Basic Concepts
Numbers, Operations, and Number Properties
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.
In a Nutshell
Recognize and apply number types, operations, and math properties to solve problems.