Basic Concepts
In a nutshell: Integers include all whole numbers and their opposites; rational numbers are numbers that can be written as fractions.
## Understanding Positive and Negative Numbers
Integers include both positive and negative numbers, as well as zero. Rational numbers are numbers that can be written as fractions, such as \( \frac{3}{4} \) or \( -2 \).
### Adding and Subtracting Integers
When you add or subtract integers, think of a number line. Adding a negative is the same as moving left, and adding a positive is moving right.
### Real-World Uses
Integers are used to show temperature changes (like -5°C), football scores, or even money owed (negative balances).
### Rational Numbers in Everyday Life
Rational numbers help measure ingredients in cooking, keep track of money, or compare fractions like \( \frac{1}{2} \) and \( \frac{3}{4} \).
### Fun Fact
Zero is the only integer that is neither positive nor negative!
Examples
- The temperature dropped from 3°C to -4°C.
- You spend $7 and your account balance goes from $5 to -$2.
Key terms
- Integer
- A whole number, positive or negative, including zero.
- Rational Number
- Any number that can be written as a fraction.