numbers gives 7.642857

7.642857 is an irrational number.

Similarly, any sum of two numbers (rational and irrational) will always result in irrational number.

Hence, Silvie is incorrect.