Absolute value of rational numbers

Learning Objectives Define the absolute value of a rational number as its distance from zero on a number line. Calculate the absolute value of any given rational number, including positive and negative fractions and decimals. Compare and order a set of rational numbers based on their absolute values. Solve simple equations of the form |x| = c, where c is a non-negative rational number. Model and interpret real-world situations involving magnitude, such as temperature changes, financial transactions, or measurement errors, using the absolute value of rational numbers. If a submarine dives 80.5 meters below sea level, how far is it from the surface? 🤔 The answer is all about magnitude, not direction! This tutorial will introduce the concept of absolute value, specifically for...

TermDefinitionExample Rational NumberAny number that can be expressed as a fraction p/q, where p and q are integers and q is not zero. This includes integers, terminating decimals, and repeating decimals.-3/4, 5, 0.25, -1.333... Absolute ValueThe distance of a number from zero on the number line. Since distance cannot be negative, the absolute value of a number is always non-negative (positive or zero).The absolute value of -7.5, written as |-7.5|, is 7.5 because it is 7.5 units away from zero. OppositesTwo numbers that have the same absolute value but different signs. They are the same distance from zero on a number line, but on opposite sides.4/5 and -4/5 are opposites. Both have an absolute value of 4/5. MagnitudeThe size or 'bigness' of a number, without regard to its sign....

Piecewise Definition of Absolute Value |x| = \begin{cases} x, & \text{if } x \ge 0 \\ -x, & \text{if } x < 0 \end{cases} This is the formal definition. If a rational number 'x' is positive or zero, its absolute value is itself. If 'x' is negative, its absolute value is its opposite (e.g., the opposite of -5/2 is -(-5/2) = 5/2). Absolute Value of a Quotient |\frac{a}{b}| = \frac{|a|}{|b|}, \text{ for } b \neq 0 The absolute value of a fraction is equal to the absolute value of the numerator divided by the absolute value of the denominator. This simplifies calculations with rational numbers.