Evaluate absolute value expressions

Learning Objectives Define absolute value as the distance from zero on a number line. Identify and correctly interpret the absolute value symbol. Evaluate the absolute value of positive and negative integers, as well as zero. Apply the order of operations to evaluate expressions containing absolute value bars. Simplify numerical expressions that include absolute value terms. Explain the real-world significance of absolute value in various contexts. Have you ever wondered how far away something is, regardless of which direction you're looking? 📏 Imagine you're at zero on a number line! In this lesson, you'll learn about absolute value, a fundamental concept in mathematics that helps us understand distance and magnitude. We'll explore what absolute value...

TermDefinitionExample Absolute ValueThe absolute value of a number is its distance from zero on the number line. It is always a non-negative value (either positive or zero).The absolute value of -5 is 5, because -5 is 5 units away from 0. The absolute value of 7 is 7, because 7 is 7 units away from 0. Absolute Value SymbolAbsolute value is denoted by two vertical bars surrounding a number or expression.$|x|$ represents the absolute value of $x$. So, $|-3|$ means 'the absolute value of negative three'. MagnitudeMagnitude refers to the size or extent of a quantity, often without regard to its direction or sign. Absolute value helps us find the magnitude of a number.The magnitude of a temperature drop of -10 degrees Celsius is 10 degrees. The magnitude of a debt of -$50 is $50. Non...

Absolute Value of a Positive Number or Zero $|x| = x \text{ if } x \ge 0$ If the number inside the absolute value bars is positive or zero, its absolute value is the number itself. Absolute Value of a Negative Number $|x| = -x \text{ if } x < 0$ If the number inside the absolute value bars is negative, its absolute value is the opposite of that number (which will be positive). Order of Operations with Absolute Value Evaluate the expression inside the absolute value bars first, treating the bars like parentheses. Just like parentheses, operations within the absolute value bars must be performed before taking the absolute value or performing operations outside the bars. Follow PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from l...