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!