Absolute value and opposite integers

Learning Objectives Define absolute value as the distance from zero. Calculate the absolute value of any given integer. Define opposite integers as numbers equidistant from zero but on opposite sides. Identify the opposite of any given integer. Compare integers using their absolute values. Apply absolute value and opposite integers to solve simple real-world problems. Ever wonder how far you are from home, no matter which direction you go? 🏠 Or how a submarine's depth relates to a bird's height? 🦅 Let's find out! In this lesson, we'll explore absolute value, which tells us the distance of a number from zero, and opposite integers, which are numbers equally far from zero but in different directions. Understanding these concepts is crucial for working wi...

TermDefinitionExample IntegerA whole number (not a fraction or decimal) that can be positive, negative, or zero. Examples include -3, 0, 5.The numbers -2, 0, and 7 are all integers. 1/2 is not an integer. Number LineA straight line on which every point corresponds to a real number, ordered from least to greatest, with zero usually at the center.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. It is always a non-negative value (positive or zero).The absolute value of -5 is 5, written as |-5| = 5. The absolute value of 5 is also 5, written as |5| = 5. Opposite IntegersTwo integers that are the same distance from zero on a number line but are on opposite sides of zero. They have the same absolute value bu...

Absolute Value Notation $|x|$ This notation means 'the absolute value of x'. The two vertical bars indicate that you should find the distance of the number inside from zero. Absolute Value Property $|x| \ge 0$ The absolute value of any number is always greater than or equal to zero. It can never be a negative number because distance cannot be negative. Calculating Absolute Value If $x \ge 0$, then $|x| = x$. If $x < 0$, then $|x| = -x$. To find the absolute value of a number, simply remove any negative sign. If the number is positive or zero, its absolute value is the number itself. If the number is negative, its absolute value is its positive counterpart. Finding Opposite Integers The opposite of an integer $a$ is $-a$. The opposite of $-a$ is $a$...