Understanding integers

Learning Objectives Define what an integer is and identify examples of integers. Distinguish between positive integers, negative integers, and zero. Represent integers on a number line accurately. Compare and order integers using appropriate symbols (<, >, =). Determine the absolute value of any given integer. Identify the opposite of any given integer. Apply the concept of integers to solve real-world problems. Have you ever checked the temperature on a freezing winter day 🥶 or seen a submarine dive deep below sea level 🚢? These situations use special kinds of numbers! In this lesson, you'll discover integers – a set of numbers that includes positive numbers, negative numbers, and zero. Understanding integers is crucial for many areas of math and helps us de...

TermDefinitionExample IntegerA whole number (not a fraction or decimal) that can be positive, negative, or zero. The set of integers is represented by the symbol $\mathbb{Z}$.... -3, -2, -1, 0, 1, 2, 3 ... Positive IntegerAn integer greater than zero. These numbers are usually written without a sign or with a '+' sign.1, 5, 100, +7 Negative IntegerAn integer less than zero. These numbers are always written with a '-' sign in front of them.-1, -5, -100, -7 ZeroThe integer that is neither positive nor negative. It is the origin point on a number line.0 Number LineA straight line on which every point corresponds to a real number. Integers are marked at equal intervals, with zero at the center, positive integers to the right, and negative integers to the left.A line with p...

Comparing Integers on a Number Line For any two integers, the integer located further to the right on the number line is greater, and the integer located further to the left is smaller. This rule helps us order integers. For example, since -2 is to the right of -5 on the number line, -2 > -5. Similarly, 3 is to the right of 0, so 3 > 0. Absolute Value Rule The absolute value of an integer $x$, denoted as $$|x|$$, is defined as: $$|x| = x \text{ if } x \ge 0$$ $$|x| = -x \text{ if } x < 0$$ This rule tells us that the absolute value of a positive number or zero is the number itself, and the absolute value of a negative number is its positive counterpart. It always results in a non-negative value. Opposite Integers Rule For any integer $x$, its opposite is $-x$...