Question

sums & products of rational & irrational numbers quick check
what does the closure property tell you about the rational and irrational numbers under subtraction? (1 point)
the difference of two rational numbers will always be a rational number.
the difference of a rational number and an irrational number cannot be determined.
the difference of a rational number and an irrational number will always be a rational number.
the difference of two irrational numbers will always be an irrational number.

Explanation:

The Closure Property states that when an operation is performed on elements of a set, the result is also an element of that set. For rational numbers, subtracting two rationals (expressed as $\frac{a}{b}$ and $\frac{c}{d}$ where $a,b,c,d$ are integers, $b,d
eq0$) gives $\frac{ad-bc}{bd}$, which is rational. The other options are incorrect: the difference of rational and irrational is always irrational, and the difference of two irrationals can be rational (e.g., $\sqrt{2}-\sqrt{2}=0$, a rational number).

Answer:

The difference of two rational numbers will always be a rational number.