The Number System

What you’ll learn

• Every rational number sits at exactly one place on the number line; opposites are mirror images across $0$.
• Adding signed numbers: same signs add magnitudes (keep the sign); different signs subtract magnitudes (keep the sign of the larger magnitude).
• Subtraction is addition of the opposite: $a - b = a + (-b)$.
• Multiplication and division of signed numbers follow the "same signs positive, different signs negative" rule; division by $0$ is undefined.
• A fraction terminates as a decimal exactly when its denominator (in lowest terms) factors into $2$s and $5$s; otherwise it repeats.
• Absolute value gives distance from $0$, and the distance between points $a$ and $b$ on a number line is $|a - b|$.