OSAT Middle Level Mathematics (225)

The real number system encompasses all numbers that can be represented on a number line. Understanding the hierarchy and relationships among different number types is fundamental for middle-level mathematics instruction.

When multiplying or dividing an inequality by a negative number, the inequality sign reverses direction. If a < b and c < 0, then ac > bc.

The absolute value of a number represents its distance from zero on the number line. For any real number a: |a| = a if a ≥ 0, and |a| = -a if a < 0. Absolute value is always non-negative. Key properties include |ab| = |a| × |b| and |a/b| = |a|/|b| when b ≠ 0.

Between any two distinct rational numbers, there exists another rational number. Similarly, between any two distinct real numbers, there exists another real number. This property means rational numbers and real numbers are densely ordered sets.