Classify (
7
)·(3) as rational or irrational, and explain your reasoning.
A) Suppose an irrational times a nonzero rational = rational, then irrational =
rational
rational
. This means irrational = rational. Thus the irrational number
7
times the rational number 3 equals 3
7
, which is both rational and irrational.
B) Suppose an irrational times a nonzero rational = rational, then irrational =
rational
rational
. This means irrational = rational, which is a contradiction. Thus the irrational number
7
times the rational number 3 equals the rational number 3
7
.
C) Suppose an irrational times a nonzero rational = rational, then irrational =
rational
rational
. This means irrational = rational, which is a contradiction. Thus the irrational number
7
times the rational number 3 equals the irrational number 3
7
.
D) Suppose an irrational times a nonzero rational = rational, then irrational =
rational
rational
. This means irrational = rational, which is a contradiction. Thus the irrational number
7
times the rational number 3 equals 3
7
, which is neither rational nor irrational.