Absolute value and opposite integers

Learning Objectives Define and identify integers, including positive, negative, and zero. Explain the concept of absolute value as distance from zero on a number line. Calculate the absolute value of any given integer. Define and identify opposite integers. Find the opposite of any given integer. Apply absolute value and opposite integers to solve real-world problems involving distance or magnitude. Have you ever wondered how far away something is, regardless of its direction? 🧭 Or how we describe numbers that are perfectly balanced on either side of zero? In this lesson, we'll explore absolute value and opposite integers, powerful mathematical tools that help us understand distance, magnitude, and balance. These concepts are fundamental for working with numbers that...

TermDefinitionExample IntegerA whole number (not a fraction or decimal) that can be positive, negative, or zero. Examples include -3, 0, 5.The set of integers includes ..., -3, -2, -1, 0, 1, 2, 3, ... Number LineA straight line on which every point corresponds to a real number, with zero usually at the center, positive numbers to the right, and negative numbers to the left.On a number line, -5 is to the left of 0, and 5 is to the right of 0. Absolute ValueThe distance of a number from zero on a number line. Since distance is always positive or zero, the absolute value of any non-zero number is always positive.The absolute value of -7 is 7, written as |-7| = 7. The absolute value of 7 is also 7, written as |7| = 7. Opposite IntegersTwo integers that are the same distance from zero on a num...

Absolute Value Notation $|x|$ This notation represents the absolute value of the number 'x'. It means 'the distance of x from zero'. Absolute Value Property $|x| \ge 0$ The absolute value of any integer 'x' is always greater than or equal to zero. It can never be negative, because distance cannot be negative. Opposite of an Integer The opposite of $x$ is $-x$. The opposite of $-x$ is $x$. To find the opposite of an integer, simply change its sign. If it's positive, make it negative. If it's negative, make it positive. The opposite of 0 is 0.