Absolute value of rational numbers

Learning Objectives Define absolute value as the distance of a number from zero on a number line. Calculate the absolute value of any given integer, fraction, or decimal. Compare and order rational numbers based on their absolute values. Interpret the meaning of absolute value in various real-world scenarios. Solve simple problems involving the absolute value of rational numbers. Imagine you're walking 5 blocks east ➡️ to a friend's house, or 5 blocks west ⬅️ to the library. In both cases, how many blocks did you walk? 🤔 In this lesson, you'll discover the concept of absolute value, which helps us understand the 'size' or 'distance' of a number from zero, regardless of its direction. This is a crucial idea for working with rational numbers...

TermDefinitionExample Absolute ValueThe absolute value of a number is its distance from zero on a number line. It is always a non-negative value.The absolute value of -5 is 5, written as |-5| = 5. The absolute value of 5 is also 5, written as |5| = 5. Rational NumberA number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. This includes integers, fractions, and terminating or repeating decimals.Examples include $-3$, $\frac{1}{2}$, $0.75$, $0$, and $-2\frac{1}{3}$. IntegerA whole number (not a fraction or decimal) that can be positive, negative, or zero.Examples include $\dots, -3, -2, -1, 0, 1, 2, 3, \dots$ FractionA number that represents a part of a whole, expressed as a ratio of two integers, a numerator and a non-zero denominator.Exampl...

Definition of Absolute Value $$|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}$$ This rule states that if a number $x$ is positive or zero, its absolute value is the number itself. If the number $x$ is negative, its absolute value is the opposite of that number (making it positive). Absolute Value of a Positive Number $$|a| = a \quad \text{for } a > 0$$ When you take the absolute value of a positive rational number, the result is the number itself. For example, $|\frac{3}{4}| = \frac{3}{4}$. Absolute Value of a Negative Number $$|-a| = a \quad \text{for } a > 0$$ When you take the absolute value of a negative rational number, the result is its positive counterpart. For example, $|-2.5| = 2.5$. Absolute Value of Zer...