Bad wording, thanks. Consider the Natural Numbers 1 to 9 for a and b. I overlooked the initial wording because irrational numbers can not be represented as a simple ratio or fraction. The most common answer I receive for this problem is 7 because it is the only denominator that doesn’t produce a repeating or terminating decimal on a calculator. This typically starts a great conversation for my students on Rational and Irrational numbers.

So what rational number produces an irrational number? Are a & b natural? Or is a/b natural and you’re choosing b to make a irrational?

Bad wording, thanks. Consider the Natural Numbers 1 to 9 for a and b. I overlooked the initial wording because irrational numbers can not be represented as a simple ratio or fraction. The most common answer I receive for this problem is 7 because it is the only denominator that doesn’t produce a repeating or terminating decimal on a calculator. This typically starts a great conversation for my students on Rational and Irrational numbers.

So how can you produce an irrational number with a fraction of 1-9/1-9? Sorry to be dense. Does always in the question mean regardless of a?

By any chance are you thinking of repeating decimals as irrational?

See my first reply.