Introduction to Integers: Videos & Practice Problems

Integers are a set of numbers that include all positive whole numbers, negative whole numbers, and zero. Positive integers are numbers greater than zero and are located to the right of zero on a number line. Negative integers are numbers less than zero and are found to the left of zero on the number line. Zero itself is considered an integer but is neither positive nor negative. This set of numbers helps represent real-world situations such as temperatures below zero, money owed, or elevations below sea level. Understanding integers is fundamental because they extend the number system beyond just positive values, allowing us to work with a broader range of numerical scenarios.

To compare integers, we use inequality symbols: the less than symbol ($<$) and the greater than symbol ($>$). On a number line, numbers to the left are less than numbers to the right. For example, since -3 is to the left of 1, we write $-3<1$. The inequality symbol always opens toward the larger number, which can be remembered by thinking of it as an alligator's mouth that wants to eat the bigger number. This method helps in comparing both positive and negative integers accurately. For instance, $5>2$ because 5 is to the right of 2, and $-6<-1$ because -6 is to the left of -1.

A number line is a visual tool that helps in understanding integers by showing their relative positions. Zero is at the center, with positive integers extending to the right and negative integers extending to the left. This layout makes it easier to see which numbers are greater or less than others. For example, any number to the right of another is greater, and any number to the left is less. This is especially helpful when comparing negative numbers, which can be confusing. By locating integers on the number line, you can quickly determine their order and use inequality symbols correctly. It also aids in graphing integers and understanding operations involving negative and positive values.

Negative numbers are important because they allow us to represent values less than zero, which occur frequently in real life. For example, if you owe someone money, that debt can be represented as a negative number. Temperatures below zero degrees, such as in cold climates, are also expressed using negative numbers. Additionally, elevations below sea level, like the Dead Sea, are represented with negative integers. Without negative numbers, it would be difficult to accurately describe these situations. Understanding negative numbers expands our ability to model and solve problems involving decreases, losses, or values below a defined zero point.

To write and interpret inequality statements involving integers, first identify the two numbers you want to compare. Use the less than symbol ($<$) if the first number is smaller, or the greater than symbol ($>$) if the first number is larger. The symbol should always open toward the larger number, like an alligator's mouth wanting to eat the bigger value. For example, $-4<0$ means -4 is less than 0, and $3>-2$ means 3 is greater than -2. Interpreting these statements helps in understanding the relative size of integers and is essential for solving inequalities and graphing on a number line.