Understanding integers
Let's explore the world of positive and negative numbers! Integers are all the whole numbers and their opposites. They help us describe things like temperature, debt, and sea level. 🌡️💸🌊
Concept
Integers are a set of numbers that include all the positive whole numbers, all the negative whole numbers, and zero. They do not include fractions or decimals. **The Number Line** A number line is the best way to visualize integers. * **Zero** is in the middle. * **Positive integers** are to the right of zero (1, 2, 3, ...). * **Negative integers** are to the left of zero (-1, -2, -3, ...). <--|---|---|---|---|---|---|---|---|---|--> -5 -4 -3 -2 -1 0 1 2 3 4 5 **Key Concepts:** * **Opposites:** Every positive integer has a negative opposite. They are the same distance from zero on the number line, just in opposite directions. * The opposite of 3 is -3. * The opposite of -10 is 10. * **Value:** Numbers to the right are always greater. Numbers to the left are always smaller. * -1 is greater than -4. * -5 is less than 2. **Real-World Examples of Integers:** * **Temperature:** A temperature of 5 degrees below zero is written as -5°. * **Money:** If you owe someone $10, you can think of your balance as -10 dollars. A deposit of $20 is +20. * **Elevation:** Sea level is 0. A mountain peak might be at +8,000 feet, while a submarine might be at -300 feet. * **Sports:** In football, a loss of 5 yards is -5 yards. In golf, 2 strokes under par is -2. **Key Idea:** Integers give us a way to talk about direction as well as quantity. The sign (+ or -) tells you the direction, and the number tells you the distance from zero.
Try it
Practice: Understanding integers.