Basic Concepts
In a nutshell: Recognize and apply number types, operations, and math properties to solve problems.
## Understanding Numbers and How They Work
Numbers are everywhere! From counting your snacks to measuring the distance you walk, understanding how numbers behave is a fundamental building block for math success.
### Main Types of Numbers
- **Whole numbers:** 0, 1, 2, 3, ...
- **Integers:** ... -3, -2, -1, 0, 1, 2, ...
- **Rational numbers:** Numbers that can be written as fractions (like \( \frac{2}{3} \))
- **Irrational numbers:** Numbers like \( \pi \) and \( \sqrt{2} \) that cannot be written as simple fractions
### Operations and Properties
Operations (adding, subtracting, multiplying, dividing) have special rules:
- **Commutative Property:** \( a + b = b + a \)
- **Associative Property:** \( (a + b) + c = a + (b + c) \)
- **Distributive Property:** \( a(b + c) = ab + ac \)
### Why Does It Matter?
These properties help you simplify problems, spot shortcuts, and check your work.
### Real-World Connections
When splitting a bill at a restaurant or figuring out how many slices of pizza each friend gets, you’re using number operations and properties!
Examples
- Splitting 24 cookies evenly among 6 friends uses division: \( 24 \div 6 = 4 \).
- Checking if \( 3 + 5 = 5 + 3 \) uses the commutative property.
Key terms
- Commutative Property
- Changing the order of numbers doesn’t change the result for addition or multiplication.
- Distributive Property
- Multiplying a sum by a number equals multiplying each part and adding: \( a(b + c) = ab + ac \).