Understanding integers

Learning Objectives Identify and classify integers as positive, negative, or zero. Represent integers on a number line. Compare and order integers using inequality symbols (<, >, =). Determine the absolute value of an integer. Find the opposite of an integer. Add integers with the same and different signs. Subtract integers. Ever wonder how we describe temperatures below zero or depths underwater? 🥶 Integers help us understand numbers that go both above and below zero! In this lesson, you'll learn what integers are, how to place them on a number line, and how to compare them. We'll also explore absolute value and opposites, which are super useful concepts for understanding quantities in the real world. Real-World Applications Temperature readings (e.g...

TermDefinitionExample IntegerA whole number (not a fraction or decimal) that can be positive, negative, or zero.The numbers -3, 0, 5 are all integers. Positive IntegerAn integer greater than zero. These are usually written without a sign or with a '+' sign.1, 2, 3, 100 are all positive integers. Negative IntegerAn integer less than zero. These are always written with a '-' sign.-1, -2, -3, -50 are all negative integers. ZeroThe integer that is neither positive nor negative. It is the point of origin on a number line.The number 0 itself. Number LineA line on which numbers are marked at regular intervals, extending infinitely in both positive and negative directions.A horizontal line with 0 in the middle, positive numbers to the right, and negative numbers to the left. O...

Comparing Integers On a number line, numbers to the right are greater, and numbers to the left are smaller. For any two integers $a$ and $b$: if $a$ is to the right of $b$, then $a > b$; if $a$ is to the left of $b$, then $a < b$. Use this rule to compare any two integers. For example, $-3 < 1$ because $-3$ is to the left of $1$ on the number line. Adding Integers (Same Signs) If two integers have the same sign, add their absolute values and keep the common sign. Example: $a + b = |a| + |b|$ (if $a, b > 0$) or $a + b = -(|a| + |b|)$ (if $a, b < 0$). Use this when adding two positive numbers or two negative numbers. For example, $3 + 5 = 8$; $(-3) + (-5) = -8$. Adding Integers (Different Signs) If two integers have different signs, subtract the smaller ab...